The Aftermath of Syllogism: Aristotelian Logical Argument from Avicenna to Hegel (Bloomsbury Studies in the Aristotelian Tradition) 9781350043527, 9781350043541, 9781350043534, 1350043524

Table of contents :
Cover page
Halftitle page
Series page
Title page
Copyright page
Contents
1 Introduction
2 Existence and Modality in Avicenna’s Syllogistic
1. Truth conditions of propositions
2. The structure of the categorical assertion
3. Conversion
4. Foundations of modality
5. The modal logic
6. Conclusions
Notes
3 Ideology and “Reception” in Renaissance Logic
Introduction
I. Ideology
1. Excessive formalism
2. Meaningless abstraction
3. Disregard of context
4. Language corruption
5. Disregard for “natural” or “ordinary language”
6. Scholastic logic is “useless”
II
7. Reception
8. Conclusion
Notes
4 Syllogistic and Formal Reasoning
1. Informative inferences
2. Inference as a means of making something self-evident
3. The natural light of reason
4. Conclusion
Notes
5 Hobbes and the Syllogism
1. Reasoning and language according to Hobbes
2. Hobbes on the logic of the syllogism
3. Hobbes on method
4. Conclusion
Notes
6 Syllogism in the Port-Royal Logic
1. Introduction
2. The analysis of propositions
3. The classification of syllogisms
4. Rules for simple syllogisms
5. Complex syllogisms
6. The General Principle for determining validity
7. Conclusion
Notes
7 Locke and Syllogism
1. Introduction: Th e fi ght against the prejudices and the aim of the Essay
2. Locke and the Reasoning : From the logical deductivism to the intuitionistic inductivism
3. Locke and the syllogism: Is it really “the great instrument of reason”?48 Pars Destruens and Pars Construens
4. Conclusion: “Another sort of Logick and Critick, than what we have been hitherto acquainted with”81
Notes
8 Leibniz’s Transformation of the Theory of the Syllogism into an Algebra of Concepts
1. Introduction. A very brief précis of the history of logic
2. Leibniz’s starting point. The seventeenth- century theory of the syllogism
3. Distilling the operator of conceptual containment
4. Inventing the operator of conceptual conjunction
5. Elaborating the laws for conceptual negation
6. The operator of conceptual possibility: An ingenious invention
7. Some steps beyond the algebra of concepts
Notes
9 Kant’s False Subtlety of the Four Syllogistic Figures in its Intellectual Context
1. Kant’s immediate predecessors on syllogism
2. Kant’s view of syllogism in the False Subtlety
3. The False Subtlety , Kant’s immediate predecessors, and Kant’s works from 1762–1764
Notes
10 “Everything Rational is a Syllogism”
1. The circle of the three syllogistic figures
2. Ontological implications of inference
3. The paradigmatic case of the solar system
4. Other triads of syllogisms
Notes
Index

Citation preview

The Aftermath of Syllogism

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Bloomsbury Studies in the Aristotelian Tradition General Editor: Marco Sgarbi, Università Ca’ Foscari, Italy Editorial Board Klaus Corcilius (University of California, Berkeley, USA); Daniel Garber (Princeton University, USA); Oliver Leaman (University of Kentucky, USA); Anna Marmodoro (University of Oxford, UK); Craig Martin (Oakland University, USA); Carlo Natali (Università Ca’ Foscari, Italy); Riccardo Pozzo (Consiglio Nazionale delle Ricerche, Rome, Italy); Renée Raphael (University of California, Irvine, USA); Victor M. Salas (Sacred Heart Major Seminary, USA); Leen Spruit (Radboud University Nijmegen, The Netherlands). Aristotle’s influence throughout the history of philosophical thought has been immense and in recent years the study of Aristotelian philosophy has enjoyed a revival. However, Aristotelianism remains an incredibly polysemous concept, encapsulating many, often conflicting, definitions. Bloomsbury Studies in the Aristotelian Tradition responds to this need to define Aristotelianism and give rise to a clear characterization. Investigating the influence and reception of Aristotle’s thought from classical antiquity to contemporary philosophy from a wide range of perspectives, this series aims to reconstruct how philosophers have become acquainted with the tradition. The books in this series go beyond simply ascertaining that there are Aristotelian doctrines within the works of various thinkers in the history of philosophy, but seek to understand how they have received and elaborated Aristotle’s thought, developing concepts into ideas that have become independent of him. Bloomsbury Studies in the Aristotelian Tradition promotes new approaches to Aristotelian philosophy and its history. Giving special attention to the use of interdisciplinary methods and insights, books in this series will appeal to scholars working in the fields of philosophy, history and cultural studies. Available titles: Elijah Del Medigo and Paduan Aristotelianism, Michael Engel Phantasia in Aristotle’s Ethics, edited by Jakob Leth Fink Pontano’s Virtues, Matthias Roick ii

The Aftermath of Syllogism Aristotelian Logical Argument from Avicenna to Hegel Edited by Marco Sgarbi and Matteo Cosci

Bloomsbury Academic An imprint of Bloomsbury Publishing Plc

LON DON • OX F O R D • N E W YO R K • N E W D E L H I • SY DN EY

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Bloomsbury Academic An imprint of Bloomsbury Publishing Plc 50 Bedford Square London WC 1B 3DP UK

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www.bloomsbury.com BLOOMSBURY and the Diana logo are trademarks of Bloomsbury Publishing Plc First published 2018 © Marco Sgarbi, Matteo Cosci, and Contributors, 2018 Marco Sgarbi and Matteo Cosci have asserted their right under the Copyright, Designs and Patents Act, 1988, to be identified as the Editors of this work. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage or retrieval system, without prior permission in writing from the publishers. No responsibility for loss caused to any individual or organization acting on or refraining from action as a result of the material in this publication can be accepted by Bloomsbury or the editors. British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. ISBN :

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978-1-3500-4352-7 978-1-3500-4354-1 978-1-3500-4353-4

Library of Congress Cataloging-in-Publication Data Names: Sgarbi, Marco, 1982– editor. Title: The aftermath of syllogism : Aristotelian logical argument from Avicenna to Hegel / edited by Marco Sgarbi and Matteo Cosci. Description: New York : Bloomsbury Academic, 2018. | Includes bibliographical references and index. Identifiers: LCCN 2017032781 (print) | LCCN 2017048151 (ebook) | ISBN 9781350043541 (ePDF) | ISBN 9781350043534 (ePUB) | ISBN 9781350043527 (hardback : alk. paper) Subjects: LCSH: Syllogism—History. | Aristotle. Classification: LCC BC185 (ebook) | LCC BC185 .A38 2018 (print) | DDC 166.09–dc23 LC record available at https://lccn.loc.gov/2017032781 Typeset by RefineCatch Limited, Bungay, Suffolk To find out more about our authors and books visit www.bloomsbury.com. Here you will find extracts, author interviews, details of forthcoming events and the option to sign up for our newsletters.

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Contents 1

Introduction Marco Sgarbi and Matteo Cosci

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Existence and Modality in Avicenna’s Syllogistic Allan Bäck

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Ideology and “Reception” in Renaissance Logic Alan R. Perreiah

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Syllogistic and Formal Reasoning: The Cartesian Critique Stephen Gaukroger

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Hobbes and the Syllogism Douglas M. Jesseph

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Syllogism in the Port-Royal Logic Russell Wahl

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Locke and Syllogism: The “Perception Grounded” Logic of the Way of Ideas Davide Poggi

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Leibniz’s Transformation of the Theory of the Syllogism into an Algebra of Concepts Wolfgang Lenzen

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Kant’s False Subtlety of the Four Syllogistic Figures in its Intellectual Context Alberto Vanzo

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10 “Everything Rational is a Syllogism”: Hegel’s Logic of Inference Georg Sans, SJ

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Index

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Introduction Marco Sgarbi and Matteo Cosci

Logician : Here it is an example of a syllogism. “The cat has four paws. Isidore and Fricot both have four paws. Therefore Isidore and Fricot are cats.” Old Gentleman: Well, my dog has got four paws. Logician: Then it’s a cat. Old Gentleman: So then, logically speaking, my dog must be a cat? Logician: Logically, yes. But the contrary is also true. E. Ionesco, Rhinocéros, act one (1959) “A syllogism,” according to Aristotle, “is an argument in which, certain premises being posited, something other than what was laid down results by necessity because these premisses are.” In the book entitled Prior Analytics, from which this initial definition comes (I, 24b, 18), the first theory of syllogistic reasoning was set forth, and it was presented in a way that was already highly developed. The syllogistic heritage left by Aristotle, however conspicuous, was discussed and reworked by his pupil Theoprasthus while he was still alive. Syllogism and its possibilities of inference were tested and developed even more during the Hellenistic age, mainly by Stoics, during the imperial age due to the prominent contributions by later Peripateticians such as Aristo of Alexandria and Boethus of Sidon, and during late antiquity and the early middle ages, with many exegetes and commentators who profitably commented on the Aristotelian texts. These latter in particular often reformulated Aristotle’s teachings in syllogistic-ish fashion and overall expanded upon his original reflection on the matter through their eager activity of retake, criticism and ordering. In this way they originated 1

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a very elaborate set of syllogistic doctrines (although not always well integrated and consistent). A very strong impulse on this object of study was certainly that given by Severinus Boethius, by way of his twofold translation of Prior Analytics and his own treatises, the De syllogismo cathegorico, the De hypotheticis syllogismis and the Introductio ad syllogismos cathegoricos. As time passed, scientific syllogism became the logical key-structure of demonstrative knowledge; its preeminence lasted and flourished with neither interruption nor competitors for centuries. The purpose of the present volume is to analyze the lines of continuity and/or discontinuity that the fortune of scientific syllogism enjoyed in the history of philosophy and particularly in the long period of time from Avicenna to Hegel. What follows is a short introductory overview on its manifold contributions on the matter, leaving to the reader the reference to the subsequent essays needed for further depth on the subject. The first essay of this collection deals with the age of Medieval Islamic philosophy, in which the incubation and development of the Aristotelian logical knowledge is strong. In his contribution, Allan Bäck examines the reception and reworking of the syllogistic doctrine by Avicenna, considering some of his additional specifications. In particular, Avicenna’s presupposition of the actual existence of the involved terms is noteworthy, together with his introduction of some complex variables, such as the temporal duration implied in existential assertions, the modal value in effect, and the status of the “quiddities” under analysis (whether the essence of the object should be understood in itself, in re or in intellectu). Taking into account such additional conditions has inevitable repercussions on the following conversion rules, as in the case of mixed-modal syllogisms. Regarding the latter, Avicenna chose to maintain the stance set by Aristotle, Alexander and Philoponus against the innovatory corrections being brought by the majority of the remaining commentators. Without going into detail, it is interesting to ascertain that some of the logical positions defended by Avicenna actually depend on metaphysical views (not vice versa) as, for example, the fact that the existential condition required by propositions of logical necessity seems to be satisfied, if not by a hypothetical existence in the intellect, by an actual existence within the divine mind, being it the supreme guarantor of the kingdom of necessity. After the splendour of medieval logic, and scholastic logic in particular, the fortunes of syllogism were largely reduced by a certain humanistic ideology that was hostile, as a matter of principle, to the excessive formalism of Christian aristotelianism which had been felt as the West thought’s cumbersome

Introduction

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inheritance. Such a humanistic ideology was carried out in an increasingly prejudiced way against scholasticism, its logic, and everything one might presume it represented (verbosity, sophistry, murkiness and so on). As we can learn, for instance from Lorenzo Valla as stated in his Dialectical Disputations, various accusations were addressed at that time against scholastic logic. Apparently, those accusations self-nourished until they became so widespread that they have influenced even our sector of studies up until a few decades ago. The content of those critiques were basically the charges of excessive formalism, of making abstractions without actual meaning, of ruining the beauty of classical Latin in favour of an almost made-up technical language whose grammar did not take into account the mundane and which disregarded the ordinary common manner of speaking. In this way the preconceived stereotype was reinforced, with the result that scholastic logic and syllogism as its key instrument were basically regarded as useless and worthless exercises. In his contribution, Alan R. Perreiah is capable of showing the superficiality of such judgements as “gratuitous, misleading, and demonstrably false,” and that, no matter how widespread, they were built on weak and self-conditioned foundations. In fact, during the Renaissance, there was an appreciation of the traditional logical studies which is proven by an impartial analysis of the publications and the editorial market on the subject between the fifteenth and sixteenth centuries. During this time, printed works on Scholastic logic greatly outnumber that of humanistic literature intended for a broad audience (e.g. Latin and Greek classics). This is a telling state of affairs that provides evidence in regard to a rather lively continuity of interest (and corrects much of what was believed up to a short time ago on this matter). So one can perhaps affirm that the history of syllogism in the Renaissance period remains to be fully covered beyond the reigning prejudice against it. Such a history remains to be investigated more thoroughly, perhaps in universities or religious colleges—environments less exposed to the influence of those who would neglect the medieval acquisitions without being aware of, or willing to give credit to, those vertiginous philosophical developments previously reached in the field of logic and, notably, in the theory of syllogism. Following this general prejudicial tendency, a progressive rejection of the empirical results of Aristotelian science is realized by the seventeenth century. This happened together with a critical devaluation of syllogism, which had traditionally been the paradigmatic way of exposition favoured for those outdated outcomes. In fact, the reason which Descartes and his contemporaries adduced for this marginalization regarded the utility and the effectiveness of

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syllogism as such, flawed by the fact of not being functional for the growth of the body of scientific knowledge. They objected to the fact that first, there was no certain criterium for distinguishing an informative syllogism from a noninformative one; and, secondly, the capacity to find something new by using such a logical structure was in doubt. The state of the structure gave the impression of being simply apt at organizing previously acquired knowledges within its own schema without concluding anything that was not already given in the premisses or that was recreated as a posteriori reasoning on the grounds of previously ascertained conclusions. In this sense, syllogism was perceived as an instrument more useful for reordering given data in a manneristic fashion, than producing new concepts. With so many discoveries being made and so much still to discover, what science required was content rather than form. Hence, the expectations of Descartes for a strong way of knowing were such that it could allow something indistinct to be established as evident; above all he was expecting that such a way of knowledge could permit the recognition of an object as self-evident and that such a discovery might become the foundation for new, grounded, certainties. From his point of view, syllogism failed to challenge intuitions on both a heuristic and a recognition level, neither being able to impose itself as the intellectual instrument to comprehend the evidence or for making new scientific detections. As is made clear by Stephen Gaukroger in his essay, Descartes’ syllogism is not “compressible” in a more immediate equation of non-inferential understanding. All in all, Descartes and the majority of his contemporaries basically contest the syllogism’s two characteristic qualities: (1) its prescriptive character and (2) its compulsory paths to which logicians of ascendant scholastics were obliged to bind their reasoning. That was why Cartesians and non-Cartesians alike found themselves favouring general common sense over what they regarded as the not-always-perceptible transparency of mnemonic schematisms and artefact figures of thought. In his turn, Hobbes expressed other concerns about the merit of traditional syllogistic; because it seemed to be something, he said, that all men endowed with a good natural logic would have already been able to understand without such additional artifice. Nonetheless, Hobbes recognized the value of such a doctrine with Aristotelian ascendence and in turn he offered an extensive treatment of syllogism, which we can still read in the first part of his De corpore. In conformity with the general consensus on the matter, Hobbes set the value of syllogisms that were not of first figure aside, focusing on those with all the universal and affirmative premisses as well as concentrating his thoughts on them, with the bonus of grounding them in some of his own peculiar linguistic

Introduction

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assumptions. As Douglas M. Jesseph noted, a hobbesian study of syllogism availed itself of a proper nominalistic theory of words which had been previously developed and which were still operating in the background. Basically, it was the idea according to which names are just mere signs of things and because their attribution to external world items is arbitrary in substance, they remain effective solely on the merits of common convention. Accordingly, although general names allow the designation of things in a universal fashion, that always happens with a meaning that works only in so far as it has been previously conventionally stipulated. The syllogistic structure too, as a superstructure with a logicallinguistic nature, is inevitably affected by this implicit stipulative assumption. Therefore, some considerable consequences of this consideration follow, as the abandonment of the existential import that was sometimes supposed in the Aristotelian categorical syllogism, and the admission of equalizing hypothetical syllogisms to the categorical ones, based on the common speculative character that comes from an essentially arbitrary act such as the imposition of names to things. Such arbitrary designations, however, do not impede the correct presumptions of inferences that may come from the associations of general names; this is exactly the role that, in Hobbes’ perspective, should be appointed to syllogism. In fact, according to Hobbes, the syllogism as an instrument for thought is a sort of combinatory or computational operation of concepts. “Sylloghisthai,” he writes, “signifies to Compute,” (i.e. adding or subtracting one general term from another by way of a third). From this starting point, Hobbes outlines his own combinatory method in which syllogisms should be linked by inferential chains that, beginning with true principles and certain definitions, can provide explicative demonstrations of phenomena on the grounds of their exhibited causal relationships. Only in this way, he judged, might one obtain deductions that were not mere ascertainments of “what” there is, but actual syllogistic proofs of “why” things are as they are, thus displaying the causal nexus with and beyond otherwise aleatory words. Although with the intent of breaking with tradition, the so-called “Port-Royal Logic,” that is the Logique ou l’Art de Penser by A. Arnould and P. Nicole, produced the unexpected outcome of giving a long-time continuity to the reception of traditional syllogistic, deeply mediated as it already was by a Cartesian approach. This manual was very successful throughout its various editions and remained popular with academic courses and among learned men for a long time. Its purpose was to teach the “art of thinking” to its readers by discerning truth from lies: syllogistic was supposed to carry out a preeminent role in this task. However, by differing from consolidated syllogistic and in line with the new Cartesian

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concerns, the peculiarity of this method resided in taking the conclusion for granted and then verifying whether it was actually pre-contained in one of the premises, with the help of the other as confirmatory support. In this way, it was possible—as the authors expected—to confirm or deny general assertions, rather than speculatively “making up” pretended syllogisms. In the course of the treatise, the analysis of syllogism always maintains a strong reference to the empirical level, while also considering the concept of extension, namely the whole set of items to which a given idea or predication is referred, with consequences for the propositional calculus and for the actual licence of certain inferences. Moreover, according to a practice that was to become the standard for all subsequent logic manuals, the text provided a list of all the syllogistic figures and moods considered to be valid. This was compiled on the basis of a restricted number of inferential rules. The validity of figures and moods of basic or “simple” syllogisms was established on the basis of their conformation to those rules. However, the authors seemed to be more interested in so-called “complex” syllogisms and their consequent pursuit of a suitable criterium for confirming (or not confirming) their validity. To this end, a simplifying restatement of the premisses (without subordinate clauses) was generally recommended for the evaluation of the deduction by the “natural light” of the intellect. The general principle proposed, however, was that of looking for alternative premisses that were in compliance with those given, but better known and accessible for our knowledge. Subsequently it remained to verify whether the conclusion was already contained conceptually in one of the two new premises (i.e. the major) with the help of the other (i.e. the minor). Conformation rules for the validity of syllogistic forms and figures were derived and checked on the grounds of this general principle. The institution of such a principle seems neither decisive nor unambiguous; nevertheless it remains an important testimony about the search for an axiological foundation of a syllogistic doctrine which otherwise remained disjointed and unfounded. Also, the choice made in the Logique of rejecting symbolic variables and preferring concrete examples facilitated the understanding of the matter and the widespread success of the work itself. However, as Russell Wahal noted at the end of his investigation, the same fact did not always create the conditions required for generalizing in the correct way the recurrent syllogistic patterns, which would have been expected from a modern theory of syllogism. The logical and philosophical theme of syllogism finds then significant support in Locke’s Essay concerning Human Understanding. On the one hand, the relevance of the syllogism as instrument for reasoning and even for discovery

Introduction

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has never been in doubt here; on the other hand, blind confidence in old-school logical sophistries was considered to be one of the most inveterate limits of the natural capacity of human understanding. As Davide Poggi points out in his essay, in order to avoid such traps, Locke notes that the premises from which syllogisms start are basically intuitions that derive from the true perceptions of particulars. Locke says that only in view of unequivocal perceptual evidence will it be possible to carry out a true reasoning without recourse to postulates or axiomatic principles; even the identity principle and the principle of noncontradiction draw their foundation from the perception of their own evidence. According to the British empiricist, syllogism as used and transmitted by the scholastic tradition does not help to improve knowledge in so far as it erects a superfluous and forced logical superstructure overlooking the natural order of things. Against this, Locke proposed to rearrange the traditional order of the premisses of categorical syllogisms and their middle term in a way that was intended to be closer to the inductive way of reasoning and its content. For him, however, the nexus between two premises which allow the conclusion to be drawn remains an object of intuition rather than of any deductive capacity. The final aim of his logical proposal was to restore the natural cognitive order, starting from immediate perceptions and intuitions of particulars as parallel to downgrading the value of abstract and universal claims: an inversion of primacies that he addressed against the vacuous formalities of traditional syllogistic in favour of a new practice of reasoning that could be closer to empirical reality than to “maximal systems.” From a more formal point of view, the theory of syllogism could be further developed thanks to Leibniz’ contribution, which was able to bring about many modifications and structural reconsiderations to a logical configuration still rigid and unmodified at its core. Benefiting from the results reached by the main European logicians of his time, Leibniz managed to develop his own “protoalgebra of concepts” whose intent was to emancipate itself from the worn-out scholastic syllogistic. In his essay,Wolfgang Lenzen explains how the advancement of new conceptual operators to express specific logical functions allowed Leibniz to raise the bar in the level of analysis and in the advancement of the progress of logical operations that could not be formalized before. In particular, an effective symbolic formalization was possible because of the individuation of an operator of conceptual containment, the introduction of an explicit operator of logical conjunction, the development of adequate laws of negation and the invention of an operator of self-consistency of concepts. Two other original Leibnizian insights to be mentioned are, on the one hand, a method for transforming

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operations of concepts into a propositional calculus and, on the other hand, the introduction of indefinite concepts that could be used as functional logical quantificators. All of this allowed Leibniz to modify the traditional syllogistic into a consistent algebra of concepts, somehow anticipating Boole’s algebra of sets by 150 years. Coming to the age of Kant and to his pre-critic period in particular, a couple of problems were the subject of debate: first, defining on which grounds valid syllogistic forms and figures should be accepted as valid and, second, answering whether and for what reason the study of those syllogisms that were valid, but were not first-figure syllogisms, should be contemplated. There were two favored solutions to the first problem: either listing some formal rules that syllogisms had to abide by to be considered valid or reducing all syllogisms to a lower number of more certain syllogisms, which could then, in their turn, be deduced from one (or a maximum of two/three) basic and incontrovertible principle(s). Regarding the second problem, two main alternative solutions were in vogue: either favoring only first-figure syllogisms (considered stronger and “more natural” for reasoning) reducing in case the rules to those, or leaving legitimate room for other syllogistic figures for the completeness of the logical system. At that time syllogism was considered a way to test the truth of a proposition, namely the conclusion, and so it was regarded by many, Kant included. For him, the attestation of truth could take place through the attribution of a “sign” (middle-term) that allowed the attribution of the interested “sign” (the predicate of the conclusion) to the chosen subject. In the treatise on The False Subtlety of Four Syllogistic Figures—a pre-critical text dated 1762—Kant proposed a solution to the first problem on the basis of such a reformulation of conceptual relations in terms of signs-references. He advanced a founding principle (Nota notae & repungans notae principium) that from his point of view was even more important than the de omni et de nullo principle proposed by Wolff. The new principle, however, could actually be applied to first-figure syllogisms and not to the others, because of the predominant role that, according to Kant, the firsts had and to which all the others could be reconducted. Such a reconduction could be possible by the help of additional “immediate” inferences that were drawn from the expansion of the premises of first-figure syllogisms which allowed to show, if the deduction was correct, the derivative and dependent character as well as the validity of non-first-figure syllogisms. Unfortunately, as Alberto Vanzo acknowledges in his article, The False Subtlety neither provides a sufficient justification for explaining its author’s silence on the reasons why syllogisms could not give any help to discoveries; nor does it expound the reasons for the

Introduction

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assigned primacy to first-figure syllogisms, nor does it adduce explicit reasons for favouring the reductive method for the foundation of syllogistic over the alternative method of the principles. Nevertheless, all these uncleared motives can perhaps be understood by looking at another contribution among Kant’s own works of that period, namely the Inquiry into the Distinctiness of the Principles of Natural Theology and Morality, paying particular attention to the method for metaphysics developed there. The task of metaphysics should have been the clarification of “given” concepts rather than their discovery, and in this sense syllogism should be suited to this. Secondly, only first-figure syllogisms exhibited those indispensable “sign”-relations that were essential for the metaphysics that he was elaborating; finally, the reduction method probably would have seemed to Kant more systematic and closer to the “architectonic” configuration of his ideal of philosophy rather than that of principles, which he regarded as too unstructured. Hegel agreed with Kant about both the criticism of the empty formalism of a certain kind of mechanical syllogistic and attributing the primacy of importance to first-figure syllogisms. In general, then, the Hegelian doctrine of syllogism deals with different perspectives from which a whole complex can be considered in its entirety: each aspect of the whole is made explicit by a syllogism whose terms stay in place at the different “moments” through which the whole develops itself. For Hegel, the moments of syllogisms are the three phases of conceptual determination that, in their turn, respectively correspond to the three determinations of the universal, particular and singular. Following this conception Hegel designed a method—the method of permutation—according to which the first three-figure syllogisms could be reciprocally founded by the circular exchange of their middle terms. Such a solution had a unifying and, at the same time, mediating value. Moreover, it avoided infinite regress in the pursuit of a justification for the first starting premises. As maintained in Hegel’s Science of Logic, the first three figures of syllogism activate a progressive dialectic of conceptual determination with important ontological implications. In fact, semantic enrichment and intensification of understanding increasingly take place in a syllogistic progression that realizes more and more the rational being of reality. As is proven by the multiple examples of different syllogistic triads recurring in his works, for Hegel, thinking syllogistically is isomorphic and coextensive in respect to the rational structure of reality itself. In the essay that closes this book, Georg Sans illustrates such a peculiar dynamic by way of the paradigmatic example of the solar system as it appears in Hegel’s section of absolute mechanicism, or by the state system, in the practical sphere: in all cases,

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the alternation of triadic syllogisms is in the play, being in force the mutual permutation of the middle terms, both on a conceptual and an ontological level. For Hegel, the entire reality can be ideally explained through recurrent patterns of interchained and systematic syllogisms because, from his perspective, syllogistic interrelation and its respective mutual permutation of middle terms constitutes the logical framework of reality. These, by and large, are the contents of this book. The editors’ gratitude goes to all the authors who have synergically contributed to tell a great part of the history of the “aftermath of the syllogism,” made by its retakes and vicissitudes, its critical dismissals and innovatory reworks, its posthumous restorations and also its openness to future reconsiderations. The collection has shown unexpected lines of continuity, leaving the impression that a large part of the evolution of the shapes that syllogism has assumed (or has not assumed) throughout the centuries still waits to be retravelled, and a lot still remains to be told. Nonetheless, this present collection provides an excellent and many-sided approach to this peculiar matter, that certainly can declare itself a safe basis for future and omnicomprehensive studies. Thus, with the conviction that the fortune of syllogism as a fundamental logical structure of human reasoning will last in the philosophical time to come in new forms and in unthought aspects, we present this book for the benefit of the benevolent reader.

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Existence and Modality in Avicenna’s Syllogistic Allan Bäck Kuztown University

Islamic philosophers like Avicenna inherited the logical theory of Aristotle along with the rest of his corpus. They commented on the texts and developed the theory. In particular, Avicenna wrote a comparatively original, enormous “commentary” on the Prior Analytics. He paid especial attention to the truth conditions for the categorical proposition and to the modal syllogistic. As we shall see, these developments have ties to his own metaphysics. Avicenna did not receive the syllogistic of the Greeks in a passive way. To be sure, in his youth he did so when he wrote literal commentaries on most of Aristotle’s works.1 These were apparently lost. However, much later, in Hammadān around 1016, Avicenna’s students asked for him to replace them: The hope of ever obtaining his lost works having dimmed, we asked him to write them and he said, “I have neither the time nor the inclination to occupy myself with close textual analysis and commentary. But if you would be content with whatever I have readily in mind [which I have thought] on my own, then I could write for you a comprehensive work arranged in the order which will occur to me.”2

Here, in his mature work, Avicenna states clearly that he shall not be explicating Aristotle’s thought. Rather, he shall be giving his own thoughts and theories on the topics and positions brought up by Aristotle. So he considers his commentary to consist in reading the text and making comments on what he thinks the truth to be. Accordingly, Avicenna set out to comment upon a great portion of Aristotle’s works, including the whole of the logic, much of the works on the natural sciences, and the Metaphysics. He completed this massive undertaking in but a few years, from 1016–27, if we are to believe the historical testimony—although it is likely that he used some earlier 11

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writings as some parts of Aš-Šhifā. His large “commentary” on syllogistic, AlQīyās, was part of it. Judging by the contents of Al-Qīyās, Avicenna had access to Stoic materials on hypothetical syllogisms as well as to Aristotle’s Prior Analytics. At any rate he has long discussions of conjunctive, disjunctive and conditional syllogism. Avicenna’s treatment of the syllogistic is far more detailed and original than that of Al-Fārābī or Averroes. As he remained the main figure in Islamic philosophy, the Qīyās continued to have influence. Still, the shorter summaries in the Ishārāt and Najāt on logic had much wider circulation and general influence, say, with the teaching of logic in the madrasa schools.3 Despite his insistence on being original, Avicenna sometimes sides with Aristotle (and the Greek commentators Alexander of Aphrodisias and John Philoponus) against the majority of the commentators. His defense of Aristotle’s account of mixed modal syllogisms illustrates this. No doubt, Avicenna would say that he is just stating the truth. In any case, he offers a new defense, from his fairly original analysis of the truth conditions of categorical propositions.

1. Truth conditions of propositions The novelty of Avicenna’s approach to the propositions comes partly from his view of predication, what I have called “the aspect theory of predication.” This theory may have had its antecedents in John Philoponus and even in Aristotle himself.4 Yet most Greek commentators followed the lead of Ammonius in having a copulative theory of predication. The copulative theory requires only that, in a simple proposition, the predicate belong or not belong to the subject. The aspect theory requires that, plus an explicit assertion of existence. So, for a singular proposition like “Theaetetus is flying,” the copulative theory requires: flying belongs to [or: is predicated of] Theaetetus. In contrast, the aspect theory requires: flying belongs to Theaetetus, and Theaetetus exists. The difference of the two theories becomes clear with denials, where the negation is intended to deny the entire affirmation. With “Theaetetus is not flying,” the former requires: flying does not belong to Theaetetus, whereas the latter requires: either flying does not belong to Theaetetus, or Theaetetus does not exist. Avicenna states these truth conditions clearly.5 I have argued that Aristotle himself has this theory.6 Accordingly, in his syllogistic he never uses the E to O inference, which does not follow on the aspect theory although it does on the copulative theory.7 E.g., take; “no goat is sitting; therefore some goat is not sitting.” It does not follow from “sitting does

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not belong to every goat, or no goat exists” that there exists a goat, and it is not sitting. However, it might seem to follow from “sitting does not belong to every goat” that sitting does not belong to some goat. Whatever is the case with Aristotle, Avicenna clearly has these positions of the aspect theory. The existence claims of the affirmative propositions perhaps prompted him to consider under just what periods of time the subject has to exist and to just what the predicate is being asserted to belong.8 At any rate, he devotes much attention to this issue, which leads him to embrace the validity of some quite contested mixed modal syllogisms. His views on this issue have a direct bearing on his view of the relation of time and modality: how an eternal, necessary being interacts in time.

2. The structure of the categorical assertion In accordance with this aspect theory, “every S is P” would assert that every S is existent as a P. To be more exact, Avicenna holds that “every S is P” is ordinarily to be read as: everything that is S, so long as its essence is existent, is P. Likewise for the other forms of simple categorical propositions.9 The assertion of existence in a proposition requires a determination of the length of time involved. Here the relevant sort of existence is usually: existing in actuality, In re. Like Aristotle, Avicenna takes a verb to signify time. Aristotle himself has remarks on how to understand a statement in the present tense. In science, he says, a statement of the form, “every S is P,” asserts that P is said of every instance of S at all times [An. Po. I.4]. He distinguishes such a universal statement from an essential statement, a statement holding per se. For instance, “every swan is white” is true since all swans at all times are white, even though it is not true per se that every swan is white: for whiteness does not belong to the essence of swan but is a mere accident.10 In the modal syllogistic Aristotle admits also that a statement may be taken “as of now” (ut nunc), to hold just at the present moment.11 For instance, “every scribe is awake” can be true ut nunc, if it just so happens that at that instant every scribe is awake, even though taken absolutely it is false, as there are times when some scribes are sleeping and not awake. Avicenna accepts both of these points. However, he has a far more complicated account than Aristotle of how to determine the temporal duration of a statement. As in the Latin medieval doctrine of supposition, for Avicenna the sentential context, sometimes along with the intention of the speaker, determines the time duration intended. With “the moon has eclipses,” the statement does not signify

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the present time, when the moon is not eclipsed, or all times, but only those times when the moon is eclipsed. The statement, “Socrates is kind,” does not signify only those times when Socrates is performing kind acts but all times when Socrates exists. Otherwise Socrates could be kind even though he regularly acts cruelly. So sometimes the subject term (“Socrates”) for the most part sets the time duration for the predication to hold, while other times the predicate term (“eclipsed”) does so. As other factors are involved as well, particular cases and a full account become quite complicated.12 Beyond the contextual features determining the time period for which the proposition is being asserted to hold, Avicenna focusses on certain more formal features. (1) A paronymous subject term “R,” derived from the name of an item in one of the accidental categories, has the implicit form “S having R-ness.” It may signify the substance S that serves as a subject so long as S exists, or it may signify that substance S only so long as it exists and has R-ness. (2) Either the connection between subject and predicate or the “quantifier” may determine the truth conditions concerning the duration of the statement (i.e., the statement may be taken as a predication (a dictum), or it may be considered as asserting an attribute to belong to an existing subject). (3) The time duration during which the predicate is asserted to belong to the subject may be fixed upon by various features of the subject or predicate term. (4) The assertion of existence may be qualified in various ways: by what might generally be described as “ad-verbial qualifiers”13 (sc., the original, general sense of “mode”14) including: tense markers, modal (“necessary” etc.) and other operators (e.g., “it is dubious that”), hypothetical and other subordinate clauses, and other qualifications (e.g., “not really”). The first point concerns paronymous terms. The subject and predicate terms can be taken in various ways: in particular they may have a referential (dhātiyya) or an attributive (wa․sfiyya) use.15 This holds especially when the terms are paronymous, sc., derived from names of items in the accidental categories, like quality and relation, as “scribe” comes from “scribehood”16 and “slave” from “slavery.” For instance, consider “this scribe is P.” The subject term can refer to the individual substance, the human being Zayd say, in two ways: during the entire existence of Zayd or only during those times when Zayd is a scribe. This distinction has its antecedents. First, Aristotle himself offers a basis for this distinction of the referential and the attributive uses of paronymous terms in Metaphysics VII . He asks: does the white have an essence? He says that “the white,” namely “what is white” (τὸ λευκόν), can be understood in two ways: as a mere thing having whiteness, as the mere paronym, or as the substance having

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whiteness, a complex of an individual substance with an accident. Again, in Topics I.5 etc. Aristotle uses ousia sometimes to mean “substance” and sometimes “essence.” This makes it possible to understand the ousia of a white thing to be, say, the substance swan or the quality whiteness. Second, Alexander, commenting on Prior Analytics I.3, raises or cites an objection about the conversion of the necessary universal denial (NE ).17 He uses the example, “it is necessary that everything grammatical [in the Arabic translation: every scribe] is a man”—the very example that Avicenna will bring up on the same point. Alexander claims that Theophrastus had discussed it, and solved it by distinguishing the simply and strictly necessary from the necessary with a determinant. He does not explain. Later on al-Fārābī discussed this issue and used the same example. He claimed similarly that distinguished per se and per accidens necessary propositions; the conversion holds only for the per se and not for per accidens necessary proposition. Avicenna critiques his analysis.18 Avicenna seems to be working out the details of this distinction as we shall see.

3. Conversion In the syllogistic, mainly in proofs in the second and third figures, the subject and predicate terms need to be switched, so as to get to a first-figure syllogism. For instance, Aristotle presents the first form of the second figure (Cesare: II EAE ): if no N is M, and every X is M, then no X is N. He proves it by converting the major premise, so as to get “no M is N,” and then using the second form of the first figure (Celarent I EAE ). [An. Pr. 27a3–18] So the conversion of propositions has central importance in the syllogistic. In respect of Avicenna’s theory of the proposition, conversion has the general problem, how to fix the reference when the subject and predicate terms switch. For instance, if the proposition has its temporal duration determined on the side of the predicate, as with “the moon is eclipsed,” then what happens? Does the same term, now on the side of the subject, continue to determine its duration— or does that switch as well? Are there any general rules determining this? Likewise for other factors: if the existence condition concerns the subject term, does that condition change when the subject term switches? Given all the different factors that Avicenna has identified as relevant for understanding categorical propositions, we can see why his discussions become quite complex. And they do. For instance, in discussing the E proposition he says:

16

The Aftermath of Syllogism Or we say: there is nothing that is C unless it is also B. There is understood from this that everything that is characterized as being C in actuality however it be, always or not always, has B denied of it. And we do not know when, whether at all times when it is characterized as being B, or at all times [when] its existence is characterized is characterized, or not characterized, as being C, or at some times of its being C, or at a time other than the time of its being C. So, if what is characterized as being C has B denied of it, at every time of its being C, then it has B denied of it, and, if it is at part of that time, it has B denied of it, and, if it is at a time before or after that one, then it has B denied of it, and, if it is at every time of its existence, then it has B denied of it. Even if we say “denied” or “has been denied” or “is denied,” we imagine a time. So that belongs to the necessity of the expression. Rather we intend that everything characterized as being C has the denial of B true of it, we know not when.19

Here Avicenna first gives a truth condition for the E proposition in terms of the relation of subject and predicate, that everything that is C is not B. This looks very much like its current textbook symbolization in predicate logic: (x)(Cx ⊃ ~Bx). But then he adds on an existence condition, that some C exists at some time. Just what the stretch of time must be depends on various factors as he indicates. Some of the factors will complicate the conversion. He ends up saying that we might just take an E proposition absolutely, as holding “we know not when.” Then the conversion is valid. If we stick to propositions using terms from the category of substance and avoid paronyms and special temporal determinants—stick to what Avicenna calls “absolute” (his usual term for the categorical) propositions20 in a common or specific mode—no unusual problems arise for such conversions. First, consider what conversions follow from the truth conditions given in the formal logic (in Ibāra), where only affirmative propositions have existential import. The standard conversions, as stated by Aristotle, hold: The universal affirmative (A) proposition converts with the particular affirmative (I), which also converts with itself. Again, the universal negative (E) converts with itself (while the particular negative (O) does not). Second, consider what conversions follow from those truth conditions plus the additional assumption of existential import for all terms, as Avicenna has said that scientific demonstrations allow only terms having instances existing in re. Once again, all these conversions follow.21 With existential import, E implies O: If P does not belong to every S, then P does not belong to some S. Given that E implies O, also E converts with O (although not always for the reasons given by Aristotle). However, these standard conversions do not hold for premises used in syllogistic that are not absolute. Avicenna has extended discussions of particular

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examples. For instance, he says that in some cases “no A is B” does not convert. He gives the example: given that no human being is laughing, it does not follow that nothing laughing is a human being.22 Offhand, by the standards of textbook syllogistics, this E conversion does seem to hold. Is then Avicenna befuddled on E conversion? He himself notes that E propositions are hard to state in Arabic. Has the translation befuddled him? Avicenna himself does admit that E conversion holds here if “no human being is laughing” is taken absolutely “in a common or specific mode.”23 Yet in some other mode, it does not hold. Here, in the Ishārāt, he does not explain himself much but at best is offering his “pointers.” Avicenna is likely reacting to the Greek commentators. As noted above, Alexander reported Theophrastus making some such distinction: the E conversion holds absolutely but not “with a determinant”; al-Fārābī took it to hold per se but not per accidens. So try this reading of the E proposition, with existential import for the terms: there is a time, let us suppose, as Aristotle often does when taking propositions ut nunc, when no man is laughing. Yet it does not follow from that that there is a time when no laughing thing is a man (given that the only things that can laugh are human). Hence the conversion of E propositions cannot be said to hold always, without some temporal restriction. This conclusion does not look befuddled.24 Note that such counterexamples cannot be constructed with substantial terms, as in “no man is a stone”: suppose that there is a time when no man is a stone. Still there is never a time when it is not the case when no stone is a man. With substantial terms, a true E proposition becomes true necessarily. So the counterexamples to E conversion need to have at least one accidental paronymous term, like “laughing.” Moreover, that term has to be taken attributively and not referentially, so as to limit its reference to those times when something is actually laughing. If it is taken referentially instead, then the inference holds. Then “laughing” refers to those things that are laughing so long as they exist. Now such laughing things are the rational substances, all the human beings let’s suppose.25 Then the E conversion follows. So fixing the reference of the terms becomes a problem in conversion especially when the subject terms derive from the accidental categories and are used attributively. This problem does not arise for terms deriving from the category of substance. A substantial term used attributively will hold of the substance being referred to as long as that substance exists, since once it loses that substantial attribute it ceases to exist. Here the attributive use amounts to

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the referential use. For instance, with “some goat is an animal,” “goat” refers to a certain hircine substance so long as it exists—or, as Avicenna puts it, so long as its essence is existent. (The essence being used is the one had by the substance of the subject.) The same holds for “animal.” The switch of subject and predicate here occasions no problems of reference. Hence: every goat is an animal, and so some animal is a goat; no goat is a rock, and so no rock is a goat. However, a paronymous accidental subject term used referentially generates difficulties.26 Consider “some slave is free.” This is false when “the slave” refers to things that are enslaved. But it may be true if “slave” refers to those human beings who are presently slaves, given that some of those human beings are not slaves their entire lives. The predication still holds “as long as the essence is existent.” However the essence used here is not the one had by the substance of the subject but one had by an accident of that substance. A term like “laughing” is likewise such a paronymous accidental term. So, when paronymous terms are used, the switch of terms in converting does raise problems. Here, to keep a simpler focus, I assume that the temporal determinants remain constant in conversion. Thus, if a proposition is being taken absolutely, ut nunc, relative to the time of an eclipse etc., its conversion will be taken in the same way. I wish to focus on the referential and the attributive ways of taking the proposition. Indeed, this seems to be the most important consideration for Avicenna himself in logic and has the strongest ties to his metaphysics. Varying this will often cause the time determinants to change as well. Likewise, following perhaps the passage from Alexander cited above, Avicenna rejects A to I conversion on some ways of taking the propositions: So it is not inseparable, when every scribe is awake, i.e., at some time, [that] it is necessary that something awake be a scribe so long as its essence is existent or so long as it is awake. And in some cases it is necessary, as when we say: every man is an animal, i.e., as long as it is existent and always, and some animal is a man, i.e., as long as its essence is existent. And the common simple includes them both.27

Avicenna is accepting A to I conversion when the terms of the proposition are substantial, like “man” and “animal.” However, when they are accidental and paronymous, he rejects A to I conversion (sometimes). He offers the counterexample “every scribe is awake; therefore something awake is a scribe.” Once again such terms raise problems for the scope of the time: At all times when something is a scribe it is awake. Still it does not follow that at all times when anything is awake it is a scribe.

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Indeed, any accidental complex, even of a substantial and an accidental term, can occasion problems in conversion (e.g., “no man is a scribe” can be true ut nunc, while “no scribe is a man” is always false). When the modality is made explicit, as in modal logic, the same problems with conversion will arise. So these problems with conversion coming from the attributive use of the terms typically arise when at least one of the terms are accidental paronyms. In Aristotelian terms, such terms occurring together in a proposition make the proposition have contingent matter. They form a complex of what Aristotle himself calls being per accidens, which occasions fallacy and sophistry.28 Perhaps Avicenna, like al-Fārābī before him, was thinking of this doctrine, although the texts are scant. Even though they occasion problems, Avicenna seems to think that the accidental paronymous terms must be used in syllogistic. Indeed, Aristotelian demonstrative science mostly uses such terms, which signify proper and common accidents: its syllogisms show why the substances have the attributes signified by them.29 Moreover, despite its problems Avicenna wants to keep this attributive use. For him it is the most proper use. To understand why, and how he saves it from fallacy, we need to make a metaphysical excursus.

4. Foundations of modality Avicenna considers the mode of a proposition to concern the relation of subject to predicate.30 Already Aristotle’s very phrasing of the modal connection in the syllogistic had suggested this: “belongs by necessity”; “possibly belongs” [25a1– 2]. So the modes are ways in which the predication relation holds: necessarily, possibly, impossibly; when a mode is not stated, that relation just holds absolutely, as with categorical propositions. However, Avicenna would again agree, the matter of a proposition concerns the necessity etc. of the items being referred to in their existing.31 In the Aristotelian tradition, the logical matter is determined by the predication relation too: if the predicate belongs to the subject necessarily, the proposition has necessary matter; if contingently, contingent matter; if impossibly, impossible matter. So a proposition connecting, say, “goat” with “animal” will have necessary matter; “goat” with “standing,” contingent matter; “goat” with “rock” impossible matter. The difference between the mode and the matter comes from the predication relation actually used. For instance, the (false) proposition, “every goat is necessarily a rock,” is necessary while its matter is impossible. Avicenna

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takes matter to be tied to existence, as opposed to form, which is tied to essence. Thus the mode of a proposition would be determined by the relations of the essences, his quiddities in themselves, say, goathood and rockiness, while the matter is determined by the existence: given that the thing referred to by the subject exists, must it, can it, or must it not have that predicate? So Avicenna takes the distinction of mode and matter to reflect that of essence and existence. He uses d․arūrī to signify the necessity of the modality, which for him concerns the essences, and wājib to signify the necessity of the matter, which for him concerns the existence of those essences.32 The former does not require any instances of the essences to exist in re; the latter does. Aristotle had perhaps marked already such a distinction in his modal logic when he distinguished P’s possibly belonging to all to which S belongs from P’s possibly belonging to all to which S possibly belongs [An. Pr. 32b15–32].33 This distinction of two types of necessity has great importance for understanding Avicenna’s thought. It is made in his logical works and absent from the discussions in Al-Ilāhiyyāt (aside from the references there to the logical works!). The logical concept of necessity is not the concept of necessity used in the metaphysical discussions of the necessary being. Avicenna says, “By the necessary (d․arūrī) in this section of logic [Al-Qīyās] there is meant a sense more general than the necessity (wājib) of existence.” [166,16–7] Here he is distinguishing d․arūrī from wājib.34 The latter is the “necessary” in Avicenna’s stock phrase, “the necessary being,” signifying God. The former is the “necessary” used as a modal operator in the syllogistic. Again, in Al-Najāt, Avicenna defines the latter (wājib) as permanence in existence or as necessity (d․arūra) in existence [17,4; 20,3–4]. So, at least in some passages Avicenna is careful to keep the two expressions distinct.35 Still he does not do so always. One reason is that he does not write carefully. Another is that the Arabic translation of On Interpretation, some version of which Avicenna was using, has a curious mixing of these terms. To translate Aristotle’s simple “necessary to be” (ἀναγκαιˆoν εἶναι) at 22a3 et passim, it has: wājib d․arūran an yajibu. (Here, perhaps, “wājib” is being taken as: “it is asserted,” but it is easy to think otherwise.) Again the translation of necessary statements for Aristotle’s Prior Analytics uses some form of dārūrī or id․․tirār.36 A third is that in making logical inferences about necessary beings the two expressions will be mixed even if Avicenna were writing carefully. For an inference from statements about the metaphysically necessary will follow by logical necessity; also some logically necessary claims will come to exist necessarily in the world, as with the matter of propositions.

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For Avicenna logical necessity may apply to subjects that always exist as well as to those that do not always exist, or even to those that never exist. It is necessary that every swan is an animal, but it is not necessary that every swan exist at all times. It is necessary that every heptagonal house is a house, but it is not necessary that any ever be built. There are many possibilities that never exist.37 So “necessary” does not imply “always” or even “sometimes.” Likewise, “always” does not imply “necessary.”38 Many things may exist always without being necessary.39 Aristotle had said the same [An. Po. 75a29–34; 72a28]. Avicenna clearly separates time from modality: human beings exist always but not necessarily; the void never exists but could exist: “Rather, man is existent always or not always, and/ while the void is non-existent always. Existence is not impossible for either of them . . .” [Qīyās 251,2–3] The logical modality, apart from time, is the one on the side of the predicate and not on the side of the quantifier: “. . . unless of course in the necessity (d․ārūrī) no attention is paid to time but to the essence of the subject and the essence of the predicate.” [Qīyās 219,9–10] So Avicenna views the logical modalities normally to concern the predication relation, based on the quiddities in themselves signified by the terms. He allows modal propositions to have two readings, one considering only the relations between the concepts of the subject and predicate (“in respect of the predication”); another considering the instances of those concepts (“in respect of the quantifier”).40 The predicational reading is a type of de dicto, compound reading, like “necessary (S is P).” The quantifier reading is a type of de re, divided reading, like “S is necessarily P.” In both cases the modality (“necessarily”) goes with the predication (“is”). Their difference becomes manifest when combined with the existence condition for (affirmative) propositions, “there exist S’s.” The quantified reading amounts to talking of necessary properties of existing S’s, especially when the existence is taken to be in re and not in intellectu. The predicational reading amounts to talking to necessary properties of all possible S’s, where the existence condition is usually in intellectu only.41 Avicenna favors the predicational reading in demonstration, as science deals with things that have real instances only at some times, like eclipses, and those that have no real instances ever, like chiliagons.42 Thus he remarks that “no eclipse is an eclipse” is false on the predicational but true on the quantifier reading (presumably when there are no eclipses).43 Avicenna says that ordinary (Arabic and Persian?) language has a strong presumption for the divided sense so as to have actually existing subjects. However, the logician does not require this.44 Still Avicenna advises using the divided sense in making inferences (in most contexts), with the presumption of existence in re.45

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On the predicational reading, Avicenna will allow for the truth of a simple affirmation having no instances in re. He says that “. . . the intellect may characterize it insofar as its existence in act is such . . .”46 Clearly, in order to make it possible that many statements about numbers or figures be true, we must allow that they need not have no instances existing in re.47 Avicenna says to consider in such cases whether the proposition is true, and not whether an existent subject has the attributed as asserted: If the existence of the subject is not considered but rather the truth of the proposition is considered, be the subject existent or non-existent, so that the simple [proposition] is that in which the judgment through its quantifier is true at some time, whether the subject be existent or non-existent . . .48

He proceeds to argue that on the quantified reading “some colors are black” cannot be true by necessity for two reasons: since there need not exist any black things at some time, and since the necessity (d․arūrī) here does not concern the existent things. Still, taken in consideration of the predication, “some colors are black by necessity” can be true, given that there is an essential relation between the genus color and its species like whiteness and blackness.49 Because such modal propositions are not restricted to what exists in re, normally they should be understood to concern the predication and not the quantifier.50 On neither reading is a modal operator being attached to the one of the terms of the proposition, as in “every necessary goat is a rock”—or, if you like, more colloquially, “everything that is a goat by necessity is a rock.”51 Such modalized terms, like “necessary goat,” appear in the syllogistic of neither Aristotle nor Avicenna. Avicenna does though seem to allow modality to be attached to the terms, when he speaks of “the necessary in existence” and “the possible in existence.” Here though the modality has a different function. E.g., in “the necessary being is necessarily unique,” “necessary” [wājib] specifies the mode of how the essence of the subject is existent, namely that it exists necessarily and always, while “necessarily” [d․arūrī] indicates there that that subject ka has an essential connection to being unique. The modality in logic concerns the predication relation; the modality in metaphysics concerns the way in which the objects being referred to by a term exist. Hence the latter are necessary in the sense of “wājib.” Similar distinctions apply to statements about “possible beings,” those that are “contingent in existence.”52 Avicenna does not have two different words for “possible” as he (sometimes!) does for “necessary,” perhaps because he

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distinguishes more than two senses of “possible.” Some of them are logical as they divorce possibility completely from time: “the possible is what is not existent and not necessary [nor impossible].”53 Others are physical as they have existence as determined by an external cause. In ordinary contexts, in speaking of “possible beings,” we are speaking about things that exist in fact but contingently so, depending upon external causes. Avicenna generally uses this sense when speaking of “possible beings” in his metaphysics: beings that do exist but need not exist.54 However, we might speak of beings that could exist but do not in fact. In contexts where the subject is being claimed to exist in re while the modality is attached to the copula as usual, then, given the existence of the subject, “necessary” can be signified by “wājib.”55 Here “necessary” implies “always,” in one of its varieties. For, when we speak of the subject having the predicate “always,” we may ask about the existence of the subject: does it exist only at some times or at all times? Does it exist at all times necessarily or contingently? Do then modal propositions taken logically in the sense of d․arūrī still have an existence condition on the predicational reading? At least their subjects “subsist” in the mode of quiddities in themselves. Avicenna does not offer much of an explicit answer; I speculate that he requires existence in the divine intellect for true modal statements. This question also has the complication that, insofar as modal propositions are propositions or terms and are being thought about in the logician’s mind, they exist in intellectu. As Marmura says, distinguish here what is being conceived from the fact that it is being conceived.56 That mental existence is not the primary focus. On the other hand, Avicenna seems to link the subsistence to existence in a divine mind, as discussed below. The distinction of logical and physical modality dovetails with Avicenna’s threefold distinction of quiddity (triplex status naturae). Logical modality concerns the interrelations of quiddities in themselves. Thus, horseness (equinitas) has animality necessarily, but whiteness possibly. Definitional statements concern this respect, of quiddities in themselves. Thus horse is animal necessarily and is white only contingently, even if in fact all horses at all times have been white or if no horses ever existed. Predications of the material accidents, typically contingent, concern the quiddities in individuals.57 (Speaking of formal features, like being a material accident or a universal, concerns the quiddities in the mind, as in “some propositions are true.”) Avicenna ties the attributive reading of the paronymous term to the level of the quiddity in itself. Such statements about “the white” considered abstractly, as not presupposing a thing, a substance, that is white, are grounded upon

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the level of quiddities in themselves.58 In this sense “everything white is necessarily colored” is true, since color is the genus for whiteness and appears in its definition. When Avicenna is taking this sense, he tends to use the qua phrasing: “the white qua white”; “the scribe qua scribe,” just as he does in talking of “horseness” as “horse qua horse.” Still, referentially, “everything white is necessarily colored” is false: there are many things existing in re that are white but only contingently so. Physical modality concerns actual existents, primarily the quiddities in re and secondarily those in intellectu, here likely those in actually existing intellects. (Only here does the notion of potentiality or ability come into play, as only actual things have “potentialities” or actual powers.59) The statements of their interrelations will hold of things existing necessarily or contingently and having necessary attributes, contingent accidents, and actual potentialities or powers. Some of these modal statements will gain their truth values from the relations of logical modality: “it is necessary that some goats are rocks” is false. The different modes, logical and physical, have their truth-makers on different levels of quiddities. What complicates this scheme is that, as these modes are attached to statements, they become attached to assertions of existence. The modalities themselves concern the relation between subject and predicate; the existence condition has a separate cause of truth. In statements, the existence condition is given by the copula; the duration is given by contextual features, typically either the subject term or the predicate term. When Avicenna talks about possible beings and necessary beings, here the necessity is de re and concerns the matter and not the mode. As well as the categorical and modal syllogistics, Avicenna has an elaborate hypothetical syllogistic, with which I shall not deal here. Still, I suggest that this division of syllogistic into the categorical and hypothetical has its basis on the distinction between quiddities in themselves and those that exist. For the latter, there is existential import and the categorical syllogistic. For the former, there is no existential import assumption. Avicenna has syllogisms like: (1) “if A is B, then C is D”; (2) “not at all, if A is B, then C is D”; (3) “it might be (that) if A is B, then C is D.” If the propositions be understood in his usual way, as in “if A exists as B, then C exists as D,” Avicenna has a way of talking about connections between the quiddities in themselves without assuming them to exist. Syllogisms of type (1) give actual connections, which may be logically necessary or physically necessary (“inseparable,” as with propria); those of type (2) give impossible connections; those of type (3) give contingent connections, between the antecedent and consequent. But this is a large claim, and I put it aside here.

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5. The modal logic The doctrine of the matter of the proposition makes easy a transition from the categorical to the modal syllogistic. When the mode and the matter match up, we get true modal propositions. Those true propositions having necessary matter turn into true necessary premises; those having possible (contingent: not necessary and not necessary not) matter into possible premises; those having impossible matter turn into the contradictories of the necessary propositions, as “impossible” is “necessary not.”60 (Avicenna tends not to use the one-sided possible (not necessary not): he holds that this use is vulgar and not suited for the experts. Similarly Aristotle had allowed for it secondarily, while making the contingent the primary sense used.61) Not surprisingly, Avicenna has doctrines about conversions in the modal syllogistic like those in the categorical syllogistic: the conversions generally fail when there are paronymous accidental terms taken attributively.62 Consider the conversion of the universal affirmative, as with “every scribe is necessarily a man.” This is true for any scribe at any time while being a scribe. Yet it is not necessary, at any time, that some man is a scribe. Once again the conversion does follow if the terms are taken referentially. Then “scribe” refers to a human being. In effect, taking such accidental terms as “scribe” attributively makes the necessary proposition have contingent matter. Avicenna seems to offer, obscurely, a way to forestall such counterexamples: to “every S is necessarily P,” where the “S” term is accidental and the “P” term essential,63 add on “qua S,” understood as “so long as the essence of S is existent” or “in respect of being S.”64 (This solution too has its Greek roots.65) E.g., “every scribe is necessarily a man so long as he is a scribe”; hence “some man is necessarily a scribe so long as he is a scribe.” The qua phrase restricts the usual reference of the terms. Given his use of such “qua” phrases in discussing the quiddities in themselves, Avicenna likely thinks that the qua phrase put here will keep the statement focused on the modal relation. The same qualification will make the E and I conversions valid. The other major issue in Avicenna’s modal logic concerns certain mixed syllogisms. Aristotle had made the surprising claim that some syllogisms having mixed premises yield the stronger conclusion: from a necessary and a categorical premise sometimes a necessary conclusion follows; from a necessary and a possible premise sometimes a categorical one does.66 Already his successor Theophrastus protested. Still some Aristotelians like Alexander of Aphrodisias defended Aristotle’s original claims. So does Avicenna.

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The famous syllogism is INAANA : If it is necessary that every B is A, and every C is B, then it is necessary that every C is A. Aristotle says by way of proof just that C is ones of the B’s [An. Pr. 30a17–23]. Theophrastus rejected its validity. He proposed a rule [Alexander, in An Pr. 124,8–13] that the conclusion is similar in modality to the weaker of the premises, here the minor, and was followed by Syrianus, Eudemus, and Proclus. They argued also that the categorical premise suggests that it is possible at some time for the predicate to be separated from the subject, and, so if we take that time, the major will not belong to the minor term (Alexander, 124,18–21). Alexander and Iamblichus followed Aristotle; cf. Ammonius, in An. Pr. 38,38. Philoponus too follows Aristotle and gives, 122,28–29, as Aristotle’s the rule that the modality of the conclusion is determined by that of the major premise. Alexander, 124,31–125,2, reports convincing counter-examples (based perhaps on the very counterexample that Aristotle gives for IANANA !!) like: “every man is an animal by necessity, and everything moving is a man [let’s suppose], but it is not necessary that everything moving is an animal by necessity” (from Alexander, 124,24–5; also Philoponus, 124,25–8). The minor premise is being taken ut nunc. Nevertheless Avicenna defends INAANA : . . . people are amazed at this conclusion’s being necessary, and disqualify this belief. And yet a single thing deceives them. And that is because they suppose that the necessary here is everything that is necessary as long as the essence of the subject is existent, or necessary as long as it is characterized by what characterizes it, so that, when it is said: “everything white is by necessity [something] having a color standing out in sight,” they suppose it to be really necessary. And likewise when it is said: “by necessity nothing that is white is black,” they suppose it to be really necessary. And, when they say: “Zayd is white, and everything white is by necessity [something] having a color standing out in sight,” it will not have been concluded for them: “Zayd has a color standing out in sight by necessity,” unless Zayd is white by necessity. And similarly when it has been concluded for them in the example of the black that Zayd is not black, not by necessity, and all of this is because they are not concerned with establishing the reality of what is being said of the whole in a necessary statement, so as to comprehend the difference between our saying: [1] “everything white is by necessity [something] standing out in sight,” since its sense is “what is characterized as being white,” however it be characterized as being white. So if it, as long as its essence is existent, is white or is not white, it is [something] having a color standing out in sight. Or, [2] “everything that is characterized

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as being white, however it be, then, as long as it is white, is [something] having a color standing out in sight, or by necessity is not black.” And you have learned above that the viewpoints explain our distinction, and how the first one is false.67

Note that Avicenna rejects the modalized predicate reading, where the major term becomes “white by necessity.” [126,12] (Remember that modalities like “necessary” and “contingent” concern the relation of predicate to subject, not modal predicates of subjects existing in re.) He also distinguishes for the accidental term between the referential and the attributive readings. On account of the time restriction, Alexander’s counterexample is complex. Avicenna offers an easier one: “Zayd is white, and everything white is by necessity [something] having a color standing out in sight; therefore Zayd has a color standing out in sight by necessity.” (In the Aristotelian tradition, “whiteness” is defined as “a color standing out in sight.”68) Replace the minor premise with “every swan is white” (so as not to have a singular term in the syllogistic). Suppose it to be true at all times, as the Aristotelian tradition did, while also claiming that it is not necessary [An Po. I.4; An Pr. 26a30–b21]. Here the problem lies in the major premise. Referentially it is false: a statue can be white for a time but is not necessarily white as it can change its color. Attributively it is false too: even if something is white as long as it is white, like a swan or a particular statue or every swan, it is not necessarily white: the statue or swan could have been black. Note that for this to work, modality and time are distinct, as Avicenna indeed asserts: “necessary” is not equivalent to “always.” Alexander’s counterexample likewise fails with the major premise, but for more complex reasons. (The following is a bit speculative as Avicenna does not discuss this particular example.) Suppose everything moving is a man at some time, say tp. The referential reading cannot apply because it would wipe out the time restriction to tp; without that time restriction the minor premise is false. As we have seen in discussing conversion, for the attributive reading to hold, the qua phrase must be understood: “insofar as it is moving.” Then the minor premise is true. Avicenna seems to hold that, once this qua phrase appears in one premise, it must also appear in the other. But then, it seems, the major premise is false: “it is necessary that every man is an animal, insofar as he is moving.” To prove this requires discussing what Avicenna means by such qua phrases. I have done so elsewhere.69 Suffice it to say here: it means “in the respect of moving” or “because it is moving.” But a man is necessarily an animal not because he is moving.

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Avicenna’s general solution to the objections to the validity of INAANA lies in distinguishing the referential and the attributive readings and then showing that on neither one are both premises true.70 Hence no counterexample and no invalidity. IANANA remains invalid: “every goat is necessarily an animal; every animal is terrestrial; therefore every goat is necessarily terrestrial.” Other modal syllogisms fare similarly. For instance, with IIENA [Cesare] Aristotle has it invalid simply 30b7–9, but Avicenna with all of these different readings of the premises can distinguish cases in which it is valid. IINAE for Avicenna as for Aristotle does not yield a valid syllogism71 [An Pr. 30b9–18; Qīyās 131,11–4]. What necessary propositions are true then for Avicenna? (1) referentially, those having substantial terms (“goat” and “animal”) in necessary matter. This gives essential connections between the terms and predictions holding so long as the subject exists. (Terms signifying differentiae and propria are substantial.) (2) attributively, the accidental terms only with the qua phrase restriction. (For substantial terms, the attributive reading and the referential one are the same.) The white necessarily stands out in sight insofar as it is white. In both cases, the truth of the necessary statements is based upon the relations of quiddities in themselves. This defense of INAANA can be seen to be a development and explanation of the solution of Alexander, al-Fārābī et  al. when they say that INAANA holds for per se but not per accidens modal statements. Think of Avicenna as working out the hints provided by his predecessors and then leaving pointers of his own.72

6. Conclusions Avicenna then received Aristotelian doctrines about the syllogistic not uncritically. He challenges and modifies some of the conversion rules for both categorical and modal propositions on logical grounds as well on metaphysical principles. He offers a defense of mixed modal syllogisms based upon his analysis of the structure of the proposition and the nature of modality. Why do those like Aristotle and Avicenna insist upon the validity of these mixed modal syllogisms? They provide a way to link up the singular features of the world with the universal principles of science. For Avicenna they connect the necessity of God with the contingency of the world. But that is another topic.

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Notes 1 Namely, Al-H ․ āsil wa-l-Ma․h․sūl (The Available and the Valid) probably in 1002 or 1003, following Gutas’ dating. 2 Al-Jūzānī, “Introduction” to Aš-Šhifā, Section 3, translated by Dmitri Gutas, Avicenna and the Aristotelian Tradition (Leiden-Boston, 1988), 101. 3 Tony Street, “Logic,” The Cambridge Companion to Arabic Philosophy, ed. P. Adamson and R. Taylor (Cambridge, 2005), 247–64, 250. 4 See Allan Bäck, Aristotle’s Theory of Predication (Leiden-Boston, 2000). 5 Al-‘Ibārā, Part One, Volume Three of Aš-Šifā (The Healing or The Cure), Avicenna’s work commenting on much of Aristotle’s corpus. I am using the text edited by M. El-Khodeiri, S. Zāyid et al. (Dar al-Katib al-Arabi, 1970); trans. & comm. Allan Bäck (München, 2013), 83,1–85,5. 6 Bäck, Aristotle’s Theory of Predication. 7 A possible exception might be at Qīyās 371,1–4, but this passage deals with conditional propositions, mostly affirmative. 8 Allan Bäck, “Avicenna on the Categorical Assertion,” Medieval Theories on Assertive and Non-assertive Language, ed. S. Maierù and L. Valente (Firenze, 2004), 141–62. 9 I focus my attention on the long discussions in the Shifāʿ. Tony Street, “Avicenna and ․tūsī on the Contradiction and Conversion of the Absolute,” History and Philosophy of Logic, Vol. 21 (2000): 45–56, has an analysis of the material in the Ishārāt. Yet that and like books of Avicenna are summaries of complex doctrines, with most of the complexities omitted. Cf. the summary discussion in Kitāb al-Najāt, ed. Kurdi (Muhy al-Din al-kurdi, 1938), 23,4–25. Al-Ishārāt wa’l Tanbīhāt, ed. S. Dunya (Dār alMa’ārif, 1971), 271, 8 ff., also is a summary, with no evident differences from the materials in the Shifāʿ—except the lack of detail. In this study, I largely omit discussing the predecessors of Avicenna’s views, both Islamic and Greek. 10 An. Po. 73b16–18; Allan Bäck, On Reduplication (Leiden-Boston, 1996), 32. 11 An. Pr. 34b7–18. 12 Allan Bäck, “Avicenna on the Categorical Assertion.” 13 Ishārāt, ch. 5.3, 328.5. 14 Ishārāt, III .5.3, 328,5. 15 N.B.: this distinction differs from Keith Donnellan’s distinction of referential and attributive uses of definite descriptions, as in both cases the subject has the predicate . . . at times. 16 This comes from the Arabic translation of “grammatical” and “grammar” in Aristotle’s Categories. 17 Alexander, in An. Pr., 36,25–30. Street, “Logic,” 256, says that the attributivereferential distinction is “unknown in the West,” although he himself admits some foundation in Aristotle.

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18 Street, “Logic,” in Cambridge Companion, 257–58, claims that Avicenna is attacking al-Fārābī at Al-Qīyās 209–10 [210,12?]. (The text of al-Fārābī is not extant). Averroes discusses the issue also. Frank Griffel, Al-Ghazālī’s Philosophical Theology (Oxford, 2009), 165, says that Avicenna’s distinction of the referential and attributive uses comes from Sophistical Refutations 166a22–30, but this seems unlikely. 19 Al-Qīyās 81,6–15. 20 E.g., Al-Qīyās 125,8; Al-Ishārāt 263, trans. p. 91: in an absolute proposition: the judgement is given “without mention of its necessity, duration, or anything else concerning its being in time, or in accordance with possibility.” 21 Still, even here Avicenna can criticize Aristotle’s proofs, as they disagree with what Avicenna takes the forms of the propositions to be. 22 Al-Ishārāt 322; trans. Shams Inati, Ibn Sīnā Remarks and Admonitions Part One: Logic (Toronto, 1984), 113–14. 23 Al-Ishārāt 322; trans., 114. 24 Actually Avicenna’s position resembles quite strongly some current ones: Adriane Rini, Aristotle’s Modal Proofs (Dordrecht, 2011); Marco Malink, Aristotle’s Modal Syllogistic (Cambridge (MA-London, 2013); “A Reconstruction of Aristotle’s Modal Syllogistic,” History and Philosophy of Logic 27 (2006): 95–141. 25 There arises also the problem whether all human beings laugh; in the Aristotelian tradition it is supposed that all human beings can laugh: risibility is a proprium of the human species. So at least if we extend the reference to what all human beings can do, we can suppose that “laughing” refers to all human beings. 26 The proper or per se accidents—the differentiae and propria—do not seem to have this difficulty. Aristotle has the position in the Categories that these are in categories other than substance: with rationality and risibility, in quality. Avicenna seems to agree about the propria but perhaps not about the differentiae. Cf. Aristotle, Topics 101b18–19; Alexander, in Top. 38,11–15; 38,27–39,2. In any case such items, like rationality and risibility have the paronyms, the rational and the risible. Since a substance that is rational or risible will be so her entire life—namely, a human substance—such paronymous terms do not occasion difficulty in conversion when used either referentially or attributively. However Avicenna still maintains that at least the propria are attached to the quiddities in themselves when they come to exist in re via an external cause. See Allan Bäck, “The Triplex Status Naturae and its Justification,” in Studies on the History of Logic, eds. I. Angelelli and M. Cerezo (Berlin-New York, 1996), 133–153. 27 Al-Qīyās 90,15–91,3. 28 As this doctrine is not applied explicitly, I omit discussing it. See Bäck, Aristotle’s Theory of Predication, 65–74. 29 Likewise, Aristotle had to accept such terms—as demonstrations typically have expressions signifying differentiae and propria as their major terms, and these are

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mostly in the accidental categories. See Bäck, Aristotle’s Theory of Predication, 150–158. 30 Al-Qīyās, 31,4–5; Al-‘Ibāra, ed. M. Al-Khudayri. (al-Hay’a al-miksriyya al’ʿāmma, 1970), 112,6; 114,18. Perhaps following Ammonius, in de Int., 216,2–4. Ishārāt 261; Shams Inati, Ibn Sīnā Remarks and Admonitions Part One: Logic (Toronto, 1984), 90 n.1, on Al-Najāt ed. Kurdi. Second ed., 18. 31 Al-‘Ibāra 112,10–15. 32 Shams Inati urges us to keep the two radically apart. He, p. 91, n. 4 urges keeping them apart; he translates wājib as “Necessary in existence” and d․ārūrī as “necessary.” On Alexander’s conception of logical matter, see Alexander, in Top. 2,16–20; in An. Pr. 26,25. J. Barnes, “Logical Form and Logical Matter,” in Logica, Mente et Persona, ed. A. Alberti (Firenze, 1990) 7–119, 11–39; Kevin L. Flannery, Ways into the Logic of Alexander of Aphrodisias (Leiden-Boston, 1995), 111–131, 140, finds Alexander’s account incomprehensible. 33 Below I suggest that this distinction motivates Avicenna’s distinction between the predicational and the quantified reading of modal propositional. 34 Al-‘Ibāra, 119,1–8; Al-Qīyās, 166,16; 168,8–10; 169,16. Avicenna, 169, 6–7, complicates the distinction by allowing further that logical necessity may be taken absolutely or hypothetically. In Al-Najāt 20,1–5, he mentions the distinction but does not use it much. He does say, though, 25,8ff. that d ․ārūrī describes everything determined in view of the intellect to exist. That is, to be necessary in this sense does not guarantee existence in re. Cf. too Al-Ishārāt, 320,1–2; 341,5; 343,15; 344,2. Al-Qīyās, 166,16–17; cf. 169,6–16. Avicenna regularly uses “d ․ārūrī” in this sense, as opposed to “wājib,” which indicates what is necessary in the existing world, and so has existential import. See Allan Bäck, “Avicenna and Averroes: Modality and Theology,” in Potentialität und Possibilität, ed. T. Buchheim et al. (Stuttgart-Bad Cannstatt, 2001), 125–145. 35 E.g., Al-Qīyās 151,14–152,5. 36 E.g., Al-Qīyās 122,1–2 the usual form of necessary propositions: by necessity (d ․arūrī) every S is P but in Ibāra 122–23 we do get “not necessary (wājib) to be.” Wisnovsky, “Avicenna,” in Cambridge Companion, 118, thinks that the translator of Ibāra uses wājib and not d․ārūrī in order to be able to cover the necessity of inference, as in “follows by necessity.” 37 Al-Qīyās, 33,11–15. 38 Marmura, “Avicenna on Causal Priority,” in Islamic Philosophy and Mysticism, ed. P. Morewedge (Delmar, 1981), 65–83, 68, agrees that for Avicenna regularity does not entail necessity. 39 Al-Ishārāt 325,1–3, trans. Inati: “And know that the permanent is non-necessary. So scribehood may be denied of some individual permanently in the state of his existence, aside from the state of his non-existence, whereas that denial is not

32

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41 42

43 44 45 46 47

The Aftermath of Syllogism necessary.” 329,1–3: “An example: we say: every C is B always, so that we are as if we are saying: each and every C, according to the explanation that we have given, has B present/existent to it always, as long as the essence is existent, without necessity.” Street, “Logic,” 130, says that Al-Najāt runs together modality and time, whereas Al-Qīyās and Al-Ishārāt do not. Al-Qīyās,142,14–17; Al-‘Ibāra, 112,15–113,5; 115,2–11. Cf. Philoponus, in An. Pr. 43,8–13. Street, “An Outline of Avicenna’s Syllogistic,” Archiv für Geschichte der Philosophie 84 (2002): 129–60, 133; Thom, Medieval Modal Systems, p. 68. Cf. Al-Burhān 91,14–16. See Bäck, “Avicenna on the Categorical Assertion.” This is Thom’s ampliated reading in Medieval Modal Systems, 67, and “Logic and Metaphysics in Avicenna’s Modal Syllogistic” 362. Street, “Logic,” 135: “I cannot find a statement in Avicenna’s works that the modals do not have the same subject-term that the temporals have.” Al-Qīyās 138,8–9. Al-‘Ibāra 115,12–116,9. Al-‘Ibāra 116,13–14. Al-Qīyās 21,6–12 Al-Qīyās 21,6–12; cf. Al-Madkhal, 66,4–7; 69,16–18 [= Logica 9r col. 2]. On intelligible matter cf. Aristotle, Metaph. 1038a7; 1058a21–25.

48 Al-Qīyās 84,16–85,2; Al-Ishārāt III .2.1, 271,8–12; Man․tiq al-Mashriqiyyīn (Cairo, 1973). 64,2–4. 49 Al-Qīyās 137,11; cf. 141,12–13; Man․tiq al-Mashriqiyyīn 68,3–5; Al-Ishārāt 337,1.33. 50 Al-Qīyās 151,9–13; 164,7. Cf. Al-Burhān 71,13ff. 51 Avicenna is aware of this option. Qīyās 127,3–6 offers the following construal of INAANA : Zayd is white by necessity and everything white by necessity is a color standing out in sight—then Avicenna says that the minor is false. This might suggest that the middle term is “white by necessity”—but then he is discussing others’ views. The passage (to 127,130, does seem to go on and use the ekethsis proof of Alexander et al. See Bäck’s hypertext on this passage in the Archelogos Project. Some construe de re necessity thus and also take Avicenna (or Aristotle) to be doing so in proving a mixed modal syllogism like INAANA . E.g., Thom, Medieval Modal Systems (Aldershot, 2004), 68; “Logic and Metaphysics in Avicenna’s Modal Syllogistic,” in The Unity of Science in the Arabic Tradition (Dodrecht, 2008), 361–76, 366–67; Asad Ahmed, “Avicenna’s Reception of Aristotle’s Modal Syllogistic,” in Avicenna’s Deliverance: Logic (Oxford, 2012), 17–18. Ahmed, 21, has Avicenna having the standard de re and de dicto readings of modal propositions. But taking Al-Najāt 37; 44 and Al-Qīyās 31 for NA to be: (x)(Bx ✇ NA x) has its problems! 52 He does note, Al-‘Ibāra 114,10–16, that Aristotle has two different words [δυνατόν and ἐνδεχόμενον] but like Aristotle he uses them interchangeably in his logic. Aristotle at times distinguishes the potential (δυνατόν) from the possible

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(ἐνδεχόμενον), e.g. at Metaph. IX .4. But not in his logical works: cf. Int. 12; An. Pr. 34a5–12; 31b8–9; J. L. Ackrill: Aristotle’s Categories and De Interpretatione (Oxford, 1963), p. 149; Robin Smith, trans. & comm., Prior Analytics (Cambridge, MA , 1989), 123; 131. 53 Al-Qīyās 164,14; the definitions are summarized at 164,12–17. 54 Al-Najāt 19,4–5; 25,21–22. Man․tiq al-Mashriqiyyīn, 73,18–74,7; Al-Ishārāt 320,30–38. 55 Al-‘Ibāra 112,8–10; Al-Najāt 16,4–5; Al-Ishārāt 314,1; 318,1–3: “And there is included in this possible the existence for whose existence there is no duration of necessity even if it has necessity in one time and in another like the eclipse.” 56 Michael E. Marmura, “Avicenna’s Chapter on Universals in the Isagoge of his Shifa,” in Essays in Islamic Philosophy, ed. G. F. Hourani (Albany, NY, 1975), 83–99, 45. Cf. p. 36: “Thus, although logical concepts exist in the mind, logic as such is not concerned with their existence in the mind. It is concerned with them in themselves and with the relationships that obtain between them.” 57 Again, the proper accidents, having a necessary connection to their subjects, present difficulties, which I shall not discuss here. See n. 26. 58 Al-Qīyās 144,9–145,10. Cf. too Al-‘Ibāra, 115–3–11; Al-Qīyās 99,9–100,12, on “scribe qua scribe” as signifying a quiddity in itself; cf. Al-Ilāhiyāt V.1, 196,8–197,5 on the equivalence of “horseness” with “horse qua horse.” On “builder qua builder,” cf. Aristotle, Physics 191b4–5. 59 Avicenna does discuss potentiality, pace Barry Kogan, Averroes and the Metaphysics of Causation (Albany, NY, 1985), 35 n. 39. Cf. Al-‘Ibāra 118,12–120,9; Al-Ilāhiyāt IV.2. 60 Cf. Lagerlund, Modal Syllogistics in the Middle Ages (Leiden-Boston, 2000), 39. 61 Aristotle, Prior Analytics I.3 and 13; On Interpretation 13. 62 Philoponus, in An. Pr. 48,18–49,31 reports what Alexander says about other objections to NE conversion, which Avicenna does not discuss. Street, “Logic,” in Cambridge Companion 259–60, claims that Avicenna takes NA to NI conversion to be invalid: at Al-Ishārāt 334–35. Asad Ahmed, “Avicenna’s Reception of Aristotle’s Modal Syllogistic,” 19, has Avicenna endorsing NA and NE conversion without exception (from Al-Najät) [but this is too strong]. Even Ahmed goes on, p. 20, to note problems with E conversion when there are accidental terms or certain time constraints. 63 With the “P” term accidental as well, there are more complications. See below. 64 Al-Qīyās 99.9–100,12. Avicenna worries about how to attach the qua phrase in conversion at 210,8–11; 100,4–12 He does not consider the case when both terms are accidental. First, in most cases they will not give a true necessary statement. When they do, as with “everything white is necessarily colored,” a single qualification, “qua white,” will suffice. Still, I suppose, a qualification of each term would be possible.

34

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66 67 68 69 70

71

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The Aftermath of Syllogism Cf. Lagerlund, “Avicenna and ․tusī on Modal Logic,” History and Philosophy of Logic Vol. 30 (2009): 233, n. 13. Thom, “Avicenna,” Medieval Modal Systems, Appendix 3; p. 24, discusses the history of adding on such qua phrases and notes that it goes back to Alexander’s teacher Sosigenes. Cf. Alexander, in An. Pr. 155,23–25. Such cases, like I NEPAE at 36a7–17, stand or fall with Aristotle’s proof for I NAANA , which then justifies I NEINO. Cf. Alexander, 173,33–174,3; 174,1–7–9. Al-Qīyās 126,5–127,3 Porphyry, in Cat. 124,5; Ammonius, in Cat., ed. A. Busse (Berlin, 1895), 45,2; 40, 13–14. Alexander, in Top. 427,19. On Reduplication, Chapter Four. Street, “Logic,” in Cambridge Companion, 260 admits this too; in “An Outline of Avicenna’s Syllogistic,” Archiv für Geschichte der Philosophie 84 (2002): 131, he says that Aristotle uses the attributive reading to save Aristotle, and the referential reading more for his own views. Ignacio Angelelli, “The Aristotelian Modal Syllogistic in Modern Modal Logic,” in Konstruklionen versus Posilionen. Beitrage zur Diskussion urn die Konstruk1ive Wissenschaftstheorie, ed. K. Lorenz (Berlin-New York, 1979), 176–215, 202–4, comes close to Avicenna’s position when he analyzes necessary in terms of o-predicates [ousia predicates] and s-predicates [sumbebekos predicates]. The former hold of the subject as long as it is existing, while the latter need not. Angelelli too is willing to consider the various combinations in a statement, “S is P”: read as “everything that is S is something that is P,” we can consider the various combinations of o- and s-predicates. Angelelli, however, sees the introduction of o- and s-predicates as “modalizing” the subject and predicate. However, Avicenna seems not to. Angelelli sees the modalities in the s- and o-sentences to give the internal modalities and an external modality attached to the statement as a whole (“N(S is P”)) as noted at Prior Analytics 32b25–37. Thom, “Avicenna,” Medieval Modal Systems, 66, claims that Avicenna recognizes no valid categorical syllogisms in second figure (Najāt 51), and, 79, says that Avicenna unlike Aristotle takes as valid Camestres and Baroco LX ; Cesare, Festino, and Boroco XL . Street, “Logic,” in Cambridge Companion, p. 259, however says: “In other words, Avicenna did not seek to exclude certain propositions from the Aristotelian rule; he just changed the rule. The Farabians changed their system to fit the text; Avicenna changed the text to fit his system.” Averroes, Quaesitum IV.3, Vol. I.2b 83vb–84ra follows al-Fārābī. Cf. Thom, Medieval Modal Syllogisms, 82–84; Lagerlund, Modal Syllogistics, 32, says that in a necessary per se proposition, its subject term “always stands for its subject,” while in one per accidens it “does not always stand for its subject.”

3

Ideology and “Reception” in Renaissance Logic Alan R. Perreiah University of Kentucky

O you tribe of Peripatetics, perverters of natural meanings! Lorenzo Valla1 All the same, that book of the Little Logicals (so named, I think, because it contains but little logic) is worth the trouble to look into for suppositions, as they call them, ampliations, restrictions, appellations. It also contains some piddling rules, not so much foolish as false . . . Thomas More2 The number of living books is exceedingly small. What a huge cemetery of dead books half alive is represented in a large library! Some of them are absolutely dead, books that no human being out of a madhouse would ever ask for. Some of them are semi-living. Some stray traveler or wandering student might ask for them at some heedless or too curious moment. Archibald Philip Primrose, Lord Rosebery3

Introduction The reception of syllogistic in the Renaissance is a complex topic that includes not only ancient and medieval logic but also the early history of printing, the new medium that disseminated learning to the modern world. It is further complicated by a mindset that has distorted research in both of these fields. Scholars new to Renaissance Studies soon encounter a distinct humanist ideology that has influenced scholarship since the fifteenth century. This ideology privileges humanism and marginalizes scholasticism in all areas but especially in 35

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the study of logic and language. Normally expressed in banter or ridicule, it has remained aloof from the details and complexities of particular theories and thus has eluded direct criticism. Few scholars devoted to the humanist legacy have questioned it, and others, wary of its specious character, have failed to expose its nature and purposes. That most humanists have accepted it uncritically is not surprising; for, as an ideology, it has served its purpose well. It has aggressively promoted a humanist perspective on the Renaissance. At the same time, in this writer’s opinion, it has had a deleterious effect on Renaissance scholarship. It has misled scholars generally about the real achievements of both humanists and scholastics in the study of language. It has not only depreciated the work of the scholastics but also blinded humanists to the conceptual limitations of their own theories. Most importantly, it has dampened debate, stifled comparison and thwarted investigation of how both traditions contributed in complementary ways to the analysis of language. It is, perhaps, superfluous to add that it has important ramifications for the topic of this volume, the reception of syllogistic in the Renaissance. In part 1 of this chapter I offer a critique of the humanist ideology that has pervaded, and in my opinion perverted, scholarship since the Renaissance. Along the way, I note several topics that Lorenzo Valla, an architect of that ideology, ignores in his scathing criticism of Aristotelian and scholastic logic. In part II of the chapter, I examine the reception of syllogistic as evidenced in Renaissance book publication. Influenced by humanist ideology, some scholars have misrepresented the proportion of humanist to scholastic texts that were produced. While humanist literature (Greek and Roman classics) comprised approximately 6 percent of books published, scholastic works numbered more than five times that amount. As a partial remedy for these distortions of history— both of logic and of books—my conclusion will propose a new way to view traditional humanist ideology.

I. Ideology Most of us have been amused at one time or another by the colorful images and clever diatribes that Renaissance humanists invented to ridicule the alleged foibles of scholasticism.4 One sign of progress today is that scholars in both traditions have begun to read those witty sayings in context and to recognize their ephemeral character. Happily, they no longer seem to stimulate in every scholar the taste for delicious mockery that once fueled Renaissance Studies.

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Erika Rummel has arranged the standard charges as clauses in the historic debates between humanists and scholastics, and her study invites an objective assessment of the evidence.5 In an otherwise balanced treatment of both traditions, Ann Moss recites uncritically the traditional clichés and slogans.6 More recently, introducing Valla’s opinions about scholastic dialectic in the Dialectical Disputations, Brian Copenhaver and Lodi Nauta have formulated the major tenets of traditional humanist ideology.7 Because of its clarity and perspicuity I will follow the order of their presentation. Reviewing earlier expressions of humanist ideology, I explore six topics that are central to constructive discussion of relations between humanism and scholasticism.

1. Excessive formalism There are any amount of “quibbles” even more refined than these about concepts, formalities, quiddities, ecceities, which no one could possibly perceive unless like Lynceus he could see through blackest darkness things which do not exist.8 [While the philosophers of Utopia] equal the ancients in almost all other subjects, they are far from matching the inventions of our modern logicians. In fact they have not discovered even one of those elaborate rules about restrictions, amplifications and suppositions which our own schoolboys study in the Small Logicals. They are so far from being able to speculate on “second intentions,” that not one of them was able to conceive of “man-in-general” though I pointed straight at him with my finger, and he is, as you well know, bigger than any giant, maybe even a colossus.9 The abstruse formalisms and arcane terminology that breed in this emptiness are worse than useless. The philosopher’s bizarre neologisms and habitual deviations from classical norms of speech are toxic to meaning and understanding.10

Humanists have claimed that scholastic logic is excessively formalistic. If “formalism” means attention to the purely structural aspects of thought or language without regard to content, this claim is partly true, but in that sense it is a necessary condition of any scientific account of language and applies equally to humanist grammar and rhetoric. In the case of scholasticism, with which I am most familiar, the texts analyze certain features of language that make a logical difference for what a sentence means, its truth or falsity, its presuppositions and implications. To describe those features objectively calls for distinctions and rules that are expressed formally. In some instances, a natural language sentence may be re-expressed to clarify its logical structure or to make transparent its

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logical form. Professor Quine has called this “regimentation” and, like most logicians, regarded it as a useful tool in language analysis. But imposing a canonical order on speech or script is not limited to the arcane practices of logicians. Humanist grammarians, philologists, lexicographers as well as rhetoric instructors who appeal to syntactical or semantical features of language also lay out their arguments in canonical form. The ideas that they express and the structures that they employ are no less formalistic than those of scholastic logic. For example, Lorenzo Valla in the Dialectical Disputations sets out syllogistic arguments in canonical form, and all of his fulminations against scholastic dialectic in that work appeal, in one way or another, to the formalities of Attic Greek or Classical Latin. Quintilian’s instructions about oratorical methods and techniques of persuasion all rest on the formalities appropriate to forensic argumentation. Both of these authors appeal to formal distinctions and rules that their examples are intended to illustrate. Without such formalities their expositions would have no scientific value. Compared to the spoken vernaculars that had no formal grammars, proof-texts in humanist and scholastic works alike would have appeared to be “formal” and “regimented.” In the field of language analysis humanists’ claims rest on formal distinctions of grammar or rhetoric no less than scholastics’ claims are based on formal distinctions of logic. With respect to formalism, humanism and scholasticism are on an equal footing. The modern charge that scholastic logic is “excessively formal” arose, I submit, not from the primary texts, whose formal aspects are clear in context, but from recent representations of scholastic logic as a precursor of modern formal logic. In the 1950s when Logical Positivism was in its prime, I. M. Bocheński’s assertion that medieval logic was “a formal logic in the modern sense,” set the theme for a generation of scholarship.11 Ernest Moody’s Truth and Consequence in Mediaeval Logic, Philotheus Boehner’s Medieval Logic, and E.J. Ashworth’s Language and Logic in the Post-Medieval Period are examples of this approach that clarified many of the rules and distinctions in the texts, but did so at a high price.12 It presented medieval logic as a primitive—and predictably flawed—effort to cultivate logic as it was done in the twentieth century. It became fashionable to reformulate the consequentiae, the medieval rules of valid inference, as theorems in a propositional calculus, but the medievals did not organize logic as a formal system. Although they knew axiomatics from Euclid, Proclus and other authors, with few exceptions (e.g. Buridan) they did not present their rules of inference as theorems in an axiomatic system. One fad, now all but extinct, held that medieval supposition theory “anticipated” modern quantification.13 Scholars pursued this line of interpretation

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despite the fact that medieval logicians had no method of conceptual inscription, symbolic notation or scribal devices that are essential to modern quantification. Many of those trends that fascinated scholars trained in formal logic led down blind alleys, raised irrelevant issues, and obscured the practical purpose of most elementary logic texts: namely, to instruct undergraduates in logic. I have argued elsewhere that the theoretical side of medieval logic was not a “formal logic” in the modern sense but was closer to what is called today a “theory of logical form.”14 This approach retains all that is important in formal logic, yet it respects natural language and recognizes that the logical functions that are indispensable to rational thought are embedded in natural language and in its everyday use. Specimen sentences in medieval logic texts are place-holders for natural language sentences of similar form. Students who studied those texts spoke primarily their own vernaculars and the exemplary propositions and arguments were translatable into those vernaculars. Modern research on medieval methods of language instruction confirms that Latin was mixed with the vernaculars in the process of language learning.15 I will develop these ideas more fully in Sections 4 and 6.

2. Meaningless abstraction No one, I think, is so stupid as to set any value on [their] foolish trifles. Nevertheless, it is astonishing how they dispute about nothing else than second intentions, common natures, quiddities, relations, ecceities, and countless other questions even more trifling than these trifles. And because they dream of these monstrosities, they appear subtle in their own eyes and contemn with stern eyebrows persons who spurn these questions and penetrate to the real things themselves.16 In Vives’ view, the language of scholastic logic is a totally artificial construction producing its own self-invented conundrums, and consequently it cannot be an instrument for discovering truth. Truth and falsehood, so Vives contends, are formulated in language or, more precisely, in languages commonly used and in the ordinary grammar of those languages. . . . To a large extent, Vives follows Valla and his successors in opposing the ordinary usage of classical Latin, its commonly agreed “usus loquendi communis,” to the Humpty Dumpty language of scholastic logic with its universe of specialized meanings closed to outsiders.17 By neglecting the ancient documents, by replacing the language of Cicero and Quintilian with the chop-logic of Boethius and semi-Latin translations of Avicenna and Averroes, the scholastics are choking themselves and their students on meaningless abstractions.18

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Closely associated with the claim of “excessive formalism” is the charge that scholastic logicians concocted “meaningless abstractions,” and “abstruse formulas.” Scholastic logic was called a second-intentional discipline because it studied first-intentional language. Let us make clear: Second intentional language is about ordinary language. First intentional language is just ordinary language. Scholastic logic has been called a “meta-language;” this is true only in the sense that it is a second-order language about a first-order language (i.e. natural language). Moreover, as a “meta-language,” it must be kept in mind that it always includes an object-language (i.e. the sentences uttered by ordinary persons at particular times in everyday places). As a second-order discipline, terminist logic specified rules that governed the logical properties of natural language terms—the “proprietates terminorum”—and the sentences that they structure. Specimen sentences in medieval logic texts were placeholders for first-order natural or ordinary language sentences: “Sortes currit” represents any sentence of similar form in any language that has subject-predicate sentence structure, and this included sentences in the vernacular languages spoken daily by most students. Compared to “concrete” sentences of everyday usage, distinctions and rules of logic are, admittedly, “abstract”; but if those abstractions express sound analyses of ordinary sentences and the arguments that follow from them, they are meaningful and true. Thus, they are not “meaningless.”

3. Disregard of context It is a sign of a poor and barren intellect . . . to be quibbling about the words and opinions of others; carping first at one thing and then at another, and analyzing everything so minutely.19 [Scholastic theologians] are too lazy to learn pure diction and to bother reading difficult authors and exercising their style (for a knowledge of letters is not achieved without keen study); instead, they come home well soused, read a little sermon from which they pluck the nauseous stuff they produce, and hold forth at dinner parties (for that’s when they are at their best). Because the common people applaud, they think they are practically perfect theologians, whereas they discuss matters of the highest importance without respect and with a filthy mouth.20 By ignoring the contexts in which words are used, philosophers lose track of meanings. Floating free from practice and usage in the thin air of pure reason, their artificial speech makes philosophical problems multiply where none really exist.21

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These statements suggest that scholastic logicians were not only out of touch with the way that ordinary people think and talk, but that they had no regard for the context of the words or sentences that they analyzed. This idea may have gained credence from the work of one school of grammar, namely Speculative Grammar or Modism that attempted to construct a universal grammatical system. It posited a rigid correspondence between cognition (modus cognoscendi), language (modus significandi) and reality (modus essendi) and that uniformity was thought to obtain apart from particular contexts of use. Modism was the best effort of medieval grammarians to develop a theory of language that was “context free.” But Modism is a short chapter in the long history of medieval grammar; it is patently not a chapter in the history of logic. Though distained by humanists from John of Salisbury, through Lorenzo Valla to Alexander Hegius, it was not the dominant logic of the Renaissance. That distinction belonged to terminist logic that stressed the analysis of ordinary terms, propositions and arguments—the primary objects of logical investigation in the ancient, medieval and modern worlds. Evidence that scholastic logic paid due attention to context can be found in many areas but especially in two: (i) the obligatio exercise and (ii) the probationes, the protocols for stating the truth-conditions of sentences. I discuss each of these in turn. The obligatio was a format to test a student’s grasp of logical relations between a proposition accepted (or rejected) as true (or false) and a wide range of other sentences that were posed at random throughout the exercise. The student was to concede, deny or doubt each sentence proffered subsequently. The student succeeded or failed the exercise if his concession or denial contradicted the original proposition or, in more complex cases, his replies to all of the previous propositions. Where “context” is defined as the field of sentences to which a given sentence is logically related, the obligatio is a marvelous invention to train and test a student’s sensitivity to context. In the late Middle Ages it was used to teach both grammar and dialectic. Scholastics cultivated it throughout the Renaissance and the renowned humanist Juan Luis Vives prescribed it for his educational program.22 As a regimen for training students in dialectical reasoning the obligatio was essential to education in the professions, especially Medicine and Law. Dialectic provided the basic method of diagnostics, and Vives considered it indispensable for instruction in Medicine. Because the obligatio was modeled after the classic cross-examination (elenchus), it was indispensable for training in Law. In both of these disciplines students gained skill at seeing the connection between a given sentence and the range of sentences that are logically related to it. But the range of sentences relevant to the

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meaning or truth of a given sentence is, simply, the definition of context. In sum, the obligatio taught students how to be attentive to context. Where “context” is more broadly defined to include the existential conditions within which a sentence has meaning and under which it is true or false, scholastic proof procedures also confirm the primacy of context. In a scholastic logic text a sentence declared to be “true” is routinely proven to be such by reference to its truth-conditions. Humanist texts follow a similar procedure. In the long passage from Quintilian that Valla repeats in Book II of Dialectical Disputations the ancient rhetorician distinguishes between factual and artificial proof based on the content of a forensic argument.23 Such an argument may be confirmed factually by a document, an accepted practice, or a custom. It may be confirmed artificially by an example or analogy. These are standard methods of rhetorical proof. Scholastic logicians teach that the premises of an argument may be confirmed or disconfirmed by any evidence or experience that is relevant to their truth or falsity. I will give some examples of the application of this principle in Section 6. For now, I want to point out simply that scholastic methods of proof and humanist methods of proof are both dependent upon artificial as well as existential contexts.

4. Language corruption Your philosophers are strawsplitters, makers of unnecessary difficulties, and if you call their jargon Latin, why then we must find some other name for the speech of Cicero.24 Ideas articulated in an idiom [i.e. scholastic Latin] humanists do not respect and refuse to use are a priori ill-judged, and the practitioners of such an idiom are blind, deluded by fancies, crazy, prone to error.25 [Valla] never doubts that scholasticism has undermined itself by misunderstanding and mishandling the Latin language, the sole channel of learned communication for educated people in Western Christendom.26

A recurrent criticism of humanists was that the scholastics had “corrupted” the Latin language and rendered it unrecognizable to classical language specialists. There is, of course, a long history of specific charges and the reasons for them. In Quattrocento Italy they condemned the “Barbari Brittani.” Later humanists decried the “barbarism,” “rebarbative Latin,” and “invented language” of the scholastics. Clearly, the Latin used in the scholastic logic curriculum was a small fragment or dialect of the Latin language taken as a whole (passing over for now

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the problematic concept of “a whole language”). At the same time, for better or worse, scholastic Latin was the common language of university discourse: lectures, discussions, disputations, exercises, studies, examinations, etc., were all conducted in it. As Pico later argued, if language is created by human convention, scholastic Latin is as legitimate as any other language agreed to by a linguistic community.27 This view implies, of course, that scholastic Latin is to be assessed according to the rules of its own syntax and semantics and not those of another language or dialect. To restrict “the Latin language” to first-century Roman usage—however noble—is an arbitrary linguistic standard and ignores the polymorphic character of a living language. Humanists of any era who declared it to be the “sole language of educated Christians” were simply airing their prejudice. They seem to have overlooked Quintilian’s remark, “[I]t would be almost laughable to prefer the language of the past to that of the present day . . .”28 Any discussion of scholastic Latin must take into consideration the linguistic milieu of the early modern university. Students entered the university speaking dialects of their native vernaculars—English, Italian, French, German, Spanish, etc. These “oral” languages had no formal grammars or rules of orthography. School Latin was a student’s first exposure to an inscribed language with grammatical rules, and university students had to become fluent in university Latin within one or two years. The research of Tony Hunt has shown how the vernaculars were an integral part of Latin language instruction. Introducing three volumes of edited school texts, he states: “The first aim of the present study was thus to emphasize that Latin and the vernacular were not rigorously separated by the techniques of medieval education, the evidence of which reaffirms the normality of language switching . . . The juxtaposition of Latin and vernacular which characterizes almost every page of teaching material edited in the present study leaves no room for doubt: schoolmasters in medieval England explained difficulties to their pupils in both French and English.”29 If language switching was common in grammar instruction, it also appears to have been done in logic instruction, and this practice would explain many peculiarities of the scholastic logic texts. For example, it explains why works like the Logica Parva have a simplistic style, a sparse vocabulary, a small set of specimen sentences repeated in various forms with predictable regularity, and plain, straight-forward arguments. These are all characteristics of an instructional method that employs a language meant to be teachable and learnable. Simply put, they were parts of a program designed to teach both logic and language to illiterates. A half-century of research based on the assumption that scholastic logic was a precursor of modern formal logic has demonstrated that the texts

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cannot be explained by formal logic alone. Beyond their espoused purpose to instruct students in logic, logic manuals functioned as descriptive grammars or translation manuals to negotiate between the vernacular dialects that students spoke and the Latin that was essential to their progress in university studies. I will develop these ideas more fully in Section 6.

5. Disregard for “natural” or “ordinary language” [Scholastic dialecticians] have invented for themselves certain meanings of words contrary to all civilized custom and usage, so that they may seem to have won their argument when they are not understood. For when they are understood, it is apparent to everyone that nothing could be more pointless, nothing more irrational. So, when their opponent has been confused by strange and unusual meanings and word-order, by wondrous suppositions, wondrous ampliations, restrictions, appellations, they then decree for themselves, with no public decision or [verdict] a triumph over an adversary not conquered but confused by new feats of verbal legerdemain.30 [Thomas More] describes a scene in which a theologian, learned in logic, makes a fool of himself at a dinner party by totally misjudging the speech milieu and applying syllogisms to any and every topic of conversation without any sense of decorum. Dialecticians talk to themselves. They do not communicate with other people; their words have lost contact with the world of things; outside of their own speech community, they are reduced to silence.31 The phantasmagoria of scholastic terminology is a different matter, in Valla’s view. The strange words spoken by the Peripatetic tribe lack the utility that might justify their ugliness and eccentricity.32

Taking first-century Roman Latin as their norm, it is not surprising that the humanists found evidence that scholastic logic and philosophy offended “normal” usage at every turn. The emphasis on logical formalism in modern scholarship may have also given the impression that scholastic logicians spoke a “private language” and that they had no interest in so-called “ordinary language.” The ordinary languages that common people and university students spoke were dialects of a diverse mix of vernaculars, and school Latin was a learned language written and governed by grammatical rules. The specimen sentences that occur in logic texts are only placeholders for ordinary sentences of the same logical form. “Sortes currit vel Sortes sedet” stands for an indefinite number of subject-predicate sentences joined disjunctively in any language that contains disjunction. The same

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holds for all of the other logical connectives, viz. signs of negation, conjunction, implication, co-implication etc. Understood in this way, logic texts bridged between university Latin and the students’ spoken vernaculars. The specimen sentences of logic were thus essentially related to the sentences of everyday speech. I have emphasized the primacy of ordinary language in scholastic logic in this chapter because I believe that the technical phrase “first and second intention” has masked the very relation it is supposed to express, namely, that of logic to language. Medieval logic leaves everyday language totally intact. The relationship of logic, grammar and rhetoric to natural language has taken on new importance with the publication in English of Lorenzo Valla’s Dialectical Disputations, for the esteemed editors and translators of those volumes have presented Valla’s work as an appeal to “common sense” that is somehow encoded in “ordinary language.”33 Professor Nauta’s masterful study of Valla’s philosophy of language also makes the same claim.34 Those influenced by humanist ideology and innocent of scholastic philosophy might be led to believe that Valla was the first to discover “ordinary language” and that it somehow embodies “common sense.” It turns out that Valla’s “ordinary language” is Silver Age Latin expressed in firstcentury Roman authors. Valla famously distained the vernaculars even more than the Latin dialects of his own day. If Valla had a concept of “ordinary language” it was plainly not the language of everyday people in Quattrocento Italy. Just how “ordinary language”—however defined—encodes “common sense” Copenhaver and Nauta, to my knowledge, nowhere explain. By contrast, scholastic logicians understood the challenges of learning university Latin and accommodated the “ordinary” languages (i.e. vernaculars, that students spoke).

6. Scholastic logic is “useless” What good is it to spend day and night on scholastic disputations? What good is it every day to weave nets to trap the innocent? What good is your verbose profundity, your inane verbosity? The writings of Holcot, Scotus, Bede, Nicolaus of Lyra, Tinctor, Scriptor, Versor, Ockham, and others whose names I pass over on purpose are widely read and ever present in our schools. O wretched loss of talent!35 [Scholastic theologians] were arrogant boasters relying on barbarous words and gross solecisms . . . [In a woodcut that accompanies the text five scholastics— Sophister, Must-eater, Phoebus-hater, Petty and Logigrackle—compete] on the threshing floor, they flail the empty straw, going after chaff; they draw doctrine from the murky raintrough; they search for wisdom in a multifarious griffin of

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The Aftermath of Syllogism complex questions and in inextricable knots; they card the useless and gross goatswool; in enigmatic coils and entangled refutations, in the wordy labyrinth of error, they look for the clear and true theological tradition. They make plain matters difficult, seek for a knot in the bulrush, want to please God with loquaciousness, whereas he cares for neither logic nor sophistic garrulity . . . and so the days pass and they make no progress.36 When philosophers study argument in general, in the abstract, they chase specters through a vacuum. . . . Detached from particulars of usage, argument is a chimera bombinating in the void, as Rabelais would say.37

Humanists have questioned the practical value of scholastic logic. Are scholastic arguments really as worthless as farts in a void? Although I do not think that it is necessary to prove to this readership the benefits of training in logic, it is important to show how scholastic logic as an academic discipline was useful in developing a student’s ability to reason. A rational person must know how: (1) to identify the premises and conclusion of an argument, (2) to know its logical structure, and (3) to assess its validity. S/he must decide whether the premises are true or false by checking them against the evidence. To excel in the exercise of reason s/he must know what Ryle called “the logical powers” of terms, to understand a sentence’s logical form, and to comprehend what Russell called its place in “logical space” (i.e. its relationships to other sentences of various forms). In order to analyze and assess ordinary argumentation scholastic logicians invented the rules of consequentiae. Consistent with syllogistic, Aristotle’s topics codified the methods of ancient dialecticians. After a long history, welldocumented by Neils J. Green-Pedersen, thirteenth-century logicians transformed Aristotle’s principles into the consequentiae, rules for both nonquantified and quantified (i.e. syllogistic) reasoning.38 By the thirteenth-century syllogistic was incorporated into the consequentiae in a form that mapped easily onto everyday reasoning patterns. Most humanists regarded the topics as “seats of argument” useful in the discovery (inventio) phase of rhetorical composition. They generally ignored the consequentiae as a set of rules that could be used to assess the validity of everyday inferences. Valla, for example, focused on the demonstrative syllogism and ultimately rejected it as not useful for rhetoric. When he turned to the hypothetical syllogism he criticized it; but he failed to see that the rules of consequentiae cover both. Valla’s failure to even mention the consequentiae is notable because they originated in the linguistic usage of ancient dialectic and Quintilian’s Institutio oratoria that Valla copies in Book II of Dialectical Disputations contains hundreds of arguments that exemplify them.

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The consequentiae were quite useful in tracking and assessing the validity of routine inferences made in “ordinary” language by everyday people. Another illustration of the practicality of scholastic dialectic is its approach to proof. The topic of proof is central to logic and to the Logica Parva’s methods of verification: “probo,” “probatur,” “potest probari” etc. occur frequently throughout the text.39 Whenever a sentence S is declared “true” or “false” a proof normally follows. A proof consists in showing an equivalence (equipollentia) between S said to be true and a conjunction of sentences s’, s,” s’’’ etc. that state the conditions under which S is true. This pattern is repeated in all of the species of proof procedure: viz. exposition, resolution, officiation, etc. Here are some examples:

1. “Every man runs,” is true is equivalent to A man runs and nothing is a man unless it runs. “Omnis homo currit est vera equipollet homo currit et nihil est homo quin illud currit.” 2. “Some man runs,” is true is equivalent to this is a man and this runs. “Aliquis homo currit” est propositio vera aequipollet iste est homo et iste currit. 3. “Socrates is stronger than Plato,” is true is equivalent to Socrates is strong and Plato is strong, and Plato is not as strong as Socrates. “Sortes est fortior quam Plato” est vera aequipollet Sortes est fortis et Plato est fortis et Plato non est fortior quam Sortes. Serious questions have been raised about the purpose of scholastic methods of proof and especially exposition (expositio). Ockham described exposition as: “a categorical [proposition] from which there follow several categorical propositions [that are] so to speak its ‘exponents’ that is, they express what the proposition conveys by its form—can be called a proposition equivalent to a hypothetical proposition.”40 By modern analytical standards, formal logicians expect “the full exposition of a proposition to be more logically perspicuous, more explicit, than its unexpounded original.”41 Paul Spade, who has studied these examples for many years, notes that the exposition includes not only anaphoric cross-reference (“it”) but also a notoriously difficult quin-clause. He objects that, far from being simpler and more explicit than the original, the analysans is more complex and includes complications not in the original proposition. Hence, as a formal analysis it fails. What, then, is the point of expositing or expounding a proposition? Spade’s careful study of exposition as a procedure akin to formal analysis demonstrates the futility of that approach to account for exposition. If formal logic cannot

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explain exposition, I propose an alternative reading close to the generic definition of exposition as “the expression of meaning in another language.” The exponents give the truth-conditions of the original sentence, and these may be expressed in more than one language. To see how this works we return to the equivalences listed above. Those can expand our knowledge if they are understood to be open to colloquial translation. For when the sentence on the right is translated into our vernacular, it tells us something new and important about the Latin sentence on the left.

1. “Every man runs,” is true and is equivalent to A man runs and nothing is a man unless it runs. “Omnis homo currit est vera equipollet homo currit et nihil est homo quin illud currit.” A man runs and nothing is a man unless it runs. [In the following examples this informal Roman font represents the vernacular translation of the Latin sentence in bold face.] 2. “Some man runs,” is true is equivalent to this is a man and this runs.“Aliquis homo currit” est propositio vera aequipollet iste est homo et iste currit. This is a man and this runs.

3. “Socrates is stronger than Plato,” is true is equivalent to Socrates is strong and Plato is strong and Plato is not as strong as Socrates. “Sortes est fortior quam Plato” est vera aequipollet Sortes est fortis et Plato est fortis et Plato non est fortior quam Sortes. Socrates is strong and Plato is strong and Plato is not stronger than Socrates.

Given their regular occurrence in Logica Parva examples, the anaphoric cross-reference of “it” and the quin-clause were apparently not problematic for what the exposition was supposed to accomplish, namely, giving truthconditions—expressible in the speaker’s own language—for the original sentence. As noted above, when the right-hand side of the equivalence is stated in the same language as the original Latin, it does not advance our knowledge beyond what we already knew when we uttered the sentence on the left-hand side. When the right-hand side is translated into our vernacular, however, there is a notable advance in knowledge. Since the job of the sentence on the right-hand side is to express the truth-conditions of the sentence on the left-hand side it increases our knowledge by stating in our vernacular (English) the meaning of the Latin sentence. Stated in the same language, the exposition is without point. Translated into a relevant vernacular, the right-hand side of the equivalence makes a world of difference: it tells us in our own vernacular what the Latin sentence means. Students in the Renaissance university were in a position similar to that of a university student today who studies English as a second language. Second-

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language learning is a specialized art similar to field linguistics. Like Donald Davidson’s “radical interpreter” or “radical translator” both the S-L student and the linguist must gain command of a language starting from scratch. Davidson offers a theory of language learning that makes translation an essential part of the process.42 He explains how a person can learn a previously unknown language within the framework of a truth-conditional semantics. Briefly, the secondlanguage learner must develop a “theory of truth” for the target language. To have a theory of truth for a language requires one to gain command of a core of sentences whose truth can be confirmed in his native language. These sentences have discernible logical features that determine their logical form, point to their truth-conditions, and govern their relationships to other sentences of various logical forms. By converse with a native speaker or classroom instructor the student learns by means of gesturing and pointing the meaning and truthconditions of particular specimen sentences. In time he gains command of a body of sentences whose truth he is able to confirm in his own language. Through exchanges with other speakers and continued practice he learns how to generate in the target language new sentences of similar forms. In time he becomes fluent in the second language. If scholastic logic were a purely theoretical pursuit—which most modern commentary might lead one to believe—it would be difficult to argue that it had a practical purpose. The fact remains that for over five centuries, university students continued to study scholastic logic. The durability and longevity of this discipline has, to my satisfaction, never been explained. I submit that scholastic logic endured because it offered an opportunity for students from various linguistic backgrounds to gain command of university Latin, and this knowledge empowered them for careers in Medicine, Law, and Commerce. Given its role in fostering a language that they hated, it is no wonder that the humanists were hostile to scholastic dialectic.

II 7. Reception Not surprisingly, humanist ideology has influenced the perspective of bibliographers and historians of early printing. At best, they have given conflicting accounts of the relative proportions of humanistic and scholastic writings. For example, Victor Scholderer introduced the Catalogue of Books Printed in the

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XVth Century Now in the British Museum by extolling the humanist contribution: “An account of the subject matter of the Italian incunabula must inevitably start with humanistic literature—the poetry, oratory, philosophy and history of classical antiquity . . . The extent to which humanistic literature dominates Italian publishing from its earliest years is evident from a glance at the lists . . . In Venice to the end of the 1480’s [humanist texts] number over 200 out of rather more than the 600 editions altogether holding their own well against the theology books which make up the next largest class (over 120).”43 Scholderer’s enthusiasm for humanist literature seems to have distracted him from two thirds of the texts in the collection that he cites. After “a glance at the lists,” he acknowledges the prevalence of theological and scientific works including what he calls logic and philosophy; however, he remains convinced that humanist literature “dominates” early publication history. For reasons that we will give below, scholastic texts comprised more than half of the incunabula published in the last quarter of the fifteenth century. S. Steinberg’s popular Five Hundred Years of Printing is ambivalent on the relation of classics to textbooks. Stating that “the ‘best seller’ provides the historian with a fairly reliable yardstick of the prevalent mode of thought and taste of a period,” he [excludes] “school-books from the consideration of best sellers, although their publication has, from the incunabula period onward always been the most profitable branch of the publishing trade.”44 After replacing “best seller” with “steady seller” he reverses himself and includes school-books which were published in the tens of thousands in the sixteenth century.45 Later scholars have analyzed the evidence differently and presented alternative accounts of early book production.46 Despite important differences in methodology, all of these studies shed doubt on Schroeder’s claim that humanistic literature “dominated printing in Italy from the earliest years.” Press economics in the last quarter of the fifteenth century tell a different story. The late Martin Lowry studied the commercial aspects of printing in this period. He discovered that “In the early 1470’s an uncontrolled enthusiasm for the classical revival probably inspired by the professional scholars who advised the printers, deluged the Italian market with more editions of the Latin classics than it could possibly absorb and left the printers with nothing but unsold copies to face their creditors. The Venetian industry reeled, its output declining by sixfive percent in 1473.”47 In a fiercely competitive market printers avoided bankruptcy by turning to the publication of scholastic texts: “Theological and liturgical as well as student texts [including Canon and Civil Law] before 1500 formed a vital part of the printers’ output.”48

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Admittedly, analysis of the patterns of book production in the fifteenth and sixteenth centuries is fraught with difficulty. With respect to humanist literature one must establish what counts as a “classic.” If Cicero, Vergil, Seneca are classics, what about medieval pseudo-works attributed to them? Are the works of the Church Fathers to be included among the classics? What about Latin translations of Greek works? Is Donatus’ grammar with medieval content a “classic”? Similar problems arise for scholastic texts. Are liturgical, theological and law books on a par with logical, scientific and theological works? Are breviaries on a par with logic manuals? These are just a few of the questions that must be answered before one undertakes an inventory of early printed books. Once criteria are defined, one must apply them to the data. A recent study states that in the incunabular period, “Approximately 35,000 editions had been printed, representing some 12,000 different titles and the total number of copies may be conservatively estimated as being close to 15 million.”49 Fortunately, in addition to smaller indices (e.g. R. Proctor’s Index) two massive inventories of incunabula are consolidating these materials and making them available to scholars. They are:

1. Gesamtkatalog der Wiegendrucke or Union Catalog of Incunabula. Published by Hiersemann since 1925 and presently comprising eleven volumes, this inventory presently details all incunabula from “Abbey Ghost” to “Hord, Jobst.” Though in fieri it has an accompanying database with search engine. Available at:www.gesamtkatalogderwiegendrucke.de/ GWEN.xhtm. 2. The Incunabula Short-Title Catalogue (ISTC ). It is the most inclusive single catalogue of incunabula yet compiled and is accessible on the internet at www.bl.uk/news/index.html. At present, based on this catalogue, Howard Jones has given the latest estimate of humanist writings (Greek and Roman classics) printed before 1500— approximately 6% of works published.50 Although the figure for scholastic works is likely to be much higher, a comparable inventory of them has yet to be made. Nonetheless, for the purposes of this paper, it is possible to make some observations about a small part of the history of publishing in the field of logic. The dissemination of Oxford philosophy in the fifteenth century by means of incunabula and in the early sixteenth century by printed manuals is especially important. In this regard the works of Paul of Venice are exemplary. In 1979– 1980 I undertook a census of over 300 manuscripts attributed to Paul of Venice (1370–1429). I established 268 manuscripts of his works.51 As important as they are for recording an author’s thoughts, manuscripts had a limited audience. Once

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the presses arrived in Italy, printed editions expanded readership exponentially and were, therefore, essential for estimating the magnitude of an author’s reception. Published in over 80 manuscripts and 26 editions Paul of Venice’s Logica Parva propagated Oxford logic throughout Italy. Based on normal estimates for the size of editions (between 300 and 500 copies) the Logica Parva reached the hands of 8,000 to 13,000 students throughout the fifteenth and early sixteenth centuries. A similar Logica by Paul of Pergola, Paul of Venice’s student, gained currency at this time. With ten manuscripts and eight editions his work would have reached more than 4,000 students.52 Freshmen in the universities of Northern Italy (especially, Padua, Pavia and Bologna) who spoke their native dialects soon learned in the trivium the simplified vocabulary and regularized syntax of Latin. This training served as bridge to the quadrivium where they read the scientific, philosophical and theological writings of the day. Paul of Venice’s expositions and commentaries on Aristotle’s works were also published in several editions that were used in this part of the curriculum. What advantages did printed texts offer over manuscripts? Printed texts greatly facilitated the mastery of logic. Paul Saenger and Michael Heinlen have analyzed incunabula from the viewpoint of the modern psychology of reading. “The late incunable printer, by establishing a close and rigorous control over punctuation and the nuances of meaning that flow from punctuation, became, in effect, an editor in the modern sense of the word.”53 Where a manuscript gave the text in a compressed scrawl, early printed books presented it in a standardized format that made for easier reading: students could discern the layout of an argument and thus comprehend its logical structure. In my experience extensive reading of scholastic arguments in the printed format trains the mind of the reader to “see” the logical connectives implicit in the arguments and to readily grasp their logical forms. As I have argued elsewhere, this is the key to understanding how scholastic logic was “received” by students in the university setting.

8. Conclusion I have tried to show that the stock humanist criticisms of scholastic dialectic betray little understanding of the nature of that discipline. Erika Rummel and Ann Moss have shown that most of those criticisms arose in circumstances where literary, political or religious ambitions were at stake. Through time the epithets born of those events gained credibility and authority in the humanist

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scholarly community. In each case I adduced evidence that confutes the criticism, and this was an easy task. While I cited Paul of Venice’s Logica Parva, comparable counter-evidence can be found in Peter of Spain’s Summulae logicales, Lambert of Auxerre’s Logica, William of Ockham’s Summa logicae, John Buridan’s Summulae de dialectica and many later works published by Professor Ashworth. Given the number of their printed editions, these works reached tens of thousands of students. The humanists were correct in saying that scholastic Greek and Latin did not meet the grammatical standards of Attic Greek or Silver Age Latin. However, there is no necessity that logic or philosophy has to be expressed in those languages. Moreover, it is plainly fallacious to argue that a philosopher’s grammar is defective; therefore, his philosophical claims are false. To argue in this way is to commit the fallacy of ignoratio elenchi: the humanist critic appears not to know what counts as refutation of a philosophical claim. Humanist criticisms of scholasticism make a good deal more sense if we consider them not as philosophical theses worthy of debate pro et contra—not as “power points” in a humanist declamation of scholastic dialectic—but rather as tenets in an ideology that has been effective in its aims. Since the eighteenth century the distinction between philosophy and ideology has marked a difference between philosophy as a theoretical pursuit whose goal is to discover and understand what is, and ideology as a practical pursuit where ideas guide action toward a practical aim or political ambition. In light of this distinction we can agree that humanist criticisms of scholasticism have been very effective as planks in an ideology: they energized the humanist community, galvanized opposition to scholasticism and contributed to its eventual demise. At the same time, when they are subjected to critical scrutiny humanist criticisms of scholastic dialectic are gratuitous, misleading and demonstrably false. In many ways they resemble the modern tweet—the instant message of less than 140 characters that can be sent to anyone who needs and awaits an assurance of solidarity with others in pursuit of a common goal. Like the tweet, most humanist criticisms are abstractions, fetched out of context or out of nowhere. They cite no texts and thus have no discernible basis of confirmation or disconfirmation. Often, they are patently ad hominem or ad populum arguments. They may contain images eventually shown to be fraudulent. All the same, they may be snatched up by a reputable news outlet or a scholarly community and broadcast to the world as fact. In the end most are found to contain a wealth of misleading information. Hopefully, given what I have argued in this paper, future scholars will be better equipped to assess humanist criticisms of scholasticism and their implications for the reception of syllogistic in the Renaissance.

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Notes 1 Lorenzo Valla, Epistole, ed. O. Besomi and M. Regoliosi (Padua, 1981), 202, 216; App. II .21. 2 Thomas More, “Letter to Martin Dorp,” in Juan Luis Vives Against the Pseudodialecticians, a Humanist Attack on Medieval Logic, ed. and tr. Rita Guerlac (Dordrecht, NL , 1979): 171. 3 Lord Rosebery, Bibliofilia, XII (Florence, 1912): 422. 4 Alan R. Perreiah, “Humanist Critiques of Scholastic Dialectic,” The Sixteenth Century Journal, XIII , no. 3 (1982): 3–22. 5 Erika Rummel, The Humanist-Scholastic Debate in the Renaissance and Reformation (Cambridge, 1995). 6 Ann Moss, Renaissance Truth and the Latin Language Turn (Oxford, 2003). 7 Brian P. Copenhaver and Lodi Nauta, eds. and tr., “Introduction” to Lorenzo Valla, Dialectical Disputations, 2 vols (Cambridge, MA , 2012): I, vii–l. 8 Folly in Desiderius Erasmus, Praise of Folly, tr. Betty Radice (Harmondsworth, 1971): 152–55. 9 Raphael Hythloday (Ralph the Fool), in Sir Thomas More, ed. and tr. Robert M. Adams (New York, 1975): 53–54. 10 Copenhaver and Nauta, Lorenzo Valla, Dialectical Disputations, I, xvi. 11 Józef M. Bocheński, A History of Formal Logic, tr. Ivo Thomas (New York, 1956): 152. 12 Ernest Moody, Truth and Consequence in Mediaeval Logic (Amsterdam, 1953); Philotheus Boehner, Medieval Logic, An Outline of Its Development from 1250 to circa 1400 (Manchester 1952); E.J. Ashworth, Language and Logic in the Post-Medieval Period (Dordrecht, 1974). 13 Alan R. Perreiah, “Approaches to Supposition Theory,” The New Scholasticism, XLV, no. 3 (1981): 381–408. 14 Alan R. Perreiah, tr., “Introduction” to Paul of Venice: Logica Parva (Munich and Washington, D.C., 1984): 17–118. 15 See below, note 27. 16 Gerald Lister, in E. L. Surtz, The Praise of Pleasure (Cambridge, 1957): 97. 17 Moss, Renaissance Truth and the Latin Language Turn, 114. 18 Copenhaver and Nauta, xvi. 19 John Colet in E.L. Surtz, The Praise of Pleasure (Cambridge, 1957): 104. 20 Philip Melanchthon, Encomium eloquentiae (1523) in Melanchthon’s Werke in Auswahl, ed. R. Stupperich, Güttersloh 1051–75, III :58, tr. Rummel, The ScholasticHumanist Debate, 142. 21 Copenhaver and Nauta, xvi 22 Juan Luis Vives, De tradendis disciplinis, Foster Watson, tr., in Vives: On Education (Cambridge, 1913): 165.

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23 Copenhaver and Nauta, Lorenzo Valla Dialectical Disputations, II , 143–207. 24 Juan Luis Vives, Causes of Corruption in the Arts excerpt tr. C.S. Lewis, Oxford History of English Literature excluding Drama (Oxford, 1954): 31. 25 Moss, Renaissance Truth and the Latin Language Turn, 8–9. 26 Copenhaver and Nauta, xv. 27 Barbaro’s three letters and Pico’s reply as well as a fourth letter replying to Pico “in behalf of Barbaro” are translated in Quirinius Breen, Christianity and Humanism (Grand Rapids, MI , 1968): 22–23. As Erika Rummel has demonstrated, the last letter, formerly attributed to Philip Melanchthon, was written by one of his students, Franz Bruchard in 1558. (E Rummel, “Epistola Hermolai nova ac subditicia: A Declamation Falsely Ascribed to Philip Melanchthon.”(1992) 83 Archiv für Reformationsgeschichte 302–305.) 28 Quintilian, Institutio Oratoria Books I–XI in four volumes, H. E. Butler (tr.) (Cambridge, MA , 1921–1996): I.6, 43. 29 Tony Hunt, Teaching and Learning Latin in Thirteenth-Century England, 3 vols. (Cambridge, 1991), vol. I: 434–35. Emphasis added. For pre-university British grammar schools see: Jo Ann Hoeppner Moran, The Growth of English Schooling 1340–1548 (Princeton, NJ, 1984): 36–62; Nicholas Orme, Medieval Schools, from Roman Britain to Renaissance England (New Haven, CN , 2006): 339 ff. For university-level grammar studies in medieval England to 1500 see: Alan Cobban, The Medieval English Universities: Oxford and Cambridge to c. 1500 (Berkeley, CA , 1988) and Alan Cobban, English University Life in the Middle Ages (Columbus, OH , 1999): 21 ff. For pre-university grammar studies in Italy see: Robert Black, Humanism and Education in Medieval and Renaissance Italy (Cambridge, 2001); Paul F. Grendler, Schooling in Renaissance Italy: Literacy and Learning 1300–1600 (Baltimore and London, 1989). Black does not find evidence of the use of vernaculars in Latin language instruction in Italy; however, he did not investigate the logical manuals. Christopher Carlsmith, A Renaissance Education, Schooling in Bergamo and the Venetian Republic, 1500–1650 (Toronto, 2010) examines the extent and nature of grammatical studies in the Venetian Republic where the majority of Logica Parva manuscripts were produced. His introduction reviews earlier work on the history of education in the Renaissance. Summarizing her study of late medieval grammar Professor Moran writes: “After beginning with the Donat and the basic grammatical rules, the grammar scholar proceeded to ‘making Latins’ with the aid of various vulgaria, dictionaries, and more complex grammars, from there turning to the reading and writing of Latin verse and to disputations. The result should have been to produce scholars who could read and speak a fluent ‘bastard’ Latin which, although highly Anglicized in syntax and vocabulary, was sufficient for both ecclesiastical and secular administrative purposes, and who could probably write the same administrative Latin in a very practical, legible cursive hand,” 39.

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30 Vives, Adversus pseudodialecticos, tr. Rita Guerlac (Boston, 1979), 56–57. 31 Thomas More, in The Complete Works of Thomas More, ed. D. Kinney, XV (New Haven, 1986): 26–29, 50–57, 72–75, cited in Moss, Renaissance Truth and the Latin Language Turn, 116. 32 Copenhaver and Nauta, xviii–xix. 33 Lorenzo Valla, Dialectical Disputations, 2 vols, Brian P. Copenhaver and Lodi Nauta, ed. and tr., “Introduction,” xxxv. 34 Lodi Nauta, In Defense of Common Sense, Lorenzo Valla’s Humanist Critique of Scholastic Philosophy (Cambridge 2009). 35 Jacob Locher, Dialogue from Theologica Emphasis (Basel, 1496), tr. Rummel, The Humanist-Scholastic Debate, 47–48. 36 Jacob Locher On Humanistic Studies and in Praise of Poetry, tr. Rummel, The Scholastic-Humanist Debate, 79. 37 Copenhaver and Nauta, xvi. 38 Neils J. Green-Pedersen, The Tradition of the Topics in the Middle Ages (Munchen, 1984). See also: Otto Bird, “The Formalizing of the Topics in Mediaeval Logic,” Notre Dame Journal of Formal Logic, vol. 1 (1960): 138–149; Otto Bird, “Topic and Consequence in Ockham’s Logic,” Notre Dame Journal of Formal Logic. vol. II , no. 2, April (1961): 65–79; Otto Bird, “The Tradition of the Logical Topics: Aristotle to Ockham,” Journal of the History of Ideas, vol. 23, (1962): 307–323; Eleanor Stump, “Topics: Their Development and Absorption into Consequences,” in The Cambridge History of Later Medieval Philosophy, eds. N. Kretzmann et al. (Cambridge, 1982), 273–299. 39 Paul of Venice, Logica Parva, ed. and tr. Perreiah, Chapter IV et passim. 40 William Ockham, Summa logicae II , 11, cited in Paul Spade, “Why Don’t Medieval Logicians Ever Tell Us What They’re Doing? Or What is This, A Conspiracy?” (2000): 6. Available online at: http://pvspade.com/ 41 Spade, “Why Don’t Medieval Logicians Ever Tell Us What They’re Doing?,” 8. 42 Donald Davidson Inquiries into Truth and Interpretation (Oxford, 1984), esp. “Essay 9.” Rita Copeland’s Rhetoric, Hermeneutics and Translation in the Middle Ages (Cambridge, UK , 1991) reviews the history of translation in the Middle Ages, but assumes that the translator knows both Latin and his own vernacular. She does not address the question of language learning or of how a person would gain command of Latin in the first place. 43 Alfred Pollard, Victor Scholderer, George Painter, Catalogue of Books Printed in the XVth Century Now in the British Museum (Oxford, 1908–) Parts V-Venice; VI Florence, Milan, Bologna, Naples; VII -Genoa, xxvii. 44 S.H. Steinberg, Five Hundred Years of Printing (Baltimore, MD, 1974), 100. 45 Steinberg, Five Hundred Years of Printing, 237. 46 John M. Lenhart, “Pre-Reformation printed books,” in Franciscan Studies, no. 14, (New York, 1935), L.V. Gerulaitis Printing and Publishing in Fifteenth-century Venice

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47 48 49 50 51 52 53

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(Chicago, 1976); Rudolf Hirsch, Printing, Selling and Reading 1450–1550 (Wiesbaden, 1967); Elizabeth Eisenstein The Printing Press as an Agent of Change (New York, 1979); Martin Lowry, The World of Aldus Manutius, Business and Scholarship in Renaissance Venice (Oxford, 1978); Otto Mazal, Die Überlieferung der antiken Literatur im Buchdruck des 15. Jahrhunderts, 4 vols. (Stuttgart, 2003); Howard Jones, Printing the Classical Text (Utrecht, 2004) and Martin Davies, Aldus Manutius: Printer and Publisher of Renaissance Venice (Tempe, AZ , 1999). Lowry, The World of Aldus Manutius, Business and Scholarship in Renaissance Venice, 13. Ibid., 21. Jones, Printing the Classical Text, 3. Jones, Printing the Classical Text, 9. Alan R. Perreiah, Paul of Venice: A Bibliographical Guide (Bowling Green, OH , 1986), 35–71. Paul of Pergua, Logica, ed. Sister Mary Anthony Brown, O.S.F., (St. Bonaventure, N.Y. 1961), I–XIII . Paul Saenger and Michael Heinlen, “Incunable Description and Its Implication for the Analysis of Fifteenth-Century Reading Habits,” in S. Hindman, Printing the Written Word: The Social History of Books (Ithaca, N.Y., 1991), 255.

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Syllogistic and Formal Reasoning The Cartesian Critique Stephen Gaukroger The University of Sydney

1. Informative inferences Argument is a means of convincing someone to believe something that they might not otherwise believe, or of confirming something that they believe, or of getting someone to behave (as in ethical arguments) in a way that they wouldn’t otherwise have behaved, and so on. In the case of knowledge, which we can confine our attention to here, it is a means of discovery of things that one didn’t know. Argument might work through authority, violence, faith, or something else. The cases that we are interested in are those where it works by inference: inference is what takes one from premises that one agrees on or believes to be true or knows, to a conclusion that follows from those premises. Aristotle had provided a formal account of inference in his syllogistic. Syllogistic marshalled arguments into a particular form, and then set out to identify all and only those forms of inference that legitimately took one from premises to conclusion: in the paradigm case, those that were guaranteed to take one from true premises to a true conclusion. Such forms of inference were formally valid. They were valid purely in virtue of form of inference, which meant that if the premises were true then the conclusion would be true: truth was preserved between premises and conclusion. It did not matter what the content of the premises was, what it was that made them true. The whole point of capturing formal validity was that it was the inference schema that did the work, not the premises. Preserving truth between premises and conclusion was not the only thing that Aristotle was seeking however. He also sought to identify forms of inference that were informative. Intuitively, there was no difficulty recognizing the 59

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difference between formally identical informative and uninformative syllogisms. So, for example, in the following two syllogisms: The planets do not twinkle That which does not twinkle is near ______________________________________ The planets are near The planets are near That which is near does not twinkle ______________________________________ The planets do not twinkle

the first is uninformative whereas the second is informative. The first syllogism is only a demonstration “of fact” whereas the second is a demonstration of “why.” The latter is informative because we are provided with a reason or cause or explanation of the conclusion: the reason why the planets twinkle is because they are near. In the case of the former, their twinkling is not the cause of their being near (An. Post. 78a13ff ). The problem is that because the two syllogisms are formally identical (they are both in Barbara mode), there is no way of distinguishing on formal grounds between informative and uninformative syllogisms. Aristotle’s solution was to posit a form of intellectual insight (nous) by which we recognize informative inferences, but he was unable to provide any details. Sixteenth-century defenders of the syllogism pursued the question. In Zabarella and Nifo, for example, a mental operation termed negotiatio is supposed to enable one to grasp the necessary connections between cause and effects as represented in the syllogism, but no account could be given of how negotiatio achieves this.1 A second kind of problem arises when we consider the aims of the demonstrative syllogism. Aristotle termed the demonstrative syllogism the “scientific” syllogism, but its aim was not to enable one to discover results, but rather to provide a means of presenting results in a systematic way, so that they could be presented to students for example. The conclusions were known in advance, and what the syllogism provided was a means of relating these conclusions to premises that would explain them.2 The skill came in discovering the requisite “middle term,” which connects the premise and conclusion. If one wanted to discover the information contained in the conclusion, for Aristotle one would deploy not the syllogism but rather one of the procedures described in the topics, which were practical and comparatively open-ended: they were designed to be useful rather than rigorous.

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By the seventeenth century, however, Aristotle’s topics were thought of as a rhetorical tool, rather than as a means of scientific discovery. It was universally assumed that the demonstrative syllogism was his tool of scientific discovery. While the results of Aristotelian cosmology, optics and matter theory were accepted this did not present any real problems (although sixteenth-century Paduan philosophers did still worry about how syllogistic could be informative). But by the seventeenth century there was a rapidly developing rejection of the results of Aristotelian science. His syllogistic was identified as the cause of the inability of Aristotelianism to produce any lasting results: it was an intrinsically uniformative procedure. In the light of this, it was regarded as unsurprising that the conclusions of Aristotelian science were so far off the mark. The view of Descartes and his contemporaries was that the syllogism doesn’t, and couldn’t, yield things we didn’t know, because its conclusions contain nothing that isn’t already in the premises.3 As he puts it in the Regulae: We must note that logicians are unable to devise by their rules any syllogism which has a true conclusion, unless they already have the whole syllogism, i.e. unless they have already ascertained in advance the very truth which is deduced in that syllogism.4 AT x.406

It is clear from this that what is at issue for Descartes is not only the question of syllogistic as a means of discovery, but also the more general question of what possible justification there could be for syllogistic. If the conclusion does not go beyond the premises—and of course in a valid deductive inference the conclusion cannot go beyond the premises in any factual sense—then the question arises whether the inference is simply redundant, simply a means of repeating, in another form, what is already in the premises. To understand Descartes’ criticism, we need to ask what he wants inference to yield.

2. Inference as a means of making something self-evident Syllogistic inference is designed to preserve truth between premises and conclusion. Syllogistic aims to establish the relation between various truths, and to explore the connections between these truths. If one already knows the truths that appear in the conclusion of the syllogism, this doesn’t invalidate the exercise; it is not the conclusion that is constitutive of the exercise but the connections. The steps in a demonstration are not simply a means to an end which can be

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abandoned once one has reached the conclusion. But this is what Descartes is, in effect, recommending. The reason is that Descartes is concerned with selfevidence, not truth as such. Consider Leibniz’s demonstration of 2 + 2 = 4 from premises including 1 + 1 = 2. The proof shows that the truth of 2 + 2 =4 depends on the truth of 1 + 1 = 2. But 2 + 2 = 4 is no less self-evident than 1 + 1 = 2, so the demonstration cannot establish the self-evidence of the former. It sets out the route from the premises to the conclusion, as it were, a route that cannot be abandoned once one has reached the conclusion. Here we have a fundamental difference between Descartes and advocates of formal demonstrations.5 In answer to the question what do demonstrations do, he wants them to establish something as evident. Second, he assimilates “evident” to “self-evident.” Both are crucial. As regards the first, the aim is to render something evident that would otherwise not be evident. The importance of self-evidence is that something cannot be self-evident if it can only be known in virtue of something else. Self-evidence is a stand-alone quality, and it is associated with the psychological quality of certainty, which evidence per se need not be. If something is self-evident then it is certain because it is an unmediated grasp. If it is merely evident, it is evident relative to an intermediary inferential process. Strictly speaking, there can be no place for an inference in which the connecting steps between premises and conclusion are set out. What Descartes seeks is an unmediated grasp, and the steps mediate it. Unmediated grasp is what he refers to, in his early writings, as an intuitus. However one clearly cannot grasp everything without help from inferential procedures of one kind or another. Descartes’ solution is to make all conclusions self-evident by compressing the steps until you see the premises and conclusion merge into one, as it were. Thus if, for example, I have first found out, by distinct mental operations, what relation exists between the magnitudes A and B, then what between B and C, between C and D, and finally between D and E, this does not entail that I will see what the relation is between A and E, nor can the truths previously learned give me a precise idea of it unless I recall them all. To remedy this I would run over them many times, by a continuous movement of the imagination, in such a way that it has an intuition of each term at the same time that it passes on to the others, and this I would do until I learned to pass from the first relation to the last so quickly that there was almost no role left for memory and I seemed to have the whole before me at the same time. AT x. 387–88

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The compression is a physical/psychological process: one runs through the chain of inference more and more rapidly until the intermediate steps in effect drop out and one sees the conclusion in the premises: one sees an advanced theorem in the basic definitions of Euclidean geometry. How is this possible? It depends a great deal on how the demonstration is presented. If the theorem to be proved is of any complexity, then a geometrical proof will routinely involve various indirect manoeuvres, including proofs of supplementary theorems, and will not follow a direct path. Rewriting the proofs in the form of a chain of syllogisms would clearly be even worse. But if we assign symbols to known and unknown quantities, we can translate the problem into the form of an equation, and we rearrange the expressions on either side of the = sign until we have the unknown value on the left and an expression containing only known values on the right.6 We hold the = sign in the centre of the page, as it were, and swap symbols around it in a systematic way until we have the unknown alone on the left-hand side. The distinctive feature of this algebraic procedure, for Descartes, is that, by contrast with the geometrical and syllogistic procedures, it is transparent. It is clear at every step how the solution is being achieved. To the extent to which transparency is a general desideratum this would not be a particularly contentious move. But Descartes is less concerned with transparency in its own right than with the inference taking the form of a procedure that can be compressed. Completely transparent connections between the steps in the demonstration means, on his account, a completely transparent connection between the first step and the last. And given this, the act of seeing the conclusion in the premises is possible in a way that it would not be with a syllogistic demonstration for example. Nevertheless, Descartes does not see this as a procedure for discovery. Here he makes a distinction that he and his generation believed (wrongly) that Aristotle had failed to make. This is the distinction between discovery and demonstration, which mirrors the traditional distinction between analysis and synthesis. Synthesis is systematic deductive demonstration from first principles. Many commentators have seen this as a Euclidean model for the Meditationes, starting from indubitable principles and generating an account of the world and mind from these. But his Géométrie is a wholly unEuclidean work as regards questions of demonstration. It does not begin with definitions, axioms, and theorems and then gradually, and deductively, build up a body of geometrical knowledge, but rather starts with difficult unsolved problems in geometry, such as Pappus’ locus problem for n lines, and displays various problem-solving techniques in resolving them.

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3. The natural light of reason Problem-solving techniques are things that one learns through practice. One picks them up by receiving practical training by mathematicians, and/or trying to solve problems oneself and gradually building up one’s skills. It’s more like an apprenticeship than something one is taught from a textbook. It is crucial to Descartes’ account that, in this process, one refines one’s natural reasoning abilities. He rejects the idea that inference can be guided by rules, such as the rules of syllogistic, which teach one how to reason. Teaching one to reason was precisely how seventeenth-century scholastic writers had construed syllogistic. Cabero (Brevis summularum recapitulatio, 1623), for example, poses the question of inference in terms of whether logic exercises a natural constraint or norm which is morally binding on thought, and Aversa (Logica, 1623) construes logic in terms of medical conceptions of a healthy functioning body, maintaining that logic—that is, syllogistic—is that ability which remedies the natural weaknesses of reasoning by establishing rules for coming by knowledge. For Descartes, we cannot be taught to reason. “Nothing can be added to the pure light of reason,” he tells us in the Regulae, “which does not in some way obscure it” (AT x. 373). It is true that he offers his own “rules for the direction of the mind” and “discourse on the method of rightly conducting the reason.” But these presuppose that we can already reason, offering not rules of logic but hints on how to avoid various errors due to inattentiveness, unnecessary complexity, and so on. They are not designed to instruct one how to think. This is evident in his Search after Truth by the Light of Nature: I cannot prevent myself from stopping you here, . . . to make you consider what common sense can do if it is well directed. In fact, is there anything in what you have said that is not exact, which is not legitimately argued and deduced? And yet all the consequences are drawn without logic or a formula for argument, thanks to the simple light of reason and good sense which is less subject to error when it acts alone and by itself than when it anxiously tries to follow a thousand diverse rules which human art and idleness have discovered, less to perfect it than to corrupt it. AT x. 521

Strictly speaking, in rejecting “rules of inference” here Descartes is concerned with rules that purport to teach one how to think properly, rather than with logical laws as such. But he tends to run the two together, presumably because he cannot see what other possible rationale laws of logic could have. Once this rationale has been dismissed, so have laws of logic.

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The failing of logic that comes to the fore again here is transparency. Transparency is a contested notion, however. Consider the case of geometry versus algebra. Descartes extolls the virtues of algebra over geometry because we can literally see what is happening in the algebra demonstration, namely the movement of expressions from one side of the = sign to the other. But Newton was later to extoll the transparency of geometry over “analysis,” which includes algebra as well as his main target, calculus. Geometry enables one to manipulate geometrical figures in a visible way, but “analysis” doesn’t reveal to us what is happening at every stage of a proof.7 Transparency alone is not sufficiently welldefined to allow us to adjudicate on this question. There are also cases in Descartes’ own work where considerations of transparency and self-evidence turn out to impose problematic requirements. In the Regulae, for example, transparency is associated with pictorial vividness (Desc 176–78). Addition, subtraction, multiplication and division are set out in terms of manipulating line segments. Here one can see exactly how the operation is functioning so can have confidence in the result. But there is a discrepancy here between Descartes’ concern to represent the operations of arithmetic algebraically, in structural terms, and the concern to provide a vindication of arithmetical processes in terms of operations so clear and distinct that one cannot fail but assent to them. But as soon as he comes to problems that must be set up in terms of several equations in several unknowns, in Rules 19–21, it is evident that there is no way in which his proposed self-evident legitimation will work. The problem is that the procedure is supposed to represent algebraic operations in terms of the manipulation of line lengths, and thereby provide them with a legitimation in terms of clear and distinct ideas, but except in the simplest case we end up invoking complex geometrical constructions, at worst being unable to provide a geometrical construction at all.

4. Conclusion Descartes was seeking aids to discovery, and this led him to some concerns about what discovery consisted in, a project in which self-evidence played a crucial role. He pitted this account against syllogistic, not in its Aristotelian version as such, but against late scholastic dialectic, which saw syllogistic in terms of discovery. His rejection of syllogistic was an influential one, but in a context where questions of factual discovery were paramount, and even if Aristotle’s

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conception of the role of syllogistic had been properly understood, it would have been considered tangential to the concerns of the time.

Notes 1 See Nicholas Jardine, “Galileo’s Road of Truth and the Demonstrative Regress,” Studies in History and Philosophy of Science 7 (1976): 277–318. 2 See Jonathan Barnes, “Aristotle’s Theory of Demonstration,” in Articles on Aristotle, vol. 1, Science, ed. Jonathan Barnes, Malcolm Schofield, and Richard Sorabji, (London, 1975): 65–87. 3 See Stephen Gaukroger, Cartesian Logic: An Essay on Descartes’s Conception of Inference (Oxford, 1989). 4 All references to Descartes’ writings are to Oeuvres de Descartes, ed. Charles Adam and Paul Tannery (11 vols, Paris, 1974–86). Abbreviated to AT followed by the volume and page numbers. 5 See Gaukroger, Cartesian Logic, ch. 4. 6 See Stephen Gaukroger, Descartes: An Intellectual Biography (Oxford, 1996), 172–81. 7 See Stephen Gaukroger, The Collapse of Mechanism and the Rise of Sensibility (Oxford, 2010), 125–45.

5

Hobbes and the Syllogism Douglas M. Jesseph University of South Florida

Thomas Hobbes’s engagement with the logic of the syllogism shows him to have held conflicting views about the merits of traditional logic. On the one hand, the opening part of De Corpore (the first section of his tripartite Elements of Philosophy) is devoted to logic and contains an extensive (though scarcely exhaustive) treatment of the syllogism. On the other hand, he occasionally expressed reservations about the value of the syllogism. In his 1640 Elements of Law, for instance, he insisted that studying syllogistic logic was of no great importance because “there be but few men which have not so much natural logic, as thereby to discern well enough” whether an inference is correct (Hobbes 1994, 138). This ambivalence is apparent in John Aubrey’s “Brief Life” of Hobbes, where he remarks that the philosopher from Malmesbury “did not much care for logic, yet he learned it, and thought himself a good disputant” (Aubrey 1898, 2: 329). Likewise, in his verse autobiography Hobbes recounted his exposure to the traditional classification of syllogistic moods and figures at Oxford, noting that he mastered the material but preferred to go his own way in logical matters.1 Among philosophers of the seventeenth century, Hobbes was in no way unusual in this assessment of the limitations of the syllogism. In the second part of his Discours de la methode Descartes notoriously held that syllogisms “are of less use for learning things than for explaining to others the things one already knows or even . . . for speaking without judgment about matters of which one is ignorant” (Descartes 1964–76, VI : 17). Likewise, the Logique du Port-Royal of Antoine Arnauld and Pierre Nicole criticized the Aristotelian presentation of logic as unhelpful in training the mind to reason correctly while nevertheless cataloguing in detail the traditional syllogistic figures and moods.2 Many British philosophers of the period were also inclined to see the traditional logic of the syllogism as of limited value.3 Thus, in the view of Hobbes and many of his 67

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contemporaries, a treatment of the syllogism was an inescapable part of any general system of philosophy, even if much of Aristotelian syllogistic theory and general methodology was deemed inadequate or misleading.4 The general structure of Hobbes’s account of logic in Part I of De Corpore has four principal parts: names, proposition, syllogism, and method. This conforms to a pattern that was common in the seventeenth-century treatises on logic. The Logique du Port-Royal (Arnauld and Nicole, 1763), for example, is divided into four parts: conception, judgment, reasoning, and ordering. Likewise, Pierre Gassendi’s Institutio logica (Gassendi 1981) employs a similar quadripartite division: idea, proposition, syllogism, and method. The unifying theme here is that the study of logic begins with fundamental units of meaning (names, conceptions, or ideas), proceeds to semantic items capable of truth or falsehood (propositions or judgments), then examines inferential connections among such items (syllogism or reasoning), and finishes with a study of how to arrange these inferences to seek new truths (method or ordering). My investigation will begin with an overview of Hobbes’s general account of reasoning and language, which are both fundamental to his approach to logic. I will then turn to the details of Hobbes’s theory of syllogistic inference, and then close with a consideration of the applications of his logical theory to questions of method and demonstration. My focus is principally upon the material in Part I of De Corpore (which contains Hobbes’s most extensive remarks on this topic),5 but I also make use of material from Leviathan and other sources.

1. Reasoning and language according to Hobbes Hobbes’s approach to the logic of the syllogism developed out of his distinctive conceptions of reasoning and language.6 As he defined it reasoning (or “ratiocination”) is a form of computation: “By Ratiocination , I mean Computation” (DCo 1.1.2; EW 1: 3). Computation, in turn, involves the paired processes of addition and subtraction. As he explained in Leviathan: “When a man Reasoneth, hee does nothing else but conceive a summe total, from Addition of parcels; or conceive a Remainder, from Substraction of one summe from another” (Leviathan 1.5; 2: 64). In contrast to mathematical cases of addition and subtraction, Hobbes held that reasoning does not operate upon numbers or magnitudes, but rather upon mental contents, or “ideas” in Hobbesian parlance.7 Hobbes illustrated this doctrine in De Corpore with an example: suppose someone discerns something off in the distance, but so indistinctly as to lack a

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precise conception of what sort of thing it is. At first, our imagined observer could attach only the idea of body to the perceived object, since it must be some material body or other. Suppose further that, upon approach, our observer sees that this body moves itself about from one place to another; this new information allows the idea of animate to be applied to the body. Imagine that further investigation shows that the animate body can converse and shows signs of intelligence. At this stage, the idea of rational can be added to the former idea; drawing these three ideas or concepts together into the sum rational animate body, our observer can form the idea of a human being. Likewise, a process of mental “subtraction” could work in the opposite direction, beginning with the relatively specific concept of human, subtracting rational to yield animal, and subtracting further to produce the very general concept of body (DCo 1.1.3; EW 1: 4–5). Hobbes summed up this computational conception of reasoning and its role in logic and philosophy in a memorable passage: We must not therefore thinke that Computation, that is, Ratiocination, has place onely in numbers; as if man were distinguished from other living Creatures (which is said to have been the opinion of Pythagoras) by nothing but the faculty of numbring; for Magnitude, Body, Motion, Time, Degrees of Quality, Action, Conception, Proportion, Speech and Names (In which all the kinds of Philosophy consist) are capable of Addition and Substraction. Now such things as we adde or substract, that is, which we put into account, we are said to consider, in Greek λογίζεσθαι; in which language also συλλογίσθαι signifies to Compute, Reason or Reckon. DCo 1.1.3; EW 1: 5

It is no wonder, then, that the first and foundational part of De Corpore bears the title “Computation, or Logique,” and it is clear that Hobbes took the syllogism to be a specific kind of computation.8 Hobbes embraced a strongly empiricist theory of concept formation, in which all concepts or ideas must ultimately trace back of sense experience. As he explained when discussing the origin of ideas in Leviathan, “The Originall of them all, is that which we call sense ; (For there is no conception in a man’s mind, which hath not at first, totally, or by parts, been begotten upon the organs of Sense.) The rest are derived from that original” (Leviathan 1.1; 2: 22). This has important consequences for his account of reasoning and logic, because it restricts all the operations of the mind to the manipulation of ideas that have arisen from prior sense experience. There is no room in Hobbes’s doctrine for a theory of logic or inference that supposes the mind to have innate, non-empirical concepts

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grasped by an intellectual faculty independent of the senses. This is a central respect in which Hobbes’s approach to logic differs from the Aristotelian tradition. Although Hobbes’s initial example of the mental arithmetic that is reasoning supposes that the idea of human is framed without the use of language, he nevertheless recognized that most cases of reasoning are language-dependent. This makes Hobbes’s philosophy of language of critical importance for his treatment of logic. The most striking feature in Hobbes’s approach to language is its strong nominalism, according to which there are no abstract objects, but only abstract names.9 The starting point for Hobbes’s linguistic theory is his distinction between marks and signs. Marks are “sensible things taken a pleasure,” and employed in the course of reasoning to remind a thinker of his or her prior thoughts (DCo 1.2.1; EW 1: 14). As such, marks serve as a kind of private language whose application is restricted to the use of a single person whose thoughts are ordered by the use of the mark. A sign, in contrast, is effectively a mark that is employed by members of a linguistic community to convey their thoughts to one another.10 Among signs, some are natural (as dark clouds are a sign of impending rain) while others are arbitrary and arise from human convention (as a stone set in the ground signifies the boundary of a field). Words are the most important kind of arbitrary sign, and among words the most important is the name, defined as “a Word taken at pleasure to serve for a Mark, which may raise in our Mind a thought like to some thought we had before, and which being pronounced to others, may be to them a Sign of what thought the speaker had or had not before his mind” (DCo 1.2.4; EW 1: 16). Hobbes distinguished names into proper and general, where proper names identify particular individuals and general names are common to many things. Propositions arise from combinations of names, where a proposition is “a speech consisting of two names copulated, by which he that speaketh signifies he conceives the latter name to be the name of the same thing whereof the former is the name; or (which is all one) that the former name is comprehended by the latter” (DCo 1.3.2; EW 1: 30). This leads quite naturally to a theory of truth in which a true utterance involves using names that signify the same thing: When two Names are joined together into a Consequence, or Affirmation; as thus A man is a living creature; or thus, if he be a man, he is a living creature, if the latter name Living Creature signifie all that the former name man signifieth, then the affirmation, or consequence, is true; otherwise false. For True and False are attributes of Speech, not of things. Leviathan 1.4; 2: 54

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As I have indicated, Hobbes endorsed a striking nominalism with respect to language and logic, taking its subject matter to be the inferential connections among names, rather than with abstract concepts or universals. This nominalism combines with a stipulative account of definitions in which names are assigned to things by arbitrary speakers’ convention, so that “Names have their constitution, not from the Species of Things, but from the Will and Consent of Men” (DCo, 1.5.1; EW 1: 56). Hobbes held that the use of general names was essential to allow a given chain of reasoning to support a universal conclusion. As he put the matter in Leviathan, it is the imposition of general names by which “we turn the reckoning of the consequences of things imagined in the mind into a reckoning of the consequences of Appellations” (Leviathan 1.4; 2: 52). He illustrated the necessity of general names with an example: imagine that someone ignorant of speech were to reason about a specific triangle and two right angles placed beside it; suppose further that this person’s reasoning leads to the consequence that, in this particular case, the interior angles of the triangle sum to two right angles. Could such a person then conclude that all triangles have this property? Hobbes answered in the negative, insisting that without the use of language the result cannot be made general. In contrast, He that hath the use of words, when he observes, that such equality was consequent, not to the length of the sides, nor to any other particular thing in his triangle; but onley to this, that the sides were straight, and the angles three; and that was all, for which he named it a Triangle, will boldly conclude Universally, that such equality of angles is in all triangles whatsoever; and register his invention in these general termes, Every right triangle hath its three angles equall to two right angles. Leviathan 1.4; 2: 52–4

This account of reasoning extends to Hobbes’s treatment of logic. Logical inferences such as syllogisms are a kind of “addition” in which the conclusion is drawn as a sum from given premises. In order for syllogistic consequences to hold with full generality, they must be expressed linguistically, where general or universal terms apply to whole classes of objects that fall within the scope of reasoning.11 We can now turn to an investigation of Hobbes’s more specific remarks on the syllogism.

2. Hobbes on the logic of the syllogism Nearly all authors who dealt with syllogistic logic from Antiquity to the seventeenth century developed their accounts against the background of the

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doctrines of terms, predicaments, and other concepts found in various Aristotelian texts, most notably Categories, On Interpretation, and Prior Analytics. In the course of centuries of commentary on these sources, a complex apparatus of intentions, predicables, suppositions, and other technical notions was elaborated, refined, and disputed.12 Hobbes was clearly familiar with much of this logical literature, but his approach generally minimizes the importance of these technical notions. Indeed, a salient consequence of Hobbes’s thoroughgoing nominalism is that he re-framed many traditional doctrines relating to the syllogism as little more than stipulations about how names are to be employed in reasoning.13 This can be seen in Hobbes’s approach to the Aristotelian “law of non contradiction,” which was regularly characterized by the tradition as the ultimate first principle of all logic, reasoning, or thought. In one of its several formulations, Aristotle expressed the law as the principle that “It is impossible to hold (suppose) the same thing to be and not to be” (Metaphysics IV 3 1005b24 cf.1005b29–30). Hobbes reduced this principle to a simple semantic fact concerning the properties of “contradictory names,” or paired names such that each is the negation of the other. Where the tradition of commentary on Aristotle had endowed the law of non-contradiction with great conceptual, ontological, and methodological significance, Hobbes took it to be a trivial semantic fact that, properly understood, was indeed the foundation of all reasoning but which had been rendered obscure by previous commentators: Besides, of Contradictory names, one is the name of any thing whatsoever; for whatsoever is, is either Man or Not-man, White or Not-white, and so of the rest. And this is so manifest, that it needs no further proofe or explication; for they that say the same thing cannot both be, and not be, speak obscurely; but they that say, Whatsoever is, either is, or is not, speake also absurdly and ridiculously. The certainty of this Axiome, viz. Of two Contradictory Names, one is the Name of any thing whatsoever, the other not, is the original and foundation of all Ratiocination, that is, of all Philosophy; and therefore it ought to be so exactly propounded, that it may be of it selfe cleare and perspicuous to all men; as indeed it is, saving to such, as reading the long discourses made upon this subject by the Writers of Metaphysicks (which they believe to be some egregious learning) thinke they understand not, when they do. DCo 1.2.8; EW 1: 19

Another instance of this aspect of Hobbes’s approach to logic appears in his discussion of the distinction between terms of the first and second intention, which has a long history in medieval discussions of logic and language. In Ockham’s formulation, an intention is “something in the soul capable of signifying something

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else” (Ockham 1974, 74). A first intention is an intention of the soul that signifies an external object, while a second intention is one that signifies a first intention. Therefore, terms of the first intention are names that signify things, whereas terms of the second intention signify terms of the first intention. According to this scheme, to assert “Socrates is mortal” is to link two terms of first intention (“Socrates” which signifies the individual who bears that name, and “mortal” which signifies the property of being mortal). In contrast, to assert “Animal is a genus” is to link the second-intention term “genus” to the first-intention term “Animal” and thereby make a claim about the status of that term, namely that it signifies a concept or a collection rather than an individual (Ockham 1974, 74–75). Hobbes formulated this distinction in a way that rigorously divested it of any significant conceptual or ontological content, and instead reduced it to a distinction between two types of names: one signifying things, another signifying other names. After noting that some names are more general than others, he declared: And from hence proceeds the third distinction of Names,14 which is, that some are called names of the First, others of the Second Intention. Of the first Intention are the names of Things, a Man, Stone, &c. of the second are the names of names and speeches, as Universall, Particular, Genus, Species, Syllogisime, and the like. But it is hard to say why those are called names of the First, and these of the Second Intention, unlesse perhaps it was first intended by us to give names to those things which are of daily use in this life, and afterwards to such things as appertaine to science, that is, that our Second Intention was to give names to Names. But whatsoever the cause hereof may be, yet this is manifest, that Genus, Species, Definition, &c. are names of Words and Names onely; and therefore to put Genus, and Species for Things, and Definitions for the nature of any thing, as the Writers of Metaphysicks have done, is not right, seeing they be only significations of what we think of the nature of Things. DCo 1.2.10; EW 1: 20–1

Whether Hobbes was serious in his speculation about the origins of the terms “first intention” and “second intention,” it is apparent that he had no interest in engaging seriously with the traditional account of first and second intentions.15 In a very similar manner, Hobbes offered an account of the Aristotelian categories or predicaments that reduced them to a “scale of names” having greater or less generality. Thus, where the tradition of commentary on Aristotle often took the categories (substance, quantity, qualification, etc.) to be “orders of being” or fundamental divisions in the world that correspond to basic structures in our cognitive or conceptual scheme, Hobbes was content to treat the categories as nothing more than an ordering of names. He remarked that “Writers of

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Logique have endeavoured to digest the Names of all kinds of Things into certain Scales or Degrees, by the subordination of Names lesse Common to Names more Common” (DCo 1.2.15; EW 1: 25). He then offered his own analysis of the predicaments body, quantity, and quality, but cautioned that “I would not have any man thinke I deliver the Forms above for a true and exact Ordination of Names,” because ordering names to match the order of nature is an empirical matter that “is to be done onely by Arguments and Ratiocination, and not by disposing of words into Classes” (DCo 1.2.16; EW 1: 28). Hobbes’s low opinion of this exercise is made clear in his closing remark on the categories when he confessed “I have not yet seen any great use of the Predicaments in Philosophy” (DCo 1.2.16; EW 1: 28). In keeping with his view that all reasoning is a form of computation, Hobbes held that every proposition involves the “addition” of two names or terms. Thus, the proposition “Snow is white” adds together the terms “snow” and “white” to make an assertion. He then defined a syllogism as “A SPEECH , consisting of three propositions, from two of which a third follows” (DCo 1.4.1; EW 1: 44). To say that the conclusion of a syllogism follows from its two premises means only that “if these be granted to be true, this must also be granted to be true” (DCo 1.4.1; EW 1: 44). The three propositions that comprise a syllogism each contain two terms (or “names”), and a syllogism can yield a conclusion only if the “middle term” appears twice: one occurrence in each premise and none in the conclusion. Likewise, two “extreme terms” must appear once separately in each premise and again in the conclusion. Hobbes further characterized the syllogism as a kind of mental addition, namely “the Collection of the summe of two Propositions, joined together by a common Term, which is called the Middle Terme. And as Proposition is the Addition of two Names, so Syllogisme is the adding together of three” (DCo 1.4.6; EW 1: 48).16 The traditional treatment of the syllogism distinguished the various combinatorial possibilities of syllogistic moods (categorical propositions using quantifiers “all,” “some,” and “none”) and figures (differing positions of the extreme and middle terms in the premises). The result was that logic texts of Hobbes’ era typically contained detailed inventories of all the possible moods and figures of valid syllogisms, as well as the familiar mnemonic devices to facilitate their memorization (Barbara, Celarent, Darii, etc.).17 As we have seen, Hobbes alluded to these in his verse autobiography when he recalled his first encounter with syllogistic logic at Oxford. Although the fourth chapter of De Corpore contains a rather cursory overview of the syllogistic moods and figures, it is evident that Hobbes held this aspect of logic in comparatively low esteem. In

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his estimation, the cataloging of moods and figures was largely wasted effort because “in Philosophy, the Profession whereof is to establish Universall Rules concerning the Properties of Things, . . . it is superfluous to consider any other Mood in direct Figure, besides that, in which all the Propositions are both Universall and Affirmative” (DCo 1.4.7; EW 1: 49). In fact, he went so far as to argue that the study of syllogistic was of no great intrinsic interest because “they that study the Demonstrations of Mathematicians, will sooner learn true Logick, then they that spend time in reading the rules of Syllogizing which Logicians have made” (DCo 1.4.13; EW 1: 53). Hobbes departed from the traditional theory of the syllogism in one clear respect with his contention that “it is manifest that a Categoricall and Hypotheticall Syllogisme are aequivalent” (De Corpore, 1.4.13; EW 1: 54). Traditionally, a categorical syllogism was defined as a syllogism whose premises and conclusions are categorical propositions, i.e. quantified propositions expressing relationships among terms. Thus, “Some As are Bs” and “All Bs are Cs” are categorical propositions dealing with terms A, B, and C. In contrast, a hypothetical syllogism employs premises that are stated in the form of conditionals, such as “If x is A, then x is B.” Hobbes argued that any categorical syllogism can be reformulated as a hypothetical syllogism. At part 1, chapter 4, section 13 of De Corpore (EW 1: 54) he considered as an example the categorical syllogism Every man is a living creature, Every living creature is a body, therefore Every man is a body.

According to Hobbes this syllogism is equivalent to the hypothetical syllogism If anything be a man, the same is also a living creature, If anything be a living creature, the same is a body, therefore If anything be a man, the same is a body.

From the standpoint of contemporary logic, this equivalence is unobjectionable; but with this doctrine Hobbes departed from an Aristotelian tradition that took universal categorical propositions to have existential import. Traditionally, the proposition “All As are Bs” was taken to entail “Some As are Bs,” and this requires that there be at least one object that is A. On this interpretation, the assertion “All men are living creatures” would be false in a world without men. However, the conditional “If anything is a man, the same is also a living creature” is always evaluated as true in case the antecedent is false, i.e. if there are no men. Thus,

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Hobbes’s argument for the equivalence of categorical and hypothetical syllogisms requires abandoning the thesis of existential import. Hobbes was by no means the first to have taken this step, but it does point out the extent to which his approach departs from much of the Aristotelian tradition.18

3. Hobbes on method Seventeenth-century treatments of the syllogism typically included an account of method, or the means of employing logical inferences to seek new truths. Hobbes was no exception to this rule: the sixth and final chapter of the “Logic” in De Corpore bears the title “Of Method” and contains a famous discussion of how logic can lead to the discovery of philosophically important truths. Hobbes prefaced his account of method with a restatement of his definition of the term “philosophy” at the very beginning of De Corpore. “Philosophy” he declared, “is the knowledge we acquire by true Ratiocination, of Appearances, or apparent Effects, from the knowledge we have of the same possible Production or Generation of the same; and of such Production as has been or may be, from the knowledge we have of the Effects” (DCo 1.6.1; EW 1: 65–6). Philosophical reasoning thus divides into two sorts: from known causes to their effects, and from known effects to their (possible) causes. From this, Hobbes concluded that “METHOD therefore in the Study of Philosophy, is the shortest way of finding out Effects by their known Causes, or of Causes by their known Effects” (DCo 1.6.1; EW 1: 66). As Hobbes characterized the two sorts of reasoning, that which proceeds from effects to causes is “analysis” and that which goes from causes to effects is “synthesis.”19 He accepted the traditional notion that analysis is the method of discovery (beginning with what is sought and reasoning back to secure principles from which the result can be derived) while synthesis is the method of demonstration (beginning with secure first principles and deriving a result from them). By phrasing the analysis/synthesis distinction in terms of causal order, Hobbes embraced the notion that the premises of a syllogism are (in some fairly strong sense) the causes of the conclusion, and he further emphasized that the true first principles of demonstration must be definitions that express the causes of the things defined.20 Hobbes offered his own explanation of light as an example of the interplay between analysis and synthesis. First, we note that whenever light is observed, some “principal object” is its source; by analysis, we take such an object as causally necessary to the production of light; analyzing further we find that a

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transparent medium and functioning sense organs are also necessary for the phenomenon of light to arise. Further analysis reveals that a motion in the object is the “principal cause” of light, and that the continuation of such motion through the medium and its subsequent interaction with the “vital motion” within the sensory apparatus are contributing causes. Hobbes concludes that “in this manner the Cause of Light may be made up of Motion continued from the Original of the same Motion, to the Original of Vitall Motion, Light being nothing but the alternation of Vitall Motion, made by the impression upon it of Motion continued from the Object” (DCo 1.6.10; EW 1: 79). This analysis ultimately terminates in the most general or “Universal things,” namely bodies in motion, which Hobbes deemed “manifest of themselves; or (as they say commonly) known to Nature; so that they need no Method at all; for they have all but one Universall Cause, which is Motion” (DCo 1.6.5; EW 1: 69). Having completed an analysis, we can then derive, by way of synthesis, a sequence of syllogisms that will show how the properties of light follow from fundamental laws of motion and impact. In general, no single syllogism will suffice to derive the properties of an object from first principles or definitions that express its causes. Hobbes thus defined a demonstration as “a Syllogism or Series of Syllogisms derived and continued from the Definitions of Names, to the last Conclusion,” and he insisted that “all true Ratiocination, which taketh its beginning from true Principles, produceth Science, and is true Demonstration” (DCo 1.6.16; EW 1: 86). The method of demonstration, then, must begin with definitions that identify the causes of things; from these, syllogisms are constructed that collectively show how the demonstrated phenomenon arises. In the Posterior Analytics Aristotle examined a particular type of syllogism, which he termed the demonstrative or scientific syllogism, namely “one in virtue of which, by having it, we understand something” (71b17–19). Such a syllogism contains premises that are “true and primitive and immediate and more familiar than and prior to and explanatory of the conclusion” (71b21–22). Syllogisms of this sort are termed demonstrations τοῦ διότι,while those that fail to satisfy such conditions are termed demonstrations του ὄτι. The demonstration του ὄτι validly concludes some fact but fails to offer an appropriately causal explanation for it, whereas the demonstration τοῦ διότι gives the reason for the fact by constructing a syllogism whose premises are causally explanatory of the conclusion. Hobbes rejected this distinction on the grounds that a proper demonstration must always proceed from definitions expressing causes, so that a του ὄτι syllogism would not be a demonstration at all. As he put the issue in the first

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dialogue of his 1660 Examinatio et emendatio mathematicae hodiernae, “a demonstration τοῦ διότι is when someone shows by what cause a subject has such an affection. And so because every demonstration is scientific, and to know that such an affection is in the subject comes from cognition of the cause that necessarily produces that affection, there can be no demonstration other than the τοῦ διότι” (Hobbes 1660, 24). We can summarize Hobbes’s conception of method as follows: the aim of all philosophical reasoning is to uncover causes from known effects, or to deduce effects from known causes. Method is the means whereby causes are sought from effects or effects are derived from causes. In the former case, the method is analytic, in the latter it is synthetic. Once appropriate causes have been identified and incorporated into definitions, syllogisms can be linked together to give τοῦ διότι demonstrations of phenomena, and the construction of a τοῦ διότι demonstration is the ultimate goal of all method.

4. Conclusion Like many seventeenth-century philosophers, Hobbes held a decidedly ambivalent attitude toward the traditional logic of the syllogism. He recognized that any general account of the world and our knowledge of it must come to terms with the Aristotelian tradition, and his response to the “logic of the schools” was decidedly critical. However, his criticisms of the traditional approach did not mean that Hobbes saw no value to analyzing and codifying correct forms of inference. Rather, he saw a very close connection between Aristotelian-Scholastic accounts of the syllogism and general theses concerning language, cognition, and metaphysics (such as the nature of the predicables or the categories). His nearly wholesale rejection of such Aristotelian-Scholastic theories accounts for his critical stance toward traditional treatments of the syllogism. Hobbes’s strict empiricist doctrine of concept formation (according to which all ideas must originate in sensation) rules out a theory of cognition or inference in which a non-sensory pure intellect grasps inferential connections among innate concepts, or where the basic logical categories are rooted in the a priori structure of human cognition. Likewise, his nominalism rules out the possibility that the terms of a syllogism might designate some sort of abstract universals; instead, Hobbes took terms to be nothing more than names imposed by speakers’ convention, and he characterized the syllogism as a computation of the consequences that follow from the imposition of names.

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Notes 1 In the anonymous English translation of Hobbes’s Latin verse autobiography, we read: And at Fourteen I was to Oxford sent; And there of Magd’len-Hall admitted, I My self to Logick first did then apply, And sedulously I my Tutor heard, Who Gravely Read, althou’ he had no Beard. Barbara, Celarent, Darii, Ferio Baralypton, These Modes hath the first Figure; then goes on Cæsare, Camestres, Festino, Baroco, Darapti, This hath Modes of the same variety. Felapton, Disamis, Datisi, Bocardo, Ferison, These just so many Modes are look’d upon, Which I, tho’ slowly Learn, and then dispense With them, and prove things after my own sense. Thomas Hobbes, The Life of Mr. Thomas Hobbes of Malmesbury. Written by himself in a Latine Poem and now Translated into English (London, 1680): 2–3. 2 This is apparent in Part III , chapters 3–10 of Antoine Arnauld and Pierre Nicole, La logique, ou l’art de penser; Contenant, outre les regles communes, plusieurs observations nouvelles, proppres à forme le jugement. Nouvelle edition (Paris, 1763):199–233. 3 On this point see Douglas Jesseph, “Logic and Demonstrative Knowledge,” in The Oxford Handbook of British Philosophy in the Seventeenth Century, ed. Peter Anstey (Oxford, 2013): 373–392. 4 Martine Pécharman (“Hobbes on Logic, or How to Deal with Aristotle’s Legacy,” in The Oxford Handbook of Hobbes, ed. A.P. Martinich and Kinch Hoekstra (Oxford, 2016): 21–60) argues that Hobbes’s critique of Scholasticism as “vain philosophy” employing empty barbarous terms was not intended to reject the logic of the syllogism. As we will see, this is generally true. Nevertheless, to the extent that traditional logic was seen as connected with Aristotelian-Scholastic metaphysics, philosophy of mind, or accounts of meaning and language, Hobbes was determined to reform it. 5 I will use the English translation of Hobbes, Elements of Philosophy, the First Section, Concerning Body (London, 1656), with references abbreviated as “DCo” followed by part, chapter, and section numbers separated by periods; a reference to The English Works of Thomas Hobbes of Malmesbury, ed. Sir William Molseworth, 11 vols (London, 1839–1845) follows after a semicolon, using the abbreviation “EW.” References to Leviathan use the text of Thomas Hobbes, Leviathan, ed. Noel Malcolm, 3 vols (Oxford, 2012), with references to part and chapter

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7

8

9

10

11

12

13

14 15

The Aftermath of Syllogism separated by periods; a reference to volume and page number follows after a semicolon. See Willem R. De Jong, “Hobbes’s Logic: Language and Scientific Method,” History and Philosophy of Logic 7 (1986): 123–142 on the relationship between Hobbes’s theories of language and logic. Gabriel Nuchelmans, Late-Scholastic and Humanist Theories of the Proposition (Amsterdam 1980): 169 sees this as a continuation of an account of reasoning that goes back at least to the work of Ramus: “Long before Hobbes wrote his Computation or Logique, the view that reasoning was a kind of calculation was a well-established element of the Ramist tradition.” Marco Sgarbi, The Aristotelian Tradition and the Rise of British Empiricism: Logic and Epistemology in the British Isles, 1570–1689 (Dordrecht, 2013): 184–195 examines Hobbes’s conception of logic as a kind of calculus in the context of late Aristotelianism. As Pécharman (“Hobbes on Logic, or How to Deal with Aristotle’s Legacy,” 41–42) notes, several of Hobbes’s seventeenth-century critics (notably John Eachard and Seth Ward) rejected this account, on the grounds that it was an unwarranted innovation that cast aside the traditional treatment of logic by reducing it to mere calculation. On Hobbes’s nominalism and its intellectual context, see Cees Leijenhorst, “ ‘Insignificant Speech’: Thomas Hobbes and Late Aristotelianism on Words, Concepts, and Things,” in Res et Verba in der Renaissance, ed. Eckhard Kessler and Ian Maclean (Wiesbaden, 2002): 337–368. As Hobbes puts the matter “The difference therefore betwixt Markes and Signes is this, that we make those for our own use, but these for the use of others” (DCo 1.2.2; EW 1:15). In Hobbes’s words “Living Creatures that have not the use of Speech, have no Conception of Thought in the Mind, answering to a Syllogisme made of Universall Propositions; seeing it is necessary to Thinke not only of the Thing, but also by turns to remember the diverse Names, which for diverse considerations thereof are applied to the same” (DCo 1.4.8; EW 1: 50). See E.J. Ashworth, “Traditional Logic,” in The Cambridge History of Renaissance Philosophy, ed. Charles B. Schmitt and Quentin Skinner (Cambridge, 1988): 143–172 on the developments in traditional logic. As Pécharman (“Hobbes on Logic, or How to Deal with Aristotle’s Legacy”) puts the issue: “through a nominalist reductionist reinterpretation, even scholastic realist terminology can find a place within Hobbes’s logic,” 28. Hobbes’s first distinction is between positive and negative names; the second is between common and proper names. Sgarbi (The Aristotelian Tradition and the Rise of British Empiricism, 190) maintains that Hobbes’s account “betrays an imperfect understanding of this distinction,” but it is probably better to say that Hobbes had no interest in the distinction, since he saw

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17

18

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it as little more than a trivial semantic fact about two different ways of employing words. The same doctrine appears in Leviathan (1.4; 2: 58) “The Greeks have but one word λόγος, for both Speech and Reason; not that they thought there was no Speech without Reason; but no Reasoning without Speech: And the act of reasoning they called Syllogisme; which signifieth summing up of the consequences of one saying to another.” The mnemonics arise from the use of the vowels A, E, I, O to signify respectively universal affirmative, universal negative, particular affirmative and particular negative propositions. The valid moods get Latin names that represent the quality of the propositions in both premises and the conclusion; thus, “Camestres” is the mood which takes A, E in the premises and concludes E. For accounts of Aristotelian syllogism that emphasize its commitment to the existential import of universal categorical propositions, see G. Patzig, Aristotle’s Theory of the Syllogism (Dordrecht, 1968) and T. Smiley, “What is a syllogism?,” Journal of Philosophical Logic 2 (1973): 155–180. For a survey of the history of the question, see A. Church, “The history of the question of existential import of categorical propositions,” in Logic, Methodology and Philosophy of Science: Proceedings of the 1964 International Congress, ed. Y. Bar-Hillel (Amsterdam, 1965): 417–424. There is an extensive literature on Hobbes’s treatment of analysis and synthesis. Richard A. Talaska, “Analytic and Synthetic Method According to Hobbes,” Journal of the History of Philosophy 26 (1988): 207–237 is a useful overview of the topic. There has been considerable scholarly debate over the question of the extent to which Hobbes’s account of analysis and synthesis is connected to Renaissance Aristotelian treatments of the subject, notably those of the “Paduan School” associated with Giacomo Zabarella and (derivatively) Galileo. J.W.N. Watkins, Hobbes’s System of Ideas: A Study in the Political Significance of Scientific Theories (London, 1965) argues at length for this connection, while Noel Malcolm (“Hobbes’ Science of Politics and his Theory of Science,” in Aspects of Hobbes, ed. Noel Malcolm (Oxford, 2002): 146–155, 153) claims that Hobbes’s account of analysis and synthesis “owed almost nothing to Galileo and very little to the Paduan tradition of commentary on Arisotle.” More recently, Sgarbi (“La logica di Thomas Hobbes e la tradizione aristotelica.” Lo Sguardo: Rivista di Filosofia 5 (2011): 59–72 and The Aristotelian Tradition and the Rise of British Empiricism) has made the case for a closer connection between Hobbes’s logic and that of the Paduans. None of what I say here depends upon resolving the issue, so I will leave it aside. As he put it in his Six Lessons to the Professors of the Mathematiques, “where there is place for Demonstration, if the first Principles, that is to say the Definitions, do not contain the Generation of the Subject, there can be nothing demonstrated as it ought to be” (Thomas Hobbes, Six Lessons to the Professors of the Mathematiques, one of Geometry, the other of Astronomy (London, 1656), Epistle, par. 2).

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Syllogism in the Port-Royal Logic Russell Wahl Idaho State University

1. Introduction La Logique ou L’Art de Penser, which first appeared anonymously in 1662, was an extremely influential work, being continuously in print from 1662 through the end of the nineteenth century.1 The 1818 English edition indicates that it was used as a textbook for the universities in Cambridge and Oxford. No doubt many students learned their syllogistic and what we would now call “traditional logic” from this book. In this fact there is some irony, for the Port Royal Logic was seen by its authors as a break with tradition. The authors were Antoine Arnauld and Pierre Nicole. According to the foreword, the work was written for “un jeune Seigneur,” who is assumed to be Charles-Honoré d’Albert, the duke of Chevreuse, who was the son of the duke of Luynes, the translator of Descartes’s Meditations. The authors claimed to have written the work in four or five days, and that it would take about that amount of time to master the subject (CG 13, B 3). This confidence was based on the attitude toward logic which they had accepted from Descartes. Descartes had held in the Rules for the Direction of the Mind that “the deduction or pure inference of one thing to another can never be performed wrongly by an intellect which is in the least degree rational.”2 Logic is therefore best seen not as a study of arguments or disputations, but as a tool for discerning the true from the false. In the “First Discourse” in the Port Royal Logic, Arnauld and Nicole set their logic in terms of the new philosophy of Descartes (CG 21, B 10), but said that they would include what they find “truly useful” from traditional logic. Under this heading they included “rules for syllogisms, the classification of terms and ideas, and some reflections on propositions.” They were more skeptical of two other topics, the conversion of propositions and the demonstrations of the rules 83

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for figures, but they included them as they found some merit in them at least as exercises of the mind (CG 22, B 10). As they agreed with Descartes that the main point of logic is being able to discern the true from the false, Arnauld and Nicole saw logic not as the art of reasoning, but as the art of thinking. Logic was to give rules for forming simple ideas and judgments as well as inferences.3 To the extent that syllogism was worth studying, it would be in its ability to assist in obtaining new knowledge. So while part of their concern was to cover these topics as they had been covered by earlier logic books (CG 22, B 10), they also thought that syllogisms did serve a purpose in arriving at new knowledge, and they phrased their discussion accordingly. They saw the syllogisms as being useful for determining whether a given proposition was true by enabling one to find other propositions, more clearly known, from which the proposition in question followed. It is for this reason that in their discussion of the syllogism, they always take the conclusion as fixed. While the first edition also included a section on the reduction of syllogisms to the first figure, this part was removed from all the later editions. Perhaps this is hardly surprising, as they had begun the chapter with the phrase “This chapter is extremely useless.” (CG 203, B 156) What remained in the later editions was instead a semantic analysis, which gave the foundations for the rules determining the validity of syllogisms. With an eye fixed on discerning the true from the false as the primary goal of logic, Arnauld and Nicole sought even to bypass these rules by an even more general rule.

2. The analysis of propositions The discussion of syllogisms in the Port-Royal Logic presupposes the discussion of propositions, since rather than providing a formal theory of the derivation of valid forms, the Port-Royal authors are interested in explaining why the individual syllogisms are valid in purely semantic terms. The rules of the syllogisms are then justified by general rules derived from their analyses of propositions. Eventually the Port-Royal Logic attempted to replace even these rules by a “general method” of evaluating syllogisms. The Port-Royal Logic follows traditional logic in holding that a proposition is an affirmation or a denial of the relation of two terms. Arnauld and Nicole understood the terms to be ideas and emphasized the distinction between the comprehension of an idea and its extension. The comprehension of an idea they characterize as “the attributes that it contains in itself, and that cannot be removed from it without destroying the idea” (CG , 59, B, 39); the extension they characterize

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as “the subjects to which the idea applies” (CG , 59, B, 40). They include in these subjects not only the particulars, but the sub-species. The comprehension of an idea is probably best understood on Cartesian lines as whatever is contained within the clear and distinct idea of something, whether someone is aware of it or not. Since it involves all the attributes that the idea contains, removing any of them would result in a different idea or as they put it, it would “destroy the idea” (CG 59, B 39). One might think that adding attributes would also involve a different idea, and so it does, in the sense that it involves a complex idea which contains the other idea as a part, but the original idea will be part of the complex. So, for example, the idea of a triangle, which contains all the attributes common to all triangles, will be part of the complex idea right triangle, which will include those attributes and the further attribute of having a right angle. This addition may have the effect of narrowing down the extension.4 The quantifier term “some” is then seen as also narrowing the extension by adding to the comprehension the idea of “an indistinct and indeterminate part” (CG 59, B 40). The extension of the idea will be narrowed although exactly to what will not be determined. Thus the syncategormatic terms “all” and “some” are seen not as part of the proposition as a whole, but as parts of the subject term. Given what the authors say about the predicate terms, they also seem to think of these as containing implicit quantifiers (e.g. “some” in the case of predicate terms of affirmative propositions and “all” in the case of predicate terms of negative propositions). Propositions are universal or particular depending on whether their subject terms are taken over the entire extension or over a part of that extension (CG 114–115, B 83). Whether a term is “taken in its entire extension” or not, corresponds to whether it is “distributed” or not in the usual language in text-books on syllogisms. The account of the extension of the terms plays an important role in the analysis of propositions and then in the account of rules of inference or rather in the account of why certain inferences are permissible and others not. In the second part of the Port-Royal Logic, in the course of discussion of conversion of propositions, the following seven axioms are given; the first four concerning affirmative propositions, the last three concerning negative:

1. 2. 3.

The attribute is put in the subject by an affirmative proposition according to the entire extension of the subject in the proposition. The attribute of an affirmative proposition is affirmed according to its entire comprehension. The attribute of an affirmative proposition is not affirmed according to its entire extension if it is in itself greater than that of the subject.

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The extension of the attribute is restricted by that of the subject, such that it signifies no more than the part of its extension which applies to the subject. A negative proposition does not separate all the parts contained in the comprehension of the attribute from the subject, but only the total and complete idea made up of all these attributes together. The attribute of a negative proposition is always taken generally (i.e. the attribute is taken over its entire extension). Every attribute denied of a subject is denied of everything contained in the extension of the subject in the proposition. CG 170, 173–4, B 130, 133

Although these are called “axioms,” arguments are given for these claims. The rules which are then given for syllogisms refer back to these axioms. From the first and second axioms we can see that in All S are P, P is affirmed of the entire extension of S, and it is the entire comprehension of P that is affirmed over this extension, in the sense that every attribute contained in this comprehension will be so affirmed. In the case of Some S are P, P is affirmed only of an indeterminate part of the extension of S, but it is still the entire comprehension of P that is being affirmed of this part of the extension. From the third and fourth axioms, it is not the case that the entire extension of P is in question, since the extension ultimately referred to is restricted by the subject term. With regard to the negative propositions, in No S are P and Some S are not P by the fifth axiom we are not denying each of the components of the comprehension of the predicate to the subject terms, but only the composite. The example they give is that in saying that matter is not a thinking substance one is not denying that matter is a substance, but only that it does not fall under the total comprehension “thinking substance.” By the sixth and seventh axioms, the attribute in each of these propositions is taken generally; so everything that is P is being excluded from the extension of the subject: in the case of the universal the entire extension of S and in the case of the particular an indeterminate part of that extension. It is very clear that Arnauld and Nicole see the comprehension and the extension as related in that an increase in the comprehension will normally cut down on the extension. In the case of the universal affirmative, All S is P, the extension of S will be contained in the extension of P. But it seems not the case that necessarily, the comprehension of P will be included in the comprehension of S. Jean-Claude Pariente suggests that axiom 2, above, holds that “an affirmation posits [pose] . . . the comprehension of the predicate as an integral part of the comprehension of the subject.”5 He cites Arnauld and Nicole’s discussion just

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prior to the axioms, where they say concerning “every human is animal” that if I say this, “I mean and I signify that everything that is a human is also an animal, and so I conceive animal in all humans” (CG 169, B 129). Axiom 2, though, asserts that the attribute “is affirmed over its entire comprehension.”6 It seems Arnauld and Nicole have in mind that when one makes an affirmative proposition, one affirms the entire comprehension of the predicate of the extension of the subject. It does not follow that one is also including the comprehension of the predicate in the comprehension of the subject, although of course it may be so included. Pariente does seem to take it this way, saying that in contemporary terms we should say that in affirmation, “the comprehension of the predicate forms a proper sub class of the comprehension of the subject.”7 Pariente’s reading is criticized by Jill Buroker, who correctly points out that such a view renders all universal affirmatives necessary, and is extremely implausible when applied to particular affirmatives.8 One point which may tell against Pariente’s view is a remark Arnauld and Nicole make when making the distinction between a clause that is a restriction on the one hand, and one that is an explication on the other. In the case of explications, they say: “An addition is merely an explication when it only develops either what is contained in the comprehension of the idea of the first term, or at least what applies to it as one of its accidents, provided that it applies generally and throughout its extension” (CG 65, B 45). The idea is that if the addition B is an explication, then in A, which is B, is C, the extension of A will not be diminished as All A is B will be true. On Pariente’s view, it seems, if this is true, then the comprehension of B would be contained in A. This is one of the options proposed by Arnauld and Nicole. But they also add “at least what applies to it as one of its accidents,” suggesting that in this case the comprehension of B will not be included in that of A, even though the proposition All A are B is true. Thus, there is room for accidentally true universal affirmatives and these will be such that the comprehension of the predicate “forms a proper sub-class of the comprehension of the subject.” We find a further piece of evidence in Arnauld’s correspondence with Leibniz. Leibniz did hold something like the thesis being discussed at least with regard to individual concepts. All true predications of Adam, e.g., are contained in his individual concept. Leibniz held this while at the same time holding that this did not make these predications necessary, since the creation of the individual was itself a contingent act of God. Arnauld had difficulty with his position that all true predications of something would be included in its individual concept. He concludes “I must consider as contained in the individual concept of myself only that which is such that I should no longer be me if it were not in me: and that all that is to the contrary such that it could be

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or not be in me without my ceasing to be me, cannot be considered as being contained in my individual concept . . ..”9 Buroker is right that there is little evidence for this view which, when fully examined, is highly implausible. Unfortunately when it comes to developing their general rule for determining the validity of syllogisms, Arnauld and Nicole appear to endorse such a position.

3. The classification of syllogisms The Port-Royal Logic does not give us a formal system in any modern sense. To the extent one thinks of the rules for reducing syllogisms to the first figure as a gesture toward a formal system, the chapter including this was omitted from the later editions as useless. What we have instead is a system of rules derived from the analysis of propositions given in the second section. First, Arnauld and Nicole divide syllogisms into the simple and conjunctive. Simple syllogisms are the basic categorical syllogisms, and conjunctive syllogisms are those which involve conditionals, disjunctions and conjunctions. They then divide the simple syllogisms into those that are complex or non-complex. The complex syllogisms are those which are not in standard form in that the middle term is not neatly or completely joined with one or both of the terms of the conclusion. Arnauld and Nicole have a special interest in these syllogisms because they think that a wooden application of the rules of syllogisms will lead to an error in these cases, and they use these syllogisms as an opportunity to present their own more general method of determining the validity which bypasses the traditional classifications and rules. The non-complex simple syllogisms are those that are presented in standard text books. These are discussed in Chapters 3 through 8. The complex syllogisms are introduced in Chapter  9 and the following chapters involve reducing them to simple syllogisms and then advocating the general rule. The later chapters then cover conjunctive syllogisms, i.e. syllogisms with conditional conclusions, enthymemes and sorites.

4. Rules for simple syllogisms The justification of the rules for syllogisms opens up with a summary of what was argued in Part II , concerning propositions. Instead of the seven axioms given at the end of part II , four axioms are given as a summary:

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1. 2. 3.

4.

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Particular propositions are contained in general propositions of the same nature (i.e. quality) and not the general in the particular. The universality or particularity of a proposition depends on whether the subject is taken universally or particularly. Since the attribute of an affirmative proposition never has a larger extension than the subject, it is always regarded as taken particularly, because it is only accidental if it is sometimes taken generally. The attribute of a negative proposition is always taken generally. CG 183, B 139

It should be noted that these axioms deal only with issues of extension, not of comprehension. From this list of axioms, Arnauld and Nicole derive six rules for determining a list of valid syllogisms. However, they do not then immediately apply these rules to the syllogisms, but use them first to give a list of syllogisms which could be valid, depending on the figure. The six rules are:

1. 2. 3. 4. 5.

6.

The middle term cannot be taken particularly twice. The terms in the conclusion cannot be taken more universally in the conclusion than in the premises. No conclusion can be drawn from two negative propositions. A negative conclusion cannot be proved from two affirmative propositions. The conclusion always follows the weaker part. That is, if one of the two propositions is negative, the conclusion must be negative; if one of them is particular, it must be particular. Nothing follows from two particular propositions. CG 183–187, B 139–142

Clearly this is not a minimal set of rules, as the fifth and sixth can be derived from the others. Arnauld and Nicole also give six corollaries, five following the second rule and one following the fifth. The last of these corollaries, that whatever implies the general implies the particular, is used to justify not treating AEO as a distinct syllogism, but simply something implied by AEE . The corollary also leads to the exclusion of AAI in the first figure and EAO in the first and second figures, as AAA is valid in the first figure and EAE is valid in the first and second figures. Following these rules, Arnauld and Nicole note that there are 64 possible ways of arranging three propositions taken from four different types, and therefore there are 64 moods. They then come up with a list of moods which could be valid, which they call “modes concluants.”10 They rule out 28 by the third

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and sixth rules, 18 by the fifth rule and 6 by the fourth rule, leaving just 10 after 54 have been excluded. These ten include four affirmative moods (AAA , AII , AAI , IAI ) and six negative moods (EAE , AEE , EAO, AOO OAO, EIO ) after AEO has been excluded. At this point they deal with the individual figures and the syllogisms which are valid in each figure. From the original rules they derive rules concerning each of the figures. All sorts of observations concerning the syllogisms follow from this, for example that the major premise of a first figure syllogism must be universal, that the minor must be affirmative, that only negative moods will be valid in the second figure, etc. They use these further rules and observations to cut down the initial list of “conclusive moods” to shorter lists for the particular figures. In addition to pointing out that these shorter lists pass these rules for the particular syllogisms, Arnauld and Nicole also give separate arguments that the remaining syllogisms are valid. They do this by introducing a “principle of affirmation” and a “principle of negation” for the first three figures. The principle of affirmation for the first figure is basically the dictum de omni, which they express as “whatever applies to an idea taken universally also applies to everything of which this idea is affirmed, or which is the subject of this idea, or which is included in the extension of this idea” (CG 193, B 147). The principle for the negative moods is the dictum de nullo, expressed as “whatever is denied of an idea taken universally is denied of everything of which this idea is affirmed. These principles are easily seen to stem from the claim that the general contains the particular, and from axiom 7 concerning negative propositions given in Part II : Every attribute denied of a subject is denied of everything contained in the extension of the subject in the proposition. The principles are then used to justify the syllogisms which have passed the rules. In the case of the second figure, only the principle of negative moods is needed, but to see how it applies, Arnauld and Nicole divide it into two, namely the case where the major premise is negative (Cesare and Festino) and the case where the minor premise is negative (Camestres and Baroco). The principle for the first two is the same as that given for the first figure. The principle for the second two is “Nothing which is included in the extension of a universal idea applies to any subject of which the idea is denied, since the attribute of a negative proposition is taken throughout its entire extension, as was proved in Part II ” (CG 197, B 150). The example they give of Camestres here is, Every true Christian is charitable. No one who is pitiless towards the poor is charitable. Therefore no one who is pitiless towards the poor is a true Christian.

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The application of the principle then is that “true Christian” is included in the extension of “charitable,” given the first premise, so since the idea “charitable” is denied of those pitiless towards the poor, “true Christian” which is included in this idea, is also denied of them. This use of these principles to justify the valid syllogisms breaks down somewhat after these two moods. The principles in the third figure concentrate on the conclusion being particular, since all third-figure syllogisms can only have a particular conclusion. The argument they provide for this is that given that the subject and predicate are united in the case of this other thing (i.e. the middle) they are “sometimes united with each other.” They point out this only works if in at least one case the middle term is taken universally. In the case of the affirmative moods in the third figure, the subject term and predicate term of the conclusion are each affirmed of a given term, namely the middle term. The principle they give is: “Whenever two terms can be affirmed of the same thing, they can also be affirmed of each other taken particularly” (CG 199, B 153). In the case of the negative moods, where again the middle term is the subject of both premises, their principle is “For any two terms, whenever one is denied and the other affirmed of the same thing, they can be denied of each other taken particularly” (CG 199, B 153). Here the argument is that “it is certain that they are not always united with each other, since they are not united in this thing [i.e. the middle term].”11 When it comes to the fourth figure, Arnauld and Nicole give four rules for the syllogism, but do not attempt to give principles as they had for the first three moods. They find the fourth figure unnatural, but include it, no doubt, because they want to emphasize that it should not be seen as a collection of indirect moods of the first figure. That way of thinking involves rearranging the syllogism so that the negation of a premise of a first figure syllogism is seen as the conclusion, and the negation of the conclusion of the first figure syllogism is seen as a premise. Arnauld and Nicole reject this line of thought because they see the argument as always starting with the conclusion and then finding premises from which it follows (CG 202, B 155).

5. Complex syllogisms Arnauld and Nicole’s real interest does not lie in the rules and principles for these figures of syllogisms. Their real interest appears to lie in their discussion of complex syllogisms and their general principle for determining validity, which is supposed to bypass all these rules.12 In keeping with their skeptical attitude

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toward formal logic, they focus on complex syllogisms which someone who has woodenly memorized the rules without genuinely understanding them would misclassify. These are the complex syllogisms, which mostly have middle terms occurring as a part of a complex term in one of the premises. Five of the six examples on which they focus are of syllogisms which are valid, but which might be taken to be invalid; only one is a case of a syllogism which might appear to be valid, but in fact is not. The solution, they believe is to “examine the soundness [solidité] of an argument by the natural light, rather than by the forms” (CG 205, B 158). While in part III , chapter 9 they use the natural light to simplify the arguments and bring them under the rules of the simple syllogisms, in chapters 10 and 11 they are more ambitious, advocating a general method for determining the validity of syllogisms without regard to the mood or figure. What is especially interesting about this section is that unlike the discussion we have just seen of the particular rules, the notion of the comprehension of an idea comes in. As we shall see, this leads to some difficulties. As is often the case, Arnauld and Nicole proceed with the help of specific examples. They give six examples in chapter 9. I will look at two of the examples. The first is: Divine law commands us to honor kings. Louis XIV is king. Therefore, divine law commands us to honor Louis XIV. CG 206, B 159

This appears superficially to be a syllogism in the second figure, containing all affirmative propositions, and thus by the rules it would be invalid. Specifically, it would appear to have an undistributed middle term, or in the terms of the PortRoyal Logic, the middle term would not be taken generally, violating the first of the six rules for syllogisms. But of course, the syllogism is not in standard form, with two terms joined by a copula. As Arnauld and Nicole put it, “kings” is not the predicate term in this premise. If we attempt to put it in standard form we will see that we have to rewrite the first premise. But how is it to be rewritten? Arnauld and Nicole think that it is clear, presumably because this is clear in the second premise, that “kings” is the middle term and that it is, in fact, taken generally (i.e. distributed) in the first premise. The first premise, they say, attributes commanding to the law, but honor to kings.13 From this observation they rewrite the syllogism as: Divine law commands that kings be honored. Louis XIV is king. Therefore, Divine law commands that Louis XIV be honored.

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We still don’t have a standard form proposition, but these can be rewritten, so the authors say, as: Kings ought to be honored. Louis XIV is king. Therefore, Louis XIV ought to be honored.

This appears to be a standard form Barbara syllogism and thus is valid. There is no argument that this procedure would work for every such complex proposition. Here the “Divine law commands” portion of the initial reading is taken as subordinate. But on their own view, it is not always the case that there is a simple method of determining which part of a proposition is to be taken as subordinate. In their discussion of such propositions in part II , Arnauld and Nicole state that it is occasionally the speaker’s intention that determines what is to be taken as subordinate, although perhaps for religious reasons we would have no reason to use the other reading. Curiously, the argument is valid even if the “kings be honored” part is taken as subordinate, as in Hobbes commands that kings should be obeyed, Louis XIV is a king, therefore etc.14 A further example of this rewriting is given: We ought to believe Scripture. Tradition is not Scripture. Therefore, Tradition ought not to be believed.

This syllogism may look like a second figure AEE syllogism and thus appear valid when it is in fact invalid. They argue that instead the syllogism should be rewritten as Scripture ought to be believed. Tradition is not Scripture. Therefore, Tradition ought not to be believed.

This is an invalid syllogism AEE of the first figure.

6. The General Principle for determining validity The real innovation of the Logic, as Arnauld and Nicole see it, is the proposal of a general principle to determine the validity of syllogisms which does not involve any of the reductions or references to standard-form syllogisms. Arnauld and Nicole recognize that for a syllogism to be valid, the premises must in some

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sense contain the conclusion. This much is not controversial. But from here they move very much away from formal logic. Recall that, for them, the purpose of a syllogism would be to determine for a given proposition whether it was true. This is why, when dealing with fourthfigure syllogisms, Arnauld and Nicole did not want to reduce these to syllogisms with different conclusions. The conclusions were always the starting points. What we then seek are propositions which are better known and which confirm the conclusion in question. But Arnauld and Nicole take this further. They identify one of the better-known propositions (i.e. premises) as the “containing proposition,” and another as the “applicative proposition,” which shows that the containing proposition actually contains the conclusion. Now this seems perhaps initially dubious: If we take, for example, a classic syllogism in Barbara, All M is P. All S is M. Therefore, All S is P.

We would be excused if we thought it was a mistake to think of either premise as “containing the conclusion.” But here is how this unfolds. Arnauld and Nicole will say that the major premise in this case states that the extension of M is included in the extension of P. The conclusion, therefore, is actually contained in this proposition; the second premise makes this explicit by indicating that the extension of S is contained in the extension of M. If this was as far as it goes, this way of putting things would be harmless enough, although it wouldn’t be clear that all of the valid syllogisms could be handled in this way. However, Arnauld and Nicole go beyond this. In the case of a Barbara syllogism, they say that either premise could be taken as the containing one. How, we might wonder, can All S is M be considered a containing premises? Here is their answer (they use as an example a syllogism with “slave of the passions” as the middle term, “unhappy” as the major term, and “evil person” as the minor): Whichever proposition you take, you could say that it contains the conclusion and the other one shows this. For the major premise contains it, because “slave of the passions” contains “evil” under itself. That is, “evil” is included in its extension and is one of its subjects, as the minor premise shows. And the minor premise also contains it, because the idea “slave of the passions” includes the idea “unhappy,” as the major premise shows. CG 212, B 163

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To see the minor as the containing proposition we have to look at the comprehension. Arnauld and Nicole are here explicitly suggesting what we objected to above, that All S is P not only says that the extension of S is included in the extension of P, but that the comprehension of P is included in the comprehension of S. Arnauld and Nicole go on to argue that the general principle of having one premise as the containing proposition and the other “applicative” as showing this will give us all the rules we had for syllogisms, i.e. the six rules given above. They only focus on the first ones, though, that the middle term must be taken universally at least once, and that the terms in the conclusion cannot be taken more universally than the terms in the premises. They think it is obvious this second rule follows from their new principle, for if the premises contained the conclusion, then the terms in the premises would have to have at least the extension of the terms in the conclusion, “For the less general does not contain the more general; ‘some man’ does not contain ‘all men’ ” (CG 212–213, B 164). When it comes to showing that the rule involving the middle term follows from the principle, Arnauld and Nicole again use the unfortunate principle that All S is P holds that the comprehension of P is contained within the comprehension of S. The syllogism they examine is one in Disamis: Some saint is poor. All saints are friends of God. So some friend of God is poor.

Again, they begin with the conclusion, “Some friend of God is poor,” and in wondering whether this is true, we reflect on another proposition we know is true, “some saint is poor.” Now the argument they give for the requirement that the middle term must be taken universally at least once is this: . . . it will never be evident that this proposition [“some saint is poor”] contains the conclusion except by another proposition where the middle term “saint” is taken universally. For it is obvious that in order for the proposition “some saint is poor” to contain the conclusion, “some friend of God is poor,” it is both necessary and sufficient for the term “some saint” to contain the term “some friend of God,” since they have the other term in common. Now a particular term has no determinate extension, and it contains with certainty only what is included in its comprehension and its idea. In consequence, in order for the term “some saint” to contain the term “some friend of God,” it is necessary for “friend of God” to be contained in the comprehension of the idea “saint.” CG 213, B 164

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As it is only in the proposition “All saints are friends of God” that we can obtain the statement that the comprehension of “friend of God” in “saints,” it is only with this proposition that we can show that the I proposition with which we started contains the I proposition with which we conclude. This analysis again seems to assume that All S are P asserts not only that the extension of S is included in the extension of P, but that the comprehension of P is included in the comprehension of S. Given the unsatisfactory nature of this last position, as it makes all universal propositions necessary, what are we to make of this? One way to understand these remarks from Arnauld and Nicole is to recognize that in these cases they are not separating out the logic of the propositions from the logic of discovery, or the epistemological situation of the inquirer. Thus, they would not have to hold that in all cases whenever someone asserts that All S are P they are asserting that the comprehension of P is contained in the comprehension of S, but rather that when the comprehension of P is contained in the comprehension of S we can take the minor premise (in the example from Barbara) as being the containing proposition and the major premise as showing that the conclusion is contained in it. Similarly in the case of the example from Disamis, which was to show that the middle term had to be taken universally at least once, we can understand that if we start with the I proposition, Some S are P, and we were trying to use this to determine whether this is true, then we would never be able to do this with simply Some M is S, because the particular terms do not have a determinate extension. Now of course if we have independent reasons for thinking All M are S is true, then we will, in fact, be able to draw this conclusion by consideration of the extensions, but then it would be hard for us to maintain that one of these premises was the containing one. Arnauld and Nicole seem to be saying that, given our epistemological situation, with Some M are P, we can see that Some S are P is true only if we can figure out a connection between M and S which will do the trick, and that will be when the comprehension of S is contained within the comprehension of M. My own view is that this mixing of epistemological situations with the issue of the rules of validity leads to confusion. The confusion calls into question the “general principle” for determining validity. Pariente has a separate criticism of the Port-Royal discussion of the “general principle.” Arnauld and Nicole say that “all the rules we have given function only to show that the conclusion is contained in one of the first propositions, and that the second reveals this, and that arguments are defective only when we fail to observe this and they are always valid when it is observed” (CG 212, B 164). As Pariente points out,15 Arnauld and Nicole argue for this only in the case of the

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first two rules (1: the middle term cannot be taken particularly twice, 2: the terms in the conclusion cannot be taken more universally in the conclusion than in the premises) and do not attempt to argue from the general principle for rules 3 and 4 (3: No conclusion can be drawn from two negative premises, 4: a negative proposition cannot be drawn from two affirmative premises), nor that part of rule 5 which involves negative propositions (if one of two propositions is negative, the conclusion must be negative). Pariente is right that there is no attempt to derive these rules from the general principle alone. Perhaps some story of the kind mentioned above could be given, from the account of the nature of negative propositions, part II , chapter 19, but it is hard to see how this would work without smuggling in what is being demonstrated. For example, Arnauld and Nicole presuppose that in the case of a negative syllogism, the negative premise will always be the containing premise. We may think then that the other premise would need to be affirmative; because only that will show that we would be licensed to substitute one term for another. Pariente would point out that this move seems to presuppose either that there will be at most one negative premise, or that the conclusion of a negative syllogism must always be negative. When Arnauld and Nicole give demonstrations of the use of the general principle, in chapter 11, part III , they do treat the principle as one that licenses substitution of terms. Example one, for example, is The duty of a Christian is not to praise those who commit criminal acts. Now those who fight duels commit criminal acts. Thus the duty of a Christian is not to praise those who fight duels.

This is a complex syllogism by the earlier definition, because “criminal acts” forms only part of the predicate of the first premise. Arnauld and Nicole point out that since “criminal acts” is taken universally in the first premise, the second premise shows that the conclusion is contained in this premise, since it shows that “fighting duels” is contained within “criminal acts.” In the third example: Divine law commands us to obey secular magistrates. Bishops are not secular magistrates. Therefore divine law does not command us to obey bishops.

We see that bishops are not included in the extension of “secular magistrates,” and so they assert, “the commandment to honor secular magistrates does not include bishops.” Nonetheless, the conclusion does not follow. Arnauld and Nicole say that it doesn’t follow because the major premise does not say that there are no other

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commandments, thus it doesn’t contain the conclusion by virtue of the minor premise. But here they seem to ignore their own position that in the case of a negative syllogism, it is the negative proposition which should always be seen as the containing proposition. To follow this they should have supplied an argument that “Bishops are not secular magistrates” does not contain the conclusion. The fourth and fifth examples which Arnauld and Nicole give of the application of the general principle were discussed by Jean-Claude Pariente and found not to involve simply the general principle.16 Of these the fifth example merits another look. The sophism is: Whoever says you are animal speaks the truth. Whoever says you are a goose, says you are an animal. Thus whoever says you are a goose speaks the truth. B, 167, CG 216

The analysis in the Port-Royal Logic using the general principle proceeds as follows. Either the conclusion is contained in the major premise, with the minor premise showing this, or the other way around. Looking at the major premise, we see it differs from the conclusion only in that the conclusion contains “goose” where the major premise contains “animal.” For this move to be justified, “animal” would have to be taken universally in the major premise, but they say, it is taken particularly in this premise. (We may note that this line of reasoning would seem to have the minor premise as simply “all geese are animals” rather than the actual minor.) It is taken particularly because it occurs in predicate position in the subordinate proposition, “you are an animal.” The thought here is that since the major is not taken over the entire extension of “animal,” we would not be licensed to substitute “goose” for “animal.” Arnauld and Nicole continue: Consequently it [the major premise] could contain “goose” only in its comprehension. To show this we would have to take the word “animal” universally in the minor premise, by affirming “goose” of every animal, which we could not do. And in fact this is not done here, since “animal” is still taken particularly in the minor premise, because, as in the major premise, it is the attribute of the subordinate affirmative proposition, “you are an animal.” B, 167, CG 216–17

Curiously, while they begin by saying that one or the other premises must contain the conclusion, they proceed only by examining the case where the major premise contains it.17 Yet when introducing the general principle, they said, using an example of Barbara, that we can either take the major premise

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as the containing one, in which case the minor will show that the minor term falls under the extension of the middle and thus the conclusion is contained in the major premise, or we can take the minor premise as the containing term, in which case the conclusion will be contained in it because the comprehension of the middle term includes the comprehension of the major term, as the major premise is supposed to show.18 In fact they cannot follow this structure, because they have not taken the whole middle term as the term to be substituted. As Pariente pointed out, their reading ignores what it was about the syllogism in the beginning which made it seem paradoxical. Instead of taking the term being substituted as “person who says you are an animal,” which is the middle term, they simply focus on the term “animal.” Pariente points out correctly that they did not do this when they gave as their first example of Barbara the syllogism (worthy of Peter Singer): Whoever lets people whom he ought to feed die of hunger commits homicide. All wealthy persons who do not give alms for public needs let those they ought to feed die from hunger. Therefore they commit homicide.

Here the middle term is “person who lets people whom he ought to feed die of hunger” and it is treated as a whole. If we treat the middle term in the syllogism above, “person who says you are an animal” as a whole, we seem to get another syllogism in Barbara. As Pariente points out we need some reason why it is not in Barbara, and his answer is that once we disambiguate, “says that you are an animal” and “says ‘you are an animal’ ” we can see the difficulty simply as a fallacy of four terms.19 What we see in all these cases is that the general principle for determining whether a syllogism is valid or not, does not seem to yield the results unambiguously without further moves, which presuppose the other rules of the syllogisms. The general principle was supposed to obviate the need to rewrite complex syllogisms as simple syllogisms, but in the end it does not avoid this.

7. Conclusion The Port-Royal authors, with their Cartesianism, began with skepticism of the syllogism. Descartes had focused on apprehending simple propositions and the immediate relations between them, and so had little use for the syllogism. Yet unlike Descartes, they saw a place for their analysis of syllogisms within the new

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logic. As we have seen, their discussion of the rules for syllogisms was based on the analysis of propositions given in part II of the Logic. They also framed their discussion of the syllogism in a very Cartesian way, by focusing on the single proposition of the conclusion, and seeing the syllogism as then giving a grounding for this conclusion. The focus on single propositions and the relations between them might also explain their advocating of the general principle presented in chapters 10 and 11 of part III . This principle saw the conclusion as actually being contained in one of the premises, and the other premise as helping reason to see that this is the case. In a sense we can see this as the Cartesian project of just examining the relation between two propositions. As I have suggested, it isn’t clear that this project will work well for all the rules of the syllogisms. Two points have often been noted about the Port-Royal Logic: its distinction between the extension and comprehension of terms, and its hostility toward formalism to the point that there are always concrete examples of specific syllogisms and never ever the use of variables.20 Pariente has gone further and suggested that the incorporation of the comprehension of ideas in the analysis of propositions and in the justification of the rules requires that specific examples be given as opposed to letters. As the suspect principle that from the proposition All S are P we can conclude that the comprehension of P is contained in the comprehension of S was the source of our difficulties with the discussion of the general principle, it may be useful to look at this point further. Pariente suggests that the exclusion of symbols “seems to result from the combination of two fundamental theses: the association of every idea with its comprehension and the intervention of the comprehension in the very mechanism of the syllogism” (Pariente, 1985, 252). He says the terms cannot be represented by symbolic letters because no comprehension is associated with such symbols. On the face of it, this seems odd, especially given Pariente’s endorsement of the suspect principle above. After all, no particular extension is associated with any letter either, but we have no difficulty using letters to explain the rules involving extensions. Pariente himself has no difficulty explaining his rules involving comprehension using the letters. The concern does not really involve explaining the rules of syllogisms, but something else. Here is Pariente’s concern: Given that the very truth of a proposition depends on the relation between the idea of the subject and the idea of the predicate, it would be impossible to assign a truth value to Some S is P as one could for

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Some man is a philosopher. In the first case, it can’t be determined; in the second case it is enough to consider the ideas of a man and of a philosopher to confirm that the comprehension of the second contains the first augmented by certain attributes. . . .21

This discussion highlights the problem. It isn’t that we cannot come up with rules for the syllogisms using letters as variables; it is rather that we cannot see from the proposition itself that it is true. What is odd is that here we seem to be able to conclude a priori by the relation of ideas that some man is a philosopher. Surely we would not want this to be a claim we would make about all such propositions. Yet if we look at the use Arnauld and Nicole made of the general principle to validate the rule that the middle term must be taken generally at least once, we see something not unlike the position Pariente gives. It was a direct result of focusing on the epistemological situation for the particular problem. The Port Royal Logic made use of the distinction between comprehensions and extensions and included the relation of the comprehension of the ideas involved in its analysis both of propositions and syllogisms. But the relations discussed work only for particular examples, and thus cannot be generalized. If we require the connections between comprehensions for all affirmative propositions, we have an implausible theory of propositions. If we restrict our discussion to propositions for which the relation of comprehensions is true, then we have a very incomplete theory of syllogisms if we see it as based on the general principle.

Notes 1 Clair and Gibral list 49 French editions after the death of the authors, the latest of these appearing in 1877. They also list 13 Latin editions, with the last mentioned appearing in 1749, and nine English editions, starting with a translation “by several hands,” in 1685 and ending with the Baynes translation, which appeared in 1851 and again in 1861 and 1872. New translations in English appeared in the twentieth century, the best being Jill Buroker’s 1996 translation. (Logic or the Art of Thinking, Cambridge, 1996). Quotations from the Port Royal Logic will be from the Clair and Gibral edition (La Logique ou l’art de penser, Paris, 1965, hereafter CG ) and the Buroker translation (hereafter B). I have also made use of the new critical edition of Dominique Descotes (La Logique, ou l’art de penser, Paris, 2014), which gives as the main text the second edition of 1664 rather than the fifth edition of 1683.

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2 René Descartes, Philosophical Writings of Descartes, trans. J. Cottingham, R. Stoothoff and D. Murdoch, vol.1 (Cambridge, 1985), 12. 3 See the discussion in the Second Discourse where they defend the title against the title The Art of Reasoning Well (CG 27, B 15). 4 I say “may have the effect,” because if all triangles happen to be right triangles, then it wouldn’t have this effect. The Port-Royal Logic uses this fact to distinguish between restrictive clauses and non-restrictive clauses which they call either a determinations or an explications. See CG 65, B 45. 5 J.-C. Pariente, L’Analyse du langage à Port-Royal (Paris, 1985), 265. 6 L’attribut d’une proposition affirmative est affirmé selon toute sa compréhension, c’est à dire, selon tous ses attributs. CG 170. 7 J.-C. Pariente. L’Analyse du langage à Port-Royal, 266. 8 See J. V. Buroker, “Judgment and Predication in the Port-Royal Logic,” in The Great Arnauld and Some of His Philosophical Correspondents, ed. E. Kremer (Toronto, 1994), 10ff. Buroker’s criticism is part of her overall criticism of Pariente’s view that the copula asserts an identity, or a partial identity. So, in the case of an affirmative proposition, what is asserted is the identity of the extension of the subject with a part of the extension of the predicate of the subject, and the identity of the comprehension of the predicate with a part of the comprehension of the comprehension of the subject, and with a negative proposition, the separation (or non-identity) of the extension of the subject from the entire extension of the predicate, and the separation or non-identity of a part of the comprehension of the predicate from the comprehension of the subject. 9 This is in the letter to Leibniz of May 13, 1686 in The Leibniz-Arnauld Correspondence, ed. and trans. H. T. Mason (Manchester, 1967), 30. Of course Leibniz responds that absolutely everything true of an individual is contained in the concept, that there is nothing that could be or not be in him without him ceasing to be Arnauld. Leibniz thinks Arnauld’s real worry is that this makes all these predicates necessary, but his own view provides a way out of that. See his remarks on Arnauld’s letter (The Leibniz-Arnauld Correspondence, 50). The important point is that twenty years after writing the Port Royal Logic, Arnauld did not think, as Leibniz did, that all affirmations involved attributing the comprehension of the predicate to the comprehension of the subject. 10 I.e. “conclusive moods” (CG 189). In this context they should not automatically be assumed to be valid. Generally Arnauld and Nicole call an argument “good” (bon) when they want to assert that an argument is what we call valid. As Buroker notes, after this Arnauld and Nicole occasionally use “concluant” to mean valid. 11 Jean-Claude Pariente (L’Analyse du langage à Port-Royal, 343) suggests correctly that this formulation is sloppy. For while it licenses the syllogism in BOCARDO, some angers are not blameworthy, every anger is a passion, therefore some passions

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are not blameworthy, it would also seem to license “Every anger is a passion, some angers are not blameworthy, therefore some blameworthy things are not angers” which is, of course, invalid with its illicit major. But it seems to be the case that this principle would allow this. The actual wording of the principle is “Lorsque de deux termes l’un peut être nié & l’autre affirmé de la même chose, ils se peuvent nier particulièrement l’un de l’autre” (CG 199). If we take the last part to say “the first can be denied of the second” perhaps “l’un peut être nié particulièrement de l’autre” we would at least insure that it was the attribute denied of the middle that would also be denied of the other term, as the minor premise of a third-figure syllogism is always affirmative, as specified by the first rule. But then the justification for the rule would need to be expanded. 12 At the beginning of chapter 3 they say that “this chapter and the following chapters up to chapter 12 are those mentioned in the Discourse as containing subtle points necessary for speculating about logic, but having little practical use” (CG 182, B 138). This remark would seem to include also chapters 10 and 11, which they do think are of practical use. Dominique Descotes points out in his new critical edition that this must be a mistake, and that the correct intention was simply to skip to chapter 10. Descotes accounts for the mistake by two as counting the suppressed chapter 9 of the earlier editions and including chapter 13, on syllogisms with conditional conclusions which they may have originally wished to put earlier. See Antoine Arnauld et Pierre Nicole, La Logique ou L’art de penser, ed. Dominque Descotes, 23–26. 13 CG 207, B 159. Actually, it would probably have been better to have said “being honored” is what is being attributed to the kings, given the context. 14 In part II , chapter 8 they give the example of the proposition “All philosophers assure us that heavy things fall to earth of their own accord.” If the speaker is intending to affirm that heavy things fall on their own, then the “all philosophers assure us . . .” operator is taken as subordinate. However, if I intend to make a statement about the philosophers, then this part isn’t subordinate (or incidental). See CG 129, B 95. Pariente also sees this rewriting as not something that can be generalized, but his discussion is further complicated by working with the discussion in part II chapter 5, which took “Brutus killed a tyrant” as really asserting two different things: Brutus killed someone and the person he killed was a tyrant. This analysis breaks the predicate up. Interpreting the rewriting of the syllogism concerning honoring kings in this way, Pariente obtains the following rewriting: If x is king, divine law commands us to honor x. If x is Louis XIV, x is king. Therefore, if x is Louis XIV, divine law commands us to honor x. (L’Analyse du langage à Port-Royal, 366). 15 J.-C. Pariente, L’Analyse du langage à Port-Royal, 354.

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16 J.-C. Pariente, L’Analyse du langage à Port-Royal, 361, 367–373. 17 Pariente’s resume of their position also only deals with the case where the major is the containing premise (L’Analyse du langage à Port-Royal, 369–370). 18 See B 163, CG 212. This involves using the principle, which I objected to previously, that when All S are P is true, the comprehension of P is included in the comprehension of S. This principle also seems to be invoked in the discussion of this fifth example. 19 J.-C. Pariente, L’Analyse du langage à Port-Royal, 372. So the first premise in the syllogism restored to three terms would be “Whoever says ‘you are an animal’ speaks the truth,” and the minor, “Whoever says ‘you are a goose’ says ‘you are an animal’ ,” would be false. If we restored it the other way, presumably the major premise “Whoever says that you are an animal” would not always be speaking the truth, if their way of saying that you are an animal was by means of saying that you are a dog or a goose, for example. 20 See R. Blanché La logique et son histoire (Paris, 1970), J.-C. Pariente. L’Analyse du langage à Port-Royal, 251ff, and Antoine Arnauld and Pierre Nicole, La Logique ou L’ art de penser, 47. 21 J.-C. Pariente. L’Analyse du language à Port-Royal, 252.

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Locke and Syllogism The “Perception Grounded” Logic of the Way of Ideas Davide Poggi University of Verona

1. Introduction: The fight against the prejudices and the aim of the Essay Together with the critical reconstruction of the knowledge of the world and of the subject, too, the “Historical, plain Method”1 shown by Locke in the Essay concerning Human Understanding (16901), intends to clarify, as a preliminary task of Bacon’s origin, the uncritically assumed truths which impede the real progress of the knowledge.2 The call to the necessity of the achievement of a “starting point,” that is a condition of ἐποχή for which the mind, far from being a white paper (since this situation of original naivety is irreproducible by an adult psyche), is rather supposed to be white paper3 (an ideal goal, an “as if ” full of a constant effort for returning to the logical-gnoseological Anfang, “the Original of those Ideas, Notions, or whatever else you please to call them, which a Man observes, and is conscious to himself he has in his Mind”),4 is firmly repeated even from the Epistle Dedicatory to Thomas Herbert, eighth Count of Pembroke and fifth Count of Montgomery: [There is] nothing more to be desired for Truth, than a fair unprejudiced Hearing [. . .]. ’Tis Trial and Examination must give it [i.e. Truth] price, and not any antick Fashion: And though it be not yet current by the publick stamp; yet it may, for all that, be as old as Nature, and is certainly not the less genuine.5

The analytical-descriptive and synthetic-reconstructive examination of the Ideas present in/to the mind/understanding has some precise recipients, which we 105

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could define as the hawkers and hunters6 of the truth, or “the Lovers of Truth”7 (an expression which certainly guided Leibniz afterwards in the choice of the characters’ names of the Nouveaux Essais): He who has raised himself above the Alms-Basket, and not content to live lazily on scraps of begg’d Opinions, sets his own Thoughts on work, to find and follow Truth.8

It is not a simple rhetorical expedient: in these truths, which are considered indisputable (real idòla of the mind, even though Locke never uses this term—in Latin or in the English equivalent—except for when it is used with its theologicalreligious meaning)9, a danger is hidden and it is, in effect, twofold. On the one hand, the truths as the (theoretical and practical) principles which are considered innate (because of education, of habit, of love for the current to which one belongs and of the blind faith in the authority)10 act a parte ante, because they compromise the starting perspective of the researches and “poison the source” (that is, referring to Locke’s famous metaphor of navigation, like giving inappropriate nautical papers to the sailors or fake reference/orientation points). So, this ends up creating an ongoing dialectic of the systems, which puts the reason into the discouragement of that sceptical result which was afterwards so dreaded and deprecated by Kant in the first edition of the Kritik der reinen Vernunft (1781): It shall suffice to my present Purpose, to consider the discerning Faculties of a Man, as they are employ’d about the Objects, which they have to do with: and I shall imagine I have not wholly misimploy’d my self in the Thoughts I shall have on this Occasion, if, in this Historical, plain Method, I can give any Account of the Ways, whereby our Understandings come to attain those Notions of Things we have, and can set down any Measures of the Certainty of our Knowledge, or the Grounds of those Perswasions, which are to be found amongst Men, so various, different, and wholly contradictory; and yet asserted some where or other with such Assurance, and Confidence, that he that shall take a view of the Opinions of Mankind, observe their Opposition, and at the same time, consider the Fondness, and Devotion wherewith they are embrac’d; the Resolution, and Eagerness, wherewith they are maintain’d, may perhaps have Reason to suspect, That either there is no such thing as Truth at all; or that Mankind hath no sufficient Means to attain a certain Knowledge of it.11

On the other hand, these truths impede that, a parte post, it could be possible to exit from that labyrinth of difficulties and contradictions described by the philosopher in the Epistle to the Reader12 (this is the equivalent, still metaphorically, to trust ourselves to inadequate instruments and pilots). It would be wrong

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indeed to think that Locke intends as “truths” only the principles, the abstract and universal propositions which, more or less risen to the consciousness, constitute the formal element of the perception: what the English philosopher addresses his critical examination to, is also the praxis with which the research and the philosophical reasoning are conducted. Thus, a modus philosophandi characterized by the adoption of the quickest explanation13 (the reference is to those that Coste, in the French translation of the Essay, defined as “les Partisans” des idées innées/principes innez)14 condemns the reason to laziness and dogmatism, while the use of a dark terminology and of a learned subtlety makes the philosophical research sterile and empty (the logic and the disputationes of the Schoolmen are pointed out as the favoured examples of the abuse of words and, even since the Draft B, Locke showed to have this problem at heart):15 In an Age that produces such Masters, as the Great–—Huygenius, and the incomparable Mr. Newton, with some other of that Strain; ’tis Ambition enough to be employed as an Under-Labourer in clearing Ground a little, and removing some of the Rubbish, that lies in the way to Knowledge; which certainly had been very much more advanced in the World, if the Endeavours of ingenious and industrious Men had not been much cumbred with the learned but frivolous use of uncouth, affected, or unintelligible Terms, introduced into the Sciences, and there made an Art of, to that Degree, that Philosophy, which is nothing but the true Knowledge of Things, was thought unfit, or uncapable to be brought into well-bred Company, and polite Conversation. Vague and insignificant Forms of Speech, and Abuse of Language, have so long passed for Mysteries of Science; And hard and misapply’d Words, with little or no meaning, have, by Prescription, such a Right to be mistaken for deep Learning, and heighth of Speculation, that it will not be easie to persuade, either those who speak, or those who hear them, that they are but the Covers of Ignorance, and hindrance of true Knowledge.16

Coming to the topic of the present essay, these remarks are fundamental in order to understand the position expressed by Locke in the Fourth Book of the Essay about the syllogism and the Aristotelian-Scholastic deductive logic: the use of the syllogism as necessary instrument for the reasoning (ars ratiocinandi or dialectica) and the discovery (ars inveniendi) must be counted amongst the truths considered to be “undisputed,” that is un-disputable de jure, when actually they are only not-disputed de facto. The link, which unifies Bacon’s project and the criticism to Aristotle’s formal logic, becomes explicit in Of the Conduct of the Understanding, which would have had to constitute an addition to the Essay (the twentieth chapter of the

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Fourth Book),17 being as it were its “discipline” (similarly to all the ending chapters of each Book, however with a more general nature). This essay begins in fact with the quotation of the criticism against the dialectica made by Bacon in Instauratio Magna. Locke considers the blind faith in the study of the logick as one of the pathological behaviors of the human understanding, which need to be corrected (and, if one wants to be a good educator, it is appropriate not to instil young people)18: The Logick now in use has soe long possessed the chair as the only art taught in the Schools for the direction of the minde in the study of the Arts and sciences that it would perhaps be thought an affectation of Noveltie to suspect that rules that have served the learned world these two or three thousand years and which without any complaint of defects the learned have rested in are not sufficiente to guide the understanding. And I should not doubt but this attempt would be censured as vanity or presumption did not the Great Lord Verulams authority justifie it. [. . .] In his preface to his Novum Organum concerning Logick he pronounces thus [. . .] Si quidem Dialectica, quæ recepta est, licet ad civilia et artes, quæ in sermone et opinione positæ sunt, rectissime adhibeatur; [. . .] ad errores potius stabiliendos et quasi figendos, quam ad viam veritati aperiendam valuit. [. . .] A few rules of Logick are thought sufficient in this case for those who pretend to the highest improvement whereas I thinke there are a great many natural defects in the understanding capable of amendment which are over looked and wholy neglected. And it is easy to perceive that men are guilty of a great many faults in the exercise and improvement of this facultie of the minde which hinder them in their progresse and keep them in ignorance and error all their lives.19

If from the examination of the faculties of the mind and of its contents, too, should arise both a “cure” for the pathologies of the understanding and a new logic, not only would Bacon’s project be fulfilled in the Essay concerning Humane Understanding, but so also would the objective of one of the works that Locke bought during his stay in France (from 1675 to 1679), the Logica vetus et nova (1654) of the Cartesian Johann Clauberg, that is to transform the logic into the “ad vitam rationalem gubernandam [. . .] necessaria”20 medicine.

2. Locke and the Reasoning: From the logical deductivism to the intuitionistic inductivism The considerations about the validity of the syllogistical-demonstrative method are a prosecution of what Locke wrote in the First Book (and they date from the

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First Draft of 1671)21 about the psychogenesis of the principles of identity and of non-contradiction (“those magnified Principles of Demonstration [. . .], which of all others I think have the most allow’d Title to innate”),22 whose self-evidence has not to be explained by recurring to the innatism, but by going into the heart of the perception, that is the level of the ideas or perceptions concretely and actually present and manifest and of the elaboration to which they are subjected by the cognitive functions of the mind. The Lockean new logic has its theoretical basis in this “subject–object dialectic” (the uniqueness of the term perception, especially in Locke as the one who denies a psychic unconscious, points out the inseparability of content and cognitive act) and, thus, it places itself on the contact point between the “logic of the ideas” and the “logic of the faculties,” far from the logic of the rules/forms of predication: Whereas had they examined the ways, whereby Men came to the knowledge of many universal Truths, they would have found them to result in the minds of Men, from the being of things themselves, when duly considered; and that they were discovered by the application of those Faculties, that were fitted by Nature to receive and judge of them, when duly employ’d about them.23

The “Maxims universally received”24 come from the perception of the agreement or the disagreement between ideas, that is from the knowledge of the connexions between psychic contents: since the first and the most certain of those relationships, grasped without fail in the concrete giving of any psychic fact “at first view [i.e. intuitively], by its [i.e. of the mind] natural power of Perception and Distinction,”25 is the one that a content has with itself (identity) and with what is other-from-itself (diversity as discordance), the principles of identity and non-contradiction are the transposition on the abstract and universal level of the nature of the apprehension of these relationships and are characterized by the maximum extension and predicability and by the self-evidence: Those first [i.e. ideas], which are imprinted by external Things, with which Infants have earliest to do, and which make the most frequent Impressions on their Senses. In Ideas thus got, the Mind discovers, That some agree, and others differ, probably as soon as it has any use of Memory; as soon as it is able, to retain and receive distinct Ideas. But whether it be then, or no, this is certain, it does so long before it has the use of Words; or comes to that, which we commonly call the use of Reason. For a Child knows as certainly, before it can speak, the difference between the Ideas of Sweet and Bitter (i.e. That Sweet is not Bitter).26

This approach allows Locke, in § 11 Chapter VII of the Fourth Book, to distinguish, on the one hand, the knowledge that the subject has about the logical principles

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as “principles” (meaning propositions constituted by terms standing for abstract and universal ideas) that the subject applies to the concrete cases, framing them into a precise epistemology (explicative order) and, on the other hand, the perception of the identity of a real content with itself and its distinction from another one (critical-gnoseological order): Would those who have this Traditional Admiration of these Propositions, that they think no Step can be made in Knowledge without the support of an Axiom, no Stone laid in the building of the Sciences without a general Maxim, but distinguish between the Method of acquiring Knowledge, and of communicating it; between the Method of raising any Science, and that of teaching it to others as far as it is advanced, they would see that those general Maxims were not the Foundations on which the first Discoverers raised their admirable Structures, nor the Keys that unlocked and opened those Secrets of Knowledge.27

Therefore, a strong re-consideration of the validity of the deductive method ex praecognitis and ex praeconcessis is implied: whereas the demonstrative knowledge, that of the scientific syllogism, is founded on premises which must be “true, primary, immediate, better known than, prior to and cause of the conclusion,”28 these premises are, ultimately, the intuitions, that is the immediate and irrefutable vision of the characters of the psychic contents and their relationships (concerning both structural and existential elements). Moreover, following what both Descartes in La recherche de la Vérité par la Lumiére naturelle (1701)29 and Arnauld in La Logique ou l’Art de penser (1662)30 had already underlined, founding a reasoning or a demonstration on axioms, such as the principles of identity and non-contradiction, is of no use either for the discovery of new ideas, or for a real demonstration (since they can be used to endorse out-and-out contradictions)31: If rightly considered, I think we may say, That where our Ideas are determined in our Minds, and have annexed to them by us known and steady, Names under those settled Determinations, there is little need, or no use at all of these Maxims, to prove the Agreement, or Disagreement of any of them. He that cannot discern the Truth or Falshood of such Propositions, without the help of these, and the like Maxims, will not be helped by these Maxims to do it.32

Following Descartes, to the foundationism of Aristotle’s epistemology Locke opposes an epistemology that, focused on the individuality of the knowledge, intends to come back to the visual-experimental origin of the de-monstrare (the intuitive knowledge is an immediate or simple view and, also in this case, the strength of the influence of the thought of both Descartes and a “Cartesian

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heterodox” as Malebranche clearly appears).33 In this sense, in the Fourth Book of the Essay, Locke states to consider plausible that the cause of “that mistaken Axiom, that all Reasoning was ex praecognitis et ex praeconcessis”34 was the constant need for an intuitive support in each step of the scientific reasoning: the reasoning correctly happens and it is conclusive insofar as it is grounded on something which has the greatest evidence (except that they are not axiomatic principles anymore, but indubitable perceptions). The mistake made by Edward Stillingfleet, in Discourse in Vindication of the Doctrine of the Trinity (1697), when objecting to Locke that the ideas do not “support” the demonstration of the existence of God, but “the good and sound Reason,”35 meaning the reasoning supported by the self-evident and universal principles (“Principles of True Reason,” as “all that exists must have a cause,” etc.),36 is that of hypostatizing the rules of composition and organization of the ideas by creating something that is not only distinct, but also heterogeneous and logically prior to the perceptions which are involved in the reasoning. In the 1697 Letter to the bishop of Worcester (the first one of the epistolary controversy which finished in 1699, the year of Stillingfleet’s death), Locke offers the example of a man who wants to demonstrate that the sum of the internal angles of a triangle is equal to the sum of two right angles (an example already presented in the Essay)37: he certainly resorted to a scheme, drawing an image. However, such visual aid has no other role in the reasoning, except for helping the inspection of the ideas implied in the problem to be solved. It is not really a question of assigning a “sensitive” nature to the demonstration (as if the ideas would be pictures similarly to Hobbes’ apparitiones), but rather of giving some “visual” facilities to a perceptive process which is intellective and goes over the mere sensitivity. Therefore, Locke writes as follows: The considering and laying these [i.e. ideas] together in such order, and with such connexion, as to make the agreement of the ideas of the three angles of the triangle, with the ideas of two right ones, to be perceived, is called right reasoning, and the business of that faculty which we call reason; which when it operates rightly by considering and comparing ideas so as to produce certainty, this showing or demonstration that the thing is so, is called good and sound reason. The ground of this certainty lies in ideas themselves, and their agreement or disagreement, which reason neither does nor can alter, but only lays them so together as to make it perceivable; and without such a due consideration and ordering of the ideas, certainty could not be had: and thus certainty is placed both in ideas, and in good and sound reason.38

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Here Locke not only insists on the “passivity” of the understanding in what pertains to the knowledge (because the mind does nothing but find or, in other terms, be aware of the characters of the ideas), but he also strongly stresses that the reasoning is not a mechanism that “happens in” the subject (inhabitatio) and he only witnesses. Actually, the understanding cooperates to the formation of the stream of ideas (Locke writes “ideas used in train”), carefully considering the characters of the psychic data, evaluating whether they agree or not and judging which order is better for the emersion/perception of those interconnections: Nothing truer than that it is not the idea that makes us certain without reason, or without the understanding: but it is as true, that it is not reason, it is not the understanding, that makes us certain without ideas. It is not the sun makes me certain it is day, without my eyes; nor it is not my sight makes me certain it is day, without the sun; but the one employed about the other. Nor is it one idea by itself, that in this, or any case, makes us certain; but certainty consists in the perceived agreement or disagreement of all the ideas that serve to show the agreement or disagreement of distinct ideas, as they stand in the proposition, whose truth or falsehood we would be certain of. The using of intermediate ideas to show this is called argumentation, and the ideas so used in train, an argument; so that, in my poor opinion, to say, that the argument makes us certain, is no more than saying, the ideas made use of make us certain.39

This kind of approach allows us to especially release the reasoning, that is the exercise of the reason in the strict sense (as cognitive function concerning the demonstration, namely the research of the intermediate ideas, proofs or mediums40 and the inference-illation),41 from the “verbal” aspect of the reasoning, which remains important (as important as it is fundamental for the man to be part of a society and to communicate his ideas to others) but is no longer crucial for the reasoning: in this context, the Lockean treatment of the mental propositions is essential. Although it is difficult to distinguish this type of propositions from the verbal propositions (because of the constant use of words, meaning verbal signs for expressive purposes and, in case of complex ideas, as abbreviation), for “mental propositions” it is not to be intended as the so-called “internal speech” (that is, that form of interior locution with imaginative basis), but as what it accompanies and defines as monologue or dialogue that the subject does with himself (with noticing or clarifying value): Locke refers to the “bare consideration of the Ideas, as they are in our Minds, stripp’d of Names.”42 This consideration is “the way our Mind takes in Thinking and Reasoning,”43 the natural and spontaneous (affirmative or negative) synthesis carried out by

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the understanding considering only the agreement/disagreement immediately perceived or supposed to be between the ideas. As we can see, the “native rustick Reason,”44 that is the use of the “not corrupted by Education”45 rational function (it should be noted that Locke uses a terminology which then became characteristic of Rousseau) is what “we usually call knowing”46 in its strict sense (subsequently, the truth of these mental propositions is the “Certainty of Knowledge”).47

3. Locke and the syllogism: Is it really “the great instrument of reason”?48 Pars Destruens and Pars Construens The natural unfolding of the reason following what, in Spinoza’s terms, could be called the ordo et connexio idearum (leaving aside, for now, the problem of the correspondence with the res, a problem which is connected to the present theme, but distinct from it), articulates in those four degrees, which go from “discovering, and finding out of the Proofs,”49 to the progressive ordering according to the criteria of clarity and evidence, so that the “Connexion and Force” of the proofs or intermediate ideas is “plainly and easily perceived”50 and it could be possible to reach the formulation of a correct conclusion. The examination of the validity and the role of the syllogism as instrument for the reasoning is inserted in this context and in this precise point of Locke’s reflection, in § 4 Chapter XVII, a paragraph whose extension, unchanged for the first three editions of the Essay (16901, 16942, 16953), quintupled in the fourth edition (1700) and whose content undergoes many changes (anyway, without being altered). The question that guides the English philosopher concerns the relationship between the spontaneous mental reasoning and that particular form of the verbal reasoning (I coin this expression, not used by Locke, inspired by the Lockean expression verbal proposition) such as the syllogism: does the latter “correspond” to the former? Is the syllogism a real support for the psychic perceptive-demonstrative process? Indeed, this is not just a passage from the mental level to the verbal one (for which it is necessary that the words are linked respecting the relationships perceived between the ideas they stand for), but it is a passage from the level of the intimate nature of the reasoning and of its spontaneous “rhythm” and the level in which the sequence and the composition of the terms happens according to precise rules and forms. Locke writes:

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Syllogism serves our Reason, but in one only of the forementioned parts of it [Locke refers to the four Degrees of Reason of which he has dealt with in the previous paragraph]; and that is, to shew the connexion of the Proofs in any one instance, and no more: but in this, it is of no great use, since the Mind can perceive such Connexion where it really is, as easily, nay, perhaps, better without it. If we will observe the Actings of our own Minds, we shall find, that we reason best and clearest, when we only observe the connexion of the Proofs, without reducing our Thoughts to any Rule of Syllogism. [. . .] And I believe scarce any one ever makes Syllogisms in reasoning within himself.51

The syllogism, as it has been used and transmitted by the Aristotelian-Scholastic tradition, instead of helping the knowledge, complicates it with superfluous superfetations and forced rules (“perplexed Repetitions, and Jumble”),52 obliging the philosopher to operate on a “super-structural” and derived level, ignoring the “structural” and decisive one (“that short natural, plain order”).53 This criticism has, in my opinion, an interesting premise in the Port-Royal Logique: introducing the treatment of the raisonnement, at the beginning of the Troisieme Partie, Arnauld seems indeed to make a distinction, in the reasoning, between a “formal” mistake (raisonner mal suivant les principes or mal tirer la conséquence) and a “material” one (raisonner sur des faux principes), giving priority to the latter. Thus, he describes the knowledge of the rules of the syllogistic construction as an exercise of the mind or, at the most, as an instrument to help the man who already has un esprit naturellement vif et pénétrant (therefore who is able to argue and discover the logical fallacies par la seule lumière de la raison): Cette partie que nous avons maintenant à traiter, qui comprend les regles du raisonnement, est estimee la plus importante de la Logique, & c’est presque l’vnique qu’on y traite avec quelque soin. Mais il y a sujet de douter si elle est aussi vtile qu’on se l’imagine. La pluspart des erreurs des hommes, comme nous avons déja dit ailleurs, viennent bien plus de ce qu’ils raisonnent sur des faux principes, que non pas de ce qu’ils raisonnent mal suivant leurs principes. Il arrive rarement qu’on se laisse tromper par des raisonnemens qui ne soient faux, que parce que la consequence en est mal tirée: Et ceux qui ne seroient capables d’en reconnoistre la fausseté par la seule lumiere de la raison, ne le seroient pas ordinairement d’entendre les regles que l’on en donne, & encore moins de les appliquer. Neanmoins quand on ne considereroit ces regles que comme des veritez speculatives, elles serviroient toûjours à exercer l’esprit: Et de plus on ne peut nier qu’elles n’ayent quelque vsage en quelques rencontres, & à l’égard de quelques personnes qui estant d’vn [esprit] naturel vif & penetrant, ne se laissent

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quelquefois tromper par de fausses consequences, que par faute d’attention, à quoy la reflexion qu’ils feroient sur ces regles seroit capable de remedier.54

Again, where Arnauld dealt with the loci argumentorum, he provided the reader with an articulated criticism against the utility of the loci as instruments to find the subjects of the argumentation, a criticism focused on the inessentiality and artfulness of those lieux compared to the natural reasoning that each man does in himself, apart from the erudition in logical and topical matters: On pourroit dire au contraire, que comme on pretend enseigner dans les lieux l’art de tirer des argumens & des syllogismes, il est necessaire de sçavoir auparavant ce que c’est qu’argument & syllogisme. Mais on pourroit peut-estre aussi repondre que la nature seule nous fournit vne connoissance generale de ce que c’est que raisonnement, qui suffit pour entendre ce qu’on en dit en parlant des lieux. [. . .] Il est vray que tous les argumens qu’on fait sur chaque sujet se peuvent rapporter à ces chefs & à ces termes generaux qu’on appelle Lieux; mais ce n’est point par cette methode qu’on les trouve. La nature, la consideration attentive du sujet, la connoissances de diverses veritez les fait produire; & ensuite l’art les rapporte à certains genres.55

Coming back to Locke, only the perceptive-cognitive level is the “substrate” common to all men: for this reason the philosopher does not hesitate to use the so “blamed” adjective native in relation to the power to perceive the agreement/ disagreement between ideas,56 “the Eye or the perceptive Faculty of the Mind,”57 whereas he underlines, similarly to what he did in the First Book to demonstrate the not-innateness of the theoretical and moral principles, that the art of the correct construction/formulation of the syllogism belongs to the narrow circle of those who have studied in the scholae and not to the greater part of mankind (who think without the instrument of Aristotle and of the Schoolmen, as the indigenous populations of Asia or America, the children or the “Country Gentlewoman” always do).58 So, with biting irony, the English philosopher goes back to the classical definition of “man” as “rational animal” and writes: God has not been so sparing to Men to make them barely two-legged Creatures, and left it to Aristotle to make them Rational, i.e. those few of them that he could get so to examine the Grounds of Syllogisms [. . .]. God has been more bountiful to Mankind than so. He has given them a Mind that can reason without being instructed in Methods of Syllogizing: The Understanding is not taught to reason by these Rules; it has a native Faculty to perceive the Coherence, or Incoherence of its Ideas, and can range them right, without any such perplexing Repetitions.59

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That does not mean that there is an absolute incompatibility between the syllogism and the illation or inference, since it is certainly possible to reduce the reasoning (in-formal logic) to the forms of syllogism (this is an interesting concession to which I will come back shortly), but it is likewise certain that they do not represent the unique mode or the best instrument to use the reason. When the syllogism itself has a conclusive result, the certainty of the truth that the syllogism allows us to acquire is always grounded on the intuition of the fact that the link searched between two ideas (major and minor terms) is a third idea connected to both (medium term): if there were not this perception, it would mean that every idea and so, in Aristotle’s terms, every medium term could be valid for the conclusion of the reasoning. After all, this does not represent only a criticism against Aristotle: the central role assigned to the intuitive knowledge in each “Link of the Chain”60 of the reasoning gives special emphasis to that relationship between the intellect and the reality which was the deepest meaning of Aristotle’s medius terminus. But this close connection with the reality is totally deprived of that metaphysic value, which it had for the Greek philosopher and it assumes merely gnoseologicalexperimental features. It remains to examine, as I said before, the fact that, even if hostile to the obscurities of the deductive-syllogistical method, Locke admits: I readily own, that all right reasoning may be reduced to his Forms of Syllogism.61

Is it simply a “rhetorical” concession, that is a kind of fair play which, due to the respect for Aristotle, comes close to put Locke in contradiction with his own words? The answer is, in my opinion, negative: the aim of the English philosopher is to propose a re-formatio of the form of the syllogism by looking at the mental reasoning, an adaequatio logicae et rationis, in order to fill the incongruity between “the Form Syllogism now has” and “that [i.e. Form] which in Reason it ought to have.”62 It is a reform proposal that Locke felt with a matter of urgency, because it does not only represent a subject of the extension of § 4 Chapter XVII, but it also persistently recurs (once again, from the fourth edition of the Essay) and, maybe, ad abundantiam, at the end of § 8 (“One thing more I crave leave to offer about Syllogism, before I leave it”),63 running the risk of bringing the speech “off topic” (indeed, this paragraph has a different subject, that is “We reason about Particulars”).64 In § 4,65 Locke invites the readers to consider the following example: given three ideas, i.e. homo, vivens and animal, of which the latter is assumed as intermediate (medius terminus), we want to prove that the man is living (homo

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est vivens). Trying to solve the question according to the Aristotelian-Scholastic logic, a syllogism should be constructed for which, from the premises omne animal est vivens (major) and omnis homo est animal (minor), it would be possible to get to the conclusion omne homo est vivens. Well, the English philosopher wonders, isn’t it easier and more immediate to understand that the idea/term of animal is the medium term between homo and vivens by putting it in the linear series of homo—animal—vivens rather than in the series of animal—vivens—homo—animal (that is a syllogism in which animal is first the subject of the major premise, then the predicate of the minor one)? Nonetheless it has to be admitted that, in this paragraph, Locke is not fully clear: he will provide a more detailed explanation in the above mentioned § 8, where he states that, if one wants to give an adequate form to the syllogism (that is, more representative of the natural reasoning), the order of the premises must be inverted. Locke writes: [It] might be easily done by transposing the Propositions, and making the Medius Terminus the predicate of the First, and the Subject of the Second. As thus, Omnis Homo est Animal, Omne Animal est Vivens, Ergo omnis Homo est Vivens. Omne corpus est extensum et solidum, Nullum extensum et solidum est pura extensio, Ergo corpus non est pura extensio.66

From the theoretical point of view, on the one hand, Locke highlights that the heart of the reasoning is the continuity of the ideas and, so, both the concatenation of the intuitions and the penetration of the reason (whose features are the strongness and the exercise, too); on the other hand, he ends up applying and proving true, as for the case of the medium term’s role, one of the principal assertions of Aristotle’s thought, that is “the nature doesn’t jump” (namely, the “principle of fullness”), which, if it is not admitted by Locke in the physical domain (because the emptiness is necessary for the motion), plays an important role in the taxonomy of beings67 and, in the present case, in the logical field: Each intermediate Idea must be such, as in the whole Chain hath a visible connexion with those two it is placed between, or else thereby, the Conclusion

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cannot be inferr’d or drawn in; for wherever any Link of the Chain is loose, and without connexion, there the whole strength of it is lost, and it hath no force to infer or draw in any thing.68

Paradoxically, the Lockean new anti-Aristotelian syllogism itself, since it avoids that solution of continuity of the ideas which is created by the traditional collocation of the medium term in the premises according to the rule de continente et contento, ends up not betraying one of the cornerstones of the Aristotelianism (as also Leibniz-Théophile will not fail to recognize to LockePhilalèthe in the Nouveaux Essais, despite the differences of opinion about the validity of syllogism and, in general, of formal logic).69 From the historical-philological point of view, it must be noted that the syllogism, which Locke refers to in the above-mentioned example, the one based on the ideas of homo—animal—vivens, is certainly ordinary and deliberately “very plain and easy,”70 but, at the same time, it is highly significant: this syllogism is in fact central in the Definitio syllogismi and, in general, in all the Tractatus tertius (dedicated to the syllogism) of Philippe Du Trieu’s Manuductio ad Logicam, one of the handbooks that Locke owned and, in the Ms. 11, fols. 7v–57 (notes written between 1661 and 1667), he said was in use at Christ Church College (together with the texts of logic of both Robert Sanderson and Samuel Smith).71 In Du Trieu’s handbook, in fact, we can read: Quid sit Syllogismus. Syllogismus est oratio, in qua quibusdam positis, aliud quiddam ab ijs quae posita sunt necessario accidit, eo quod haec sunt. Id est, syllogismus est oratio, in qua duabus praemissis simplicibus in modo & figura rectè dispositis, conclusio à praemissis diversa colligitur per necessariam & formalem consequentiam, propter legitimam praemissarum in modo & figurâ dispositionem, vt. Omne animal est vivens, Omnis homo est animal, ergo Omnis homo est vivens.72

Even the use of Latin leads us to think that Locke’s aim was that of making a focused reference to Du Trieu’s work (without quoting it expressly), similarly to what Locke did in the First Book about the notitiae communes found in Lord Herbert of Cherbury’s De Veritate73 and the exotic tales of Martin von Baumgarten’s Peregrinatio in Aegyptum, Arabiam, Palaestinam & Syriam.74 Instead, in § 8, the purpose seems to be that of giving an academic shape to the contents of §§ 12–14 Chapter VII (Fourth Book), that is the demonstration

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that the Cartesian equation of corpus and extensio and the consequent refusal of the vacuum or space without a body are based on the application of the principle of identity and non-contradiction to terms which stand for different ideas. Thus, Locke can show, at the same time, that the way of ideas provides this confutation with greater clarity thanks to the new type of syllogism. This purpose could have an indirect reason (a plausible hypothesis, in my opinion, without falling in an exaggerated “hermeneutic of the unsaid”) in the exchange of letters with William Molyneux between 1692 and 1695 and with John Wynne in 1695.75 As Kenneth Winkler has recently reminded us (2003),76 the philosopher of Dublin had suggested to Locke (in two letters of 169277 and 1693 respectively) to rearrange the Essay, on the occasion of the preparation of its second edition, “into the Scholastick form of a Logick and Metaphysicks.”78 Furthermore, he had already openly affirmed, in the Letter Dedicatory of his Dioptrica Nova (1692), that Locke’s work was in his opinion a real new Logick, which increased the goals achieved thanks to Arnaud’s and Malebranche’s works.79 Locke never openly agreed with these suggestions, but, as we can understand from a letter to Molyneux of 1695, he welcomed the news that John Wynne was composing an Abridgement for the “young students,” with the aim of introducing Locke’s work into Oxford University “in the place of an ordinary system of logick.”80 Given the chronological coincidence of the exchange of letters and of the variations made in the above-mentioned paragraphs of Chapter XVII of the Fourth Book, we can suppose that Locke’s attention has been further attracted by the schools’ environment and sensitized to both the pedagogical method and the academic language.

4. Conclusion: “Another sort of Logick and Critick, than what we have been hitherto acquainted with”81 As Jonathan Barnes stressed in his essay Locke and the Syllogism (2001), the polemic that Locke engages in (a fight which worsened in the passage from the third edition of the Essay concerning Humane Understanding of 1695, to the fourth of 1700), is not led against a precise receiver, contested by explicit and detailed quotations or references pertaining to contents82: although the criticism (full of invectives and biting irony) is expressly addressed against Aristotle and the Schoolmen, these receivers simply constitute the “masks.” As in the case of

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theatrical works of the commedia dell’arte or, even before, of the Greek new comedy of the Hellenistic Age, they do not represent characters which are either historically determined or determinable, but the “types.” As it happened in the First Book of the Essay, where the supporters of the innateness of both principles and ideas were neither Descartes nor the Cambridge Platonists, but the philosophers whom we could define as a-critical or “dogmatic” (Herbert of Cherbury was the only quoted philosopher),83 in the Fourth Book, Locke’s real opponent is the modus philosophandi of the formal logic, whose many personifications are not so important (one of these could, perhaps, be Du Trieu’s Manuductio), but its features. These can be merged into one: the betrayal and the overturning of the real and natural process and of the cognitive order, which is based on the immediate perceptions or the intuitions, on the grasping of the structural and existential elements of the ideas and also on their mutual agreement/disagreement (the English philosopher underlines on several occasions that the knowledge does not concern only the possession of the single psychic contents, but also, above all, the relationships between them). Starting from such materials, the understanding builds, by natural synthesis, all the argumentative chains. What Locke writes in the above-mentioned § 8 Chapter XVII, as “ideal” conclusion of the section about the syllogism, must, in my opinion, be read in the sense previously illustrated (and not as a simple ignoratio elenchi): Having here had an occasion to speak of Syllogism in general, and the Use of it, in Reasoning, and the Improvement of our Knowledge, ’tis fit, before I leave this Subject, to take notice of one manifest Mistake in the Rules of Syllogism; viz. That no Syllogistical Reasoning can be right and conclusive, but what has, at least, one general Proposition in it. As if we could not reason, and have Knowledge about Particulars. Whereas, in truth, the Matter rightly considered, the immediate Object of all our Reasoning and Knowledge, is nothing but Particulars. Every Man’s Reasoning and Knowledge, is only about the Ideas existing in his own Mind, which are truly, every one of them, particular Existences: and our Knowledge and Reasoning about other Things, is only as they correspond with those our particular Ideas. So that the Perception of the Agreement, or Disagreement of our particular Ideas, is the whole and utmost of all our Knowledge.84

Locke does not ignore that the syllogisms characterized by singular premises were included in the Aristotelian-Scholastic logic, as both Leibniz and, more recently, Barnes seemed to accuse him85: he simply wanted to draw the reader’s attention to the fact that the re-foundation of both the logic and the syllogism

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according to the realistic-critical exigency of his philosophy (so that both are cum fundamento in re, not in the metaphysical sense, but primarily and principally in the experimental one), must also take account of the gnoseological natural order, which proceeds from the concrete to the abstract: In particulars, our Knowledge begins, and so spreads it self, by degrees, to generals. Though afterwards, the Mind takes the quite contrary course, and having drawn its Knowledge into as general Propositions as it can, makes those familiar to its Thoughts, and accustoms it self to have recourse to them, as to the Standards of Truth and Falshood. By which familiar Use of them, as Rules to measure the Truth of other Propositions, it comes in time to be thought, that more particular Propositions have their Truth and Evidence from their Conformity to these more general ones, which in Discourse and Argumentation, are so frequently urged, and constantly admitted. And this, I think, to be the Reason why amongst so many Self-evident Propositions, the most general only have had the Title of Maxims.86

Locke’s principal aim is the de-absolutization of the cognitive scientific value and of the reasoning carried out only on the level of the abstract and universal propositions (“Universality is but accidental to it, and consists only in this, That the particular Ideas, about which it is, are such, as more than one particular Thing can correspond with, and be represented by”)87: in order to reach this goal, Locke is willing to relegate to a much lower priority the fact that, in the Fourth Book (chapters XI and XII ), he stated that the consideration of the abstract ideas (and, thus, the reasoning based on the universal propositions) constitutes the “true method of advancing Knowledge”88 (although it cannot happen in the natural philosophy) and, even before, in the Second Book, he clearly affirmed (gaining Leibniz’s approval) that the abstraction (as psychic function without which the naming would not realize its intrinsic social purpose) is the peculiarity, the insurmountable gap between the brutes and the man (putting the latter in a condition of qualitative excellence which seems to even break that chain of beings that is Nature).89

Notes 1 John Locke, An Essay Concerning Human Understanding, ed. Peter H. Nidditch (Oxford, 1975), I, 1, 2, p. 44. The titles of the works classified as primary sources are written with the intention to preserve their original spelling. Also in the quotations from the original texts I followed the same approach.

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2 This character of the Lockean philosophy was later emphasized by one of the main popularizers of Locke’s thought in Germany, Georg Friedrich Meyer: see Davide Poggi, “Introduction to Georg Friedrich Meier Zuschrift an Seine Zuhörer, worin er Ihnen seinen Entschluß bekannt macht, ein Collegium über Locks Versuch vom Menschlichen Verstande zu halten,” ed. Davide Poggi, in Philosophical Academic Programs of the German Enlightenment. A Literary Genre Recontextualized, eds. Seung-Kee Lee, Riccardo Pozzo and Marco Sgarbi (Stuttgart-Bad Cannstatt, 2012), 113–118. 3 See ivi, II , 1, 2, p. 104. 4 Ivi, I, 1, 3, p. 44. 5 Ivi, Epistle Dedicatory, pp. 3–4. 6 See ivi, Epistle to the Reader, p. 6. 7 Ivi, II , 21, 72, p. 285; IV, 7, 11, p. 601; IV, 17, 4, p. 675; IV, 19, 1, p. 697. 8 Ivi, Epistle to the Reader, p. 6. 9 See ivi, I, 3, 26, p. 83; I, 4, 8, p. 88. 10 See ivi, I, 3, 26–27, pp. 83–84; I, 4, 23–24, pp. 100–102. 11 Ivi, I, 1, 2, pp. 43–44. 12 See ivi, Epistle to the Reader, p. 7. 13 “When Men have found some general Propositions that could not be doubted of, as soon as understood, it was, I know, a short and easy way to conclude them innate. This being once received, it eased the lazy from the pains of search, and stopp’d the enquiry of the doubtful, concerning all that was once stiled innate: And it was of no small advantage to those who affected to be Masters and Teachers, to make this the Principle of Principles, That Principles must not be questioned: For having once established this Tenet, That there are innate Principles, it put their Followers upon a necessity of receiving some Doctrines as such; which was to take them off from the use of their own Reason and Judgment, and put them upon believing and taking them upon trust, without farther examination: In which posture of blind Credulity, they might be more easily governed by, and made useful to some sort of Men, who had the skill and office to principle and guide them” (ivi, I, 4, 24, pp. 101–102). 14 See John Locke, Essai Philosophique concernant l’Entendement Humain, trans. Pierre Coste (Amsterdam and Leipzig, 17555), facs. ed. by Émilienne Naert (Paris, 1998), I, 1, 10, p. 11; I, 1, 14, p. 13; I, 1, 18, p. 16; I, 1, 21, p. 18; I, 1, 27, p. 23; I, 2, 20, p. 38; I, 3, 6, p. 44. 15 See Locke, An Essay Concerning Human Understanding, III , 10, 6–9, pp. 493–495. About the Draft B, see John Locke, Drafts for the Essay Concerning Human Understanding and Other Philosophical Writings, ed. Peter H. Nidditch and Graham A. J. Rogers (Oxford, 1990), vol. 1, §§ 88–89, pp. 194–197. 16 Ivi, Epistle to the Reader, p. 10.

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17 Paul Schuurman, “General Introduction,” in John Locke, Of the Conduct of the Understanding, ed. Paul Schuurman (University of Keele, 2000), 82–85. 18 John Locke, Some Thoughts concerning Education, ed. John W. Yolton and Jean S. Yolton (Oxford, 1989), §§ 188–189, pp. 240–241. 19 Locke, Of the Conduct of the Understanding, Pars. 2–5, pp. 154–155. Locke quotes from Francis Bacon, Instauratio Magna, in Francis Bacon, Works, ed. James Spedding, Robert Leslie Ellis and Douglas Denon Heath (London, 1858), facs. ed. (StuttgartBad Cannstatt, 1989), vol. 1, Praefatio, p. 129. 20 Johann Clauberg, Logica vetus et nova, Modum inveniendae ac tradendae veritatis, in Genesi simul & Analysi, facili methodo exhibens. Editio secunda mille locis emendata novisque Prolegomenis aucta (Amstelaedami, 16582), Logicae Prolegomena, V, p. 34. Locke owned the first edition of Clauberg’s Logica vetus et nova (Amstelodami, 1654). About the books that are part of the Lockean Library, see John Harrison—Peter Laslett, The Library of John Locke (Oxford, 1965). See also: John Lough, “Locke’s Reading during his Stay in France (1675–1679),” The Library, 8 (1953): 229–258; Id., Locke’s Travels in France 1675–1679. As related in his Journals, Correspondence and other Papers (Cambridge, 1953); Gabriel Bonno, Les Relations intellectuelles de Locke avec la France (d’après des documents inédits) (Berkeley-Los Angeles, 1955). 21 See Locke, Drafts for the Essay Concerning Human Understanding and Other Philosophical Writings, vol. 1, §§ 27–31, pp. 44–60. 22 See Locke, An Essay Concerning Human Understanding, I, 2, 4, p. 49. 23 Ivi, I, 4, 24, p. 102. 24 Ivi, I, 2, 4, p. 49. 25 Ivi, IV, 1, 4, p. 526. 26 Ivi, I, 2, 15, p. 55. 27 Ivi, IV, 7, 11, p. 599. 28 I refer to Aristotle’s Posterior Analytics: “ ’Aπόδειξιν δὲ λέγω συλλογισμὸν ἐπιστημονικόνֹ ἐπιστημονικὸν δὲ λέγω καθ᾽ ὃν τῷ ἔχειν αὐτὸν ἐπιστάμεθα. εἰ τοίνυν ἐστὶ τὸ ἐπίστασθαι οἷον ἔθεμεν, ἀνάγκη καὶ τὴν ἀποδεικτικὴν ἐπιστήμην ἐξ ἀληθῶν τ᾽ εἶναι καὶ πρώτων καὶ ἀμέσων καὶ γνωριμωτέρων καὶ προτέρων καὶ αἰτίων τοῦ συμπεράσματος” (Aristot. Anal. Post. I, 2, 71 b 17–22). 29 See René Descartes, La recherche de la Vérité par la Lumiére naturelle, in René Descartes, Œuvres de Descartes, ed. Charles Adam and Paul Tannery (Paris 1996), vol. X, p. 522. The Adam-Tannery edition reproduces the text published in: René Descartes, Opuscula posthuma (Amsterdam, 1701). 30 See Antoine Arnauld—Pierre Nicole, La Logique ou l’Art de penser. Contenant, outre les Regles communes, plusieurs observations nouvelles propres à former le jugement (Paris, 16621), facs. ed. Bruno Baron von Freytag Löringhoff and Herbert E. Brekle (Stuttgart-Bad Cannstatt, 1965), vol. 1, IV, 6, p. 332.

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31 About the sterility of these principles, see Locke, An Essay concerning Human Understanding, IV, 7, 8–20, pp. 595–608. 32 Ivi, IV, 7, 19, pp. 607–608. 33 About the “Cartesian root” (in primis, Descartes and Malebranche) of the Lockean intuition (similarities, textual references and critical sources), see Davide Poggi, Lost and Found in Translation? La gnoseologia dell’Essay lockiano nella traduzione francese di Pierre Coste (Firenze, 2012), 162–177. 34 Locke, An Essay concerning Human Understanding, IV, 2, 8, p. 534. 35 Edward Stillingfleet, A Discourse in Vindication of the Doctrine of the Trinity: with an Answer to the late Socinian Objections against it from Scriptures Antiquity, and Reason. And a Preface concerning the different Explications of the Trinity, and the Tendency of the present Socinian Controversie (London, 1697), facs. ed in Edward Stillingfleet, Three Criticisms of Locke (Hildesheim-New York, 1987), p. 250. 36 Ivi, p. 251. 37 See Locke, An Essay concerning Human Understanding, IV, 2, 2, p. 532. 38 John Locke, A Letter to the Right Reverend Edward, Lord Bishop of Worcester, Concerning some Passages relating to Mr. Locke’s Essay of Human Understanding: in a late Discourse of his Lordship’s, in Vindication of the Trinity (London, 17949), facs. ed. in John Locke, Works (London, 1997), vol. 3, p. 59. 39 Ivi, pp. 59–60. 40 The use of this expression (see Locke, An Essay concerning Human Understanding, IV, 17, 15–16, pp. 684–685), borrowed from the terminology of the AristotelianScholastic logic, has been rightly emphasized in: David Owen, Hume’s Reason (Oxford, 1999), 36. 41 See Locke, An Essay concerning Human Understanding, IV, 17, 2, pp. 668–669. About the use and the meaning of demonstration, deduction and inference, not only in the Essay, but also in the Lockean works in general, it is useful to consult: John W. Yolton, A Locke Dictionary (Oxford–Cambridge, MA , 1993), 55–56 (“Deduction”), 57–63 (“Demonstration”), 99–100 (“Inference”). 42 Ivi, IV, 5, 3, p. 574. 43 Ivi, IV, 5, 4, pp. 574–575. 44 Ivi, IV, 17, 6, p. 679. 45 Ivi, IV, 7, 11, p. 601. 46 Ivi, IV, 6, 3, p. 580. 47 See Ivi, IV, 6, 3, p. 579. 48 Ivi, IV, 17, 4, p. 670. 49 Ivi, IV, 17, 3, p. 669. 50 Ibidem. 51 Ivi, IV, 17, 4, p. 670. 52 Ivi, IV, 17, 4, p. 673.

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53 Ivi, IV, 17, 4, pp. 673–674. 54 Arnauld—Nicole, La Logique ou l’Art de penser. Contenant, outre les Regles communes, plusieurs observations nouvelles propres à former le jugement, III , pp. 174–175. It is to be noted that the analogy with what Locke writes in Of the Conduct of the Understanding, par. 98: “The faculty of Reasoning seldom or never deceives those who trust to it. Its consequences from what it builds on are evident and certain but that, which it oftenest if not only misleads us in, is that the principles from which we conclude the grounds upon which we bottom our reasoning are but a part some thing is left out which should goe into the reconing to make it just and exact” (Locke, Of the Conduct of the Understanding, par. 98, p. 246). 55 Ivi, III , 15, pp. 240–242. 56 If Locke inherits this “functional innatism” from Nathaniel Culverwell’s Elegant and Learned Discourse of the Light of Nature (1652), he diverges from the Cambridge Platonist’s thought with regard to the role of both the logic and the syllogism as instruments useful to direct the natural light, that is the man’s reason: see Nathaniel Culverwell, An Elegant and Learned Discourse of the Light of Nature, ed. Robert A. Greene and Hugh MacCallum (Toronto-Buffalo, 1971), XIV, p. 119. See also Douglas M. Jesseph, “Logic and Demonstrative Knowledge,” in British Philosophy in the Seventeenth Century, ed. Peter R. Anstey (Oxford, 2013), 383–385. 57 Locke, An Essay concerning Human Understanding, IV, 17, 4, p. 674. 58 Ivi, IV, 17, 4, p. 672. 59 Ivi, IV, 17, 4, p. 671. 60 Ivi, IV, 17, 4, p. 673. 61 Ivi, IV, 17, 4, p. 671. 62 Ivi, IV, 17, 8, p. 681. 63 Ibidem. 64 Ivi, IV, 17, 8, p. 680. 65 Ivi, IV, 17, 4, p. 675. 66 Ivi, IV, 17, 8, p. 681. 67 “In all the visible corporeal World, we see no Chasms, or Gaps. All quite down from us, the descent is by easy steps, and a continued series of Things, that in each remove, differ very little one from the other. [. . .] There are some Brutes, that seem to have as much Knowledge and Reason, as some that are called Men: and the Animal and Vegetable Kingdoms, are so nearly join’d, that if you will take the lowest of one, and the highest of the other, there will scarce be perceived any great difference between them; and so on till we come to the lowest and the most inorganical parts of Matter, we shall find every-where, that the several Species are linked together, and differ but in almost insensible degrees. And when we consider the infinite Power and Wisdom of the Maker, we have reason to think, that it is suitable to the magnificent Harmony of the Universe, and the great Design and infinite Goodness of the Architect, that the

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Species of Creatures should also, by gentle degrees, ascend upward from us toward his infinite Perfection, as we see they gradually descend from us downwards” (ivi, III , 6, 12, pp. 446–447). This passage is quoted in: Arthur O. Lovejoy, The Great Chain of Being. A Study of the History of an Idea (Cambridge, MA-London, England, 200122), 184. Locke, An Essay concerning Human Understanding, IV, 17, 4, p. 673. See Gottfried Wilhelm von Leibniz, Nouveaux Essais sur l’Entendement par l’Auteur du Systéme de l’Harmonie Préétablie, ed. André Robinet and Heinrich Schepers in Gottfried Wilhelm von Leibniz, Sämtliche Schriften und Briefe, Reihe VI , Band VI (Berlin, 20063), IV, 17, 8, p. 486. On the difference of opinions between Locke and Leibniz in matters of logic, the following essay is very interesting: David Sherry, “Locke and Leibniz on the Utility of Formal Logic” (2009): 9–16, online available on the website philonoeses.org. Locke, An Essay concerning Human Understanding, IV, 17, 4, p. 675. See Paul Schuurman, Ideas, Mental Faculties and Method. The Logic of Ideas of Descartes and Locke and its Reception in the Dutch Republic, 1630–1750 (LeidenBoston, 2004), 11–12. In the wide and detailed introduction to the critical edition of Locke’s Of the Conduct of the Understanding, Schuurman points out that, in this manuscript, Locke cites the names of some others logicians (whilst failing to mention the titles of their works): Martin Smiglecki, John Flavell, Griffith Powell and Jacobus Zabarella. See Locke, Of the Conduct of the Understanding, pp. 53–54. John Milton, in the very accurate article “The Scholastic Background to Locke’s Thought”, stresses that Locke was acquainted with the most recent Scholastic philosophers (in primis, Philippe du Trieu and Robert Sanderson, of whom he owned, respectively, the Manuductio ad Logicam [Colonia, 1657] and the Logicae Artis Compendium [Oxford, 1615]). See John R. Milton, “The Scholastic Background to Locke’s Thought,” The Locke Newsletter, 15 (1984), 25–34. Smith’s work which Locke refers to is the following: Samuel Smith, Aditus ad logicam. In usum eorum qui primò Academiam salutant (London, 1613). It is not, however, among the books owned by Locke, nor is Franco Petri Burgersdijck’s Institutionum logicarum libri duo (Lugduni Batavorum, 16342), although they are mentioned by Locke in both the first Letter to Stillingfleet (see Locke, A Letter to the Right Reverend Edward, Lord Bishop of Worcester, Concerning some Passages relating to Mr. Locke’s Essay of Human Understanding, in Locke, Works, vol. 3, p. 8) and in the second Reply (see John Locke, Mr. Locke’s Reply to the Right Bishop of Worcester’s Answer to his Second Letter, in Locke, Works, vol. 3, p. 449). About the presence of Aristotelianism and the role of the handbooks of logic in the English philosophical reflection during the seventeenth century, see Marco Sgarbi, The Aristotelian Tradition and the Rise of British Empiricism. Logic and Epistemology in the British Isles, 1570–1689 (Dordrecht-Heidelberg-New York-London, 2013).

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72 Philippe Du Trieu, Manuductio ad Logicam, sive Dialectica studiosae juventuti ad logicam praeparandae (Coloniae, 1657) p. 116. This syllogism also recurs in pp. 115, 117, 118, 120, 127, 167. 73 Locke, An Essay concerning Human Understanding, I, 3, 15, p. 77. See Edward Herbert Lord of Cherbury, De Veritate [16241], in Edward Herbert Lord of Cherbury, De Veritate, De Causis Errorum, De Religione Laici, Parerga (London, 16453), facs. ed. by Günter Gawlick (Stuttgart-Bad Cannstatt, 1966), pp. 11, 29. Locke’s quotations are from the 1656 edition of the De Veritate. 74 See Martin von Baumgarten, Peregrinatio in Aegyptum, Arabiam, Palaestinam & Syriam (Norimbergae, 1594). See Ann Talbot, “The Great Ocean of Knowledge.” The Influence of Travel Literature on the Works of John Locke (Leiden-Boston, 2010), 143–147, 318–319. 75 Letter 1843. John Wynne to Locke (31 January 1695), in Esmond S. de Beer (ed.), The Correspondence of John Locke (Oxford, 20072), vol. 5, 262. 76 See Kenneth Winkler, “Lockean Logic,” in Peter R. Anstey (ed.), The Philosophy of John Locke. New Perspectives (London-New York, 2003), 155–156. 77 Letter 1579. William Molyneux to Locke (22 December 1692), in The Correspondence of John Locke, ed. de Beer, vol. 4, 601–602. 78 Letter 1609. William Molyneux to Locke (2 March 1693), in The Correspondence of John Locke, ed. de Beer, vol. 4, 649. 79 William Molyneux, Dioptrica Nova. A Treatise of Dioptricks, In Two Parts. Wherein the Various Effects and Appearances of Spherick Glasses, both Convex and Concave, Single and Combined, in Telescopes and Microscopes, Together with Their Usefulness in many Concerns of Humane Life, are explained (London, 1692), pp. XL –XLI . 80 Letter 1887. Locke to William Molyneux (26 April 1695), in The Correspondence of John Locke, ed. de Beer, vol. 5, 351. About the appreciation received by Locke’s Essay within the academic world, see Schuurman, “General Introduction,” in Locke, Of the Conduct of the Understanding, 88–90. 81 Locke, An Essay concerning Human Understanding, IV, 21, 4, p. 721. 82 Jonathan Barnes, “Locke and the Syllogism,” in John Locke. Critical Assessments of Leading Philosophers. Series II, ed. Peter Anstey (London-New York, 2006), vol. 2, 299–301. This essay was previously published in: Robert W. Sharples (ed.), Whose Aristotle? Whose Aristotelianism? (Aldershot, 2001), 105–132. 83 This process, in its various developments, has been carefully examined in the following essay: Mirella Capozzi and Gino Roncaglia, “Logic and Philosophy of Logic from Humanism to Kant,” in The Development of Modern Logic, ed. Leila Haaparanta (Oxford-New York, 2009), 78–158. 84 Locke, An Essay concerning Human Understanding, IV, 17, 8, pp. 680–681. 85 See Barnes, “Locke and the Syllogism,” in John Locke. Critical Assessments of Leading Philosophers. Series II, ed. Anstey, 304–308.

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86 Locke, An Essay concerning Human Understanding, IV, 7, 11, p. 603. The difference between the theses exposed in Bacon’s Instauratio Magna (Pars secunda of the Distributio Operis) and the Lockean approach is that Locke is more attentive to the gnoseological order (a concern which has a clear Cartesian origin) rather than to the contraposition of a new method (a “new logic”) grounded on induction to the traditional logic founded on syllogism and on deduction (albeit in the context of a substantial unity of spirit and continuity of project between Locke and Bacon): “Est ea quam adducimus ars (quam Interpretationem Naturae appellare consuevimus) ex genere logicae; licet plurimum, atque adeo immensum quiddam, intersit. Nam et ipsa illa logica vulgaris auxilia et praesidia intellectui moliri ac parare profitetur: et in hoc uno consentiunt. Differt autem plane a vulgari rebus praecipue tribus: viz. ipso fine, ordine demonstrandi, et inquirendi initiis. Nam huic nostrae scientiae finis proponitur, ut inveniantur non argumenta sed artes, nec principiis consentanea sed ipsa principia, nec rationes probabiles sed designationes et indicationes Operum. Itaque ex intentione diversa diversus sequitur effectus. Illic enim adversarius disputatione vincitur et constringitur, hic natura opere. Atque cum hujusmodi fine conveniunt demonstrationum ipsarum natura et ordo. In logica enim vulgari opera fere universa circa Syllogismum consumitur. De Inductione vero Dialectici vix serio cogitasse videntur; levi mentione eam transmittentes, et ad disputandi formulas properantes. At nos demonstrationem per syllogismum rejicimus, quod confusius agat, et naturam emittat e manibus. [. . .] Itaque ordo quoque demonstrandi plane invertitur. Adhuc enim res ita geri consuevit; ut a sensu et particularibus primo loco ad maxime generalia advoletur, tanquam ad polos fixos circa quos disputationes vertantur; ab illis caetera per media deriventur: via certe compendiaria, sed praecipiti, et ad naturam impervia, ad disputationes vero proclivi et accommodata. At secundum nos, axiomata continenter et gradatim excitantur, ut nonnisi postremo loco ad generalissima veniatur: ea vero generalissima evadunt non notionalia, sed bene terminata, et talia quae natura ut revera sibi notiora agnoscat, quaeque rebus haereant in medullis” (Bacon, Instauratio Magna, in Bacon, Works, vol. 1, Distributio Operis, Pars secunda, pp. 135–137). 87 Ivi, IV, 17, 8, p. 681. 88 Ivi, IV, 12, 7, p. 643. 89 See Ivi, II , 11, 9–11, pp. 159–160.

8

Leibniz’s Transformation of the Theory of the Syllogism into an Algebra of Concepts Wolfgang Lenzen Universität Osnabrück

1. Introduction. A very brief précis of the history of logic In an oft-quoted passage from the Critique of Pure Reason, Kant expressed his view that until his time (i.e. until the late eighteenth century) logic had not made any real progress since its foundation by Aristotle. Somewhat more exactly, Kant believed that logic—which he defined as the science “in which the formal rules of all thinking [. . .] are extensively exhibited and strictly proved”—represented the paradigm of a “complete and finished” discipline which, once its basic laws had been discovered, could not make “any step beyond,” nor “any step behind,” the original version.1 Of course, Kant was not an expert in the history of logic and he apparently had no deeper knowledge of the sophisticated logical investigations of, say, the medieval or post-medieval period.2 However, most of these innovations fall into the field of propositional logic while in the field of term-logic no comparable progress had taken place.3 Even in modern textbooks on the history of logic it is widely acknowledged that the theory of the syllogism—either in its »Aristotelian« form or in some elaborated version of a »Scholastic syllogistic«—remained the dominating logical theory for more than two millennia.4 From a post-Fregean point of view, logic may roughly be divided into two levels: Propositional logic and (1st order) predicate logic. The propositional calculus (PC ) is usually built up from a set of propositional letters p, q, . . . with the help of the truth-functional connectives ¬p

not p,

p∧q

p and q,

p∨q

p or q, 129

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The Aftermath of Syllogism

p⊃q

if p, then q,

p≡q

p if and only if q.

Furthermore, from Aristotle onwards, the investigation of diverse modal operators (such as alethic, causal, deontic, epistemic, . . . modalities) gave rise to various expansions of classical PC . For reasons of space, only the alethic modalities □p

necessarily p

◊p

possibly p

p⇒q p strictly implies q p⇔q p is strictly equivalent to q shall be taken into account here. On the second level of logic, the formerly primitive propositions p, q, . . . are more closely analyzed by means of singular terms (or names) a, b, . . . and predicates F, G, . . . as having the functional structure F(a), G(b,c), . . ., where in general a basic proposition has the form F(a1, . . ., an) (for some n ≥1). With the help of individual variables x, y, . . . one can then introduce the usual quantifiers Λx

for every (object) x

Vx

for at least one (object) x.5

On the background of this two-level model, a very brief précis of the history of logic from Aristotle up to Frege (or even a little beyond) might be sketched as follows.6 Propositional logic: When Aristotle developed his theory of the syllogism, he did not seriously deal with the laws and rules of PC but rather presupposed the validity of certain propositional inferences. In particular, he relied on the basic assumptions of classical, two-valued logic, which later came to be called the »Law of contradiction« and the »Law of the excluded middle«.7 Furthermore, he used the inference-scheme of contraposition according to which, if one proposition p logically entails another proposition q, then the falsity of q in turn entails the falsity of p. As a matter of fact, in the Topics he put forward a generalization of this inference to the effect that “if a number of propositions jointly entail a conclusion, then, if the conclusion is false, at least one of the premises must be false.”8 The first self-contained investigation of the propositional connectives was carried out by philosophers of the Megarian and Stoic school such as Diodorus

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131

Cronus, Philo, Chrysippus, etc. A much more extensive elaboration of PC , however, was undertaken in the thirteenth and fourteenth centuries by Scholastic logicians like R. Kilwardby, Petrus Hispanus, J. Buridanus, W. Burleigh, who not only investigated the truth-functional connectives, but also diverse modal operators. In particular, W. Ockham already possessed a rather comprehensive knowledge of the laws of modal propositional logic which justifies speaking of his “system of strict implication.”9 The next milestone in the development of the PC was set in the middle of the nineteenth century by George Boole who not only provided a complete algebra of sets, but also a complete truth-functional propositional logic.10 The development of the syntax and semantics of (non-modal) PC was rounded off towards the end of the nineteenth century by the outstanding work of Gottlob Frege, while modal propositional logic was finished in the early twentieth century by C. I. Lewis’ systems of strict implication.11 Predicate logic: From the perspective of contemporary logic, the traditional theory of the syllogism covers just a small section of the logic of monadic predicates. The basic propositions of syllogistic logic are the four categorical forms: Universal Affirmative (UA )

SaP

Every S is P

Λx(Sx ⊃ Px)

Universal Negative (UN )

SeP

No S is P

Λx(Sx ⊃ ¬Px)

Particular Affirmative (PA )

SiP

Some S is P

Vx(Sx ∧ Px)

Particular Negative (PN)

SoP

Some S isn’t P

Vx(Sx ∧ ¬Px).

According to the laws of opposition, the particular propositions are equivalent to the negations of corresponding universal ones: Opp 1 Opp 2

SiP ⇔ ¬SeP SoP ⇔ ¬SaP.

Moreover, the traditional syllogistic is based on the laws of subalternation according to which the universal propositions logically entail their particular counterparts12: Sub 1 Sub 2

SaP ⇒ SiP SeP ⇒ SoP.

The theory of opposition together with the theory of subalternation is often summarized in the well-known square of opposition (probably invented by Apuleius)13:

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The Aftermath of Syllogism

Figure 8.1

Another group of »simple« inferences deals with the conversion of the subject- and predicate-term. According to the traditional doctrine, the UN and the PA admit of a straightforward or »simple« conversion, while the UA can only be converted »accidentally«: Conv 1 Conv 2 Conv 3

SeP ⇒ PeS SiP ⇒ PiS SaP ⇒ PiS.

The »Scholastic« theory of the syllogism differs from its »Aristotelian« counterpart mainly by the treatment of negative (or »infinite«) terms. Technically speaking, this amounts to the introduction of a new operator which, when applied to an arbitrary term T, yields the negative term not-T. In what follows this operator shall be symbolized as ∼T

not-T.

The law of double negation not only holds for propositions in the form ¬¬p ⇔ p, but also for concepts in the form ∼∼T = T. Similarly, the law of contraposition may be transferred from the field of propositions into the field of terms in such a way that “the subject is turned into the predicate and vice versa, where the quality and quantity remain the same but the finite terms are changed into infinites.”14 E.g., “Every man is an animal” can be transformed into “Every notanimal is a not-man,” or more generally:

An Algebra of Concepts

Contra

133

SaP ⇒ ∼Pa∼S.

The admission of negative terms gives rise to another group of »simple« inferences called obversion. The most important law states that a UN like “No man is just” can be transformed into a UA with a negated predicate, “Every man is unjust,” or more generally: Obv 1

SeP ⇔ Sa∼P.15

Another law states that a PN like “ ‘Some man isn’t white’ can be reduced to a PA with a negative predicate, thus bringing out “that as a whole [the PN ] is no less affirmative than [the PA ] ‘Some man is not-white.’ ”16 More generally one obtains Obv 2

SoP ⇔ Si∼P.

Besides these »simple« inferences there are the proper syllogistic inferences which lead from two premises P1, P2 to a conclusion Q. All three propositions, of course, have to be categorical forms and a syllogism has to contain exactly three terms B, C, and D such that the following restriction is fulfilled: If B is the subject (or major-term) and D the predicate (or minor-term) of the conclusion, then B must be conjoined with a third (or middle) term C in one premise while the other premise has to connect C and D. The most famous examples of valid syllogisms are: Barbara Celarent Darii Ferio

CaD, BaC ⇒ BaD CeD, BaC ⇒ BeD CaD, BiC ⇒ BiD CeD, BiC ⇒ BoD.

As was mentioned before, the theory of the syllogism had been discovered to a large extent already by Aristotle and it remained the dominating logical theory until it was superseded by Boole’s »Algebra of Logic«. From a contemporary point of view, Boole’s logic itself corresponds to a complete theory of monadic predicates and it is thus only a small fragment of the full system of 1st order logic as invented by Frege.17

2. Leibniz’s starting point. The seventeenth-century theory of the syllogism It is not easy to determine the sources used by Leibniz when, as a youth, he began to study logic or when he later developed his own logical calculi. “Early in his teens he launched himself into an intensive study of logic,” and Leibniz’s main

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The Aftermath of Syllogism

teacher in this field appears to have been Jacob Thomasius who himself adopted some important logical doctrines from Petrus Ramus.18 Leibniz acquired a profound knowledge of Aristotle’s theory of the syllogism, and in the Dissertatio de Arte Combinatoria of 1666 (written at the age of nineteen!) he critically examined several theses concerning the validity of syllogistic inferences as put forward by J. Hospinianus and by J. C. Sturm.19 In a “Catalogus Inventionum in Logicis” written around 1681, Leibniz gathered a list of the most important logicians and their contributions to the development of logic.20 Starting with Plato and Aristotle, he mentions R. Lullus, Petrus Hispanus, “Joh. Suisset” (i.e. R. Swineshead), J. Hospinianus and, above all, Petrus Ramus to whom he credits many important discoveries.21 Next he briefly drops the names of “Zwingerus, Freigius, Keckermannus, Alstedius, aliique solidiores” before emphasizing the big achievements of J. Jungius who had shown that “not all logical inferences can be reduced to syllogisms.” Leibniz’s high estimation of Jungius also becomes evident from the fact that he made many detailed excerpts from the Logica Hamburgensis.22 Furthermore, in another short “Tabula Autorum,” probably compiled in 1678, just two eminent authors were listed under the heading “Logica,” namely, besides Jungius, the Frenchman Honoré Fabry, whose Logica Analytica had been published in the very year of Leibniz’s birth.23 It would certainly be rewarding to inquire the influence of the afore-mentioned authors on the development of Leibniz’s logical thoughts in more detail, but this task lies outside the scope of this chapter. In order to delineate the background of Leibniz’s logic, let us rather summarize the contents of one of the most influential logic-textbooks of his time, viz. the Logique de Port Royal, published by A. Arnauld and P. Nicole in 1662.24 There can be little doubt that Leibniz studied this book quite extensively. He referred to the logic of Port Royal (e.g. in the “Tabula Autorum”) and to some of their syllogistic doctrines in “De Formis Syllogismorum Mathematice Definiendis.”25 Furthermore, in “Meditationes de Cognitione, Veritate, et Ideis,” he explicitly praised the “excellent book de arte bene cogitandi” of the “most famous man Antonius Arnaldus.”26 From a systematic point of view, the logic of Port-Royal contains three main doctrines which bear some relevance to Leibniz’s own logic. First, the familiar canon of »simple« inferences as summarized in the previous section.27 Second, various rules concerning the »quality« and »quantity« of terms such as: Syll 1 Syll 2

The medius-term must not be particular in both premises. If a term is universal in the conclusion, then it must also be universal in the corresponding premise.28

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135

These rules became particularly relevant for Leibniz’s attempt to prove the »completeness« of the theory of the syllogism in the paper “Mathesis rationis.”29 The third important doctrine of the logic of Port Royal is the distinction between the extension and the intension (or comprehension) of a term: Now, in these universal ideas there are two things, which it is very important accurately to distinguish, comprehension and extension. I call the comprehension of an idea those attributes which it involves in itself, and which cannot be taken away from it without destroying it; as the comprehension of the idea triangle includes extension, figure, three lines, three angles, and the equality of these angles to two right angles, etc. I call the extension of an idea those subjects to which that idea applies, which are also called the inferiors of a general term [. . .].30

The latter definition of the extension of an »idea« fairly agrees with the modern understanding according to which the extension of a unary predicate F is the set of all things x to whom F may truthfully be ascribed, {x: F(x)}. However, there is a big difference between the traditional and our modern understanding of what constitutes the intension of an »idea«. Since the development of modal logic in the early twentieth century, the intension of an expression is normally considered as something heavily depending on the respective possible world.31 According to the traditional view, however, the »intension« of F is not relativized to different worlds but only mirrors the extension of F in the actual world. More concretely, Arnauld and Nicole define the comprehension of F as the set of all essential attributes of F (i.e. the set of all properties G which are contained in F and which cannot be removed from F without »destroying« F). According to Leibniz’s slightly different approach, however, the restriction to essential attributes may be dropped so that the »intension« of F is taken more generally as the set of all attributes G which are contained in F.32 This »definition« entails the following law of reciprocity of intension and extension: Rezi 1

Ext(F) ⊆ Ext(G) ↔ Int(F) ⊇ Int(G).

Leibniz defended this law in many writings. In the “Elementa Calculi” of April 1679 he wrote: (11) [. . .] For example, the concept of gold and the concept of metal differ as part and whole; for in the concept of gold there is contained the concept of metal and something else—e.g. the concept of the heaviest among metals. Consequently, the concept of gold is greater than the concept of metal.

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The Aftermath of Syllogism

(12) The Scholastics speak differently; for they consider, not concepts, but instances which are brought under universal concepts. So they say that metal is wider than gold, since it contains more species than gold, and if we wish to enumerate the individuals made of gold on the one hand and those made of metal on the other, the latter will be more than the former, which will therefore be contained in the latter as a part in the whole. [. . .] However, I have preferred to consider universal concepts, i.e. ideas, and their combinations, as they do not depend on the existence of individuals. So I say that gold is greater than metal, since more is required for the concept of gold than for that of metal [. . .]. Our language and that of the Scholastics, then, is not contradictory here, but it must be distinguished carefully.33

The law Rezi 1 entails that two concepts with the same extension must also have the same intension: Rezi 2

Ext(F) = Ext(G) → Int(F) = Int(G).

According to the contemporary understanding of “intension,” this principle is invalid because one can construct predicates F and G which have the same extension but not the same intension. To quote a famous example of Quine, it seems plausible to assume that (at least on our planet) all animals with a heart have a kidney, and vice versa.34 Therefore the predicates “animal with heart” and “animal with kidney” have the same extension (although only contingently) while their intensions (or »meanings«) differ widely. But this discrepancy between the modern and the traditional conception fails to justify the verdict of L. Couturat who claimed that the »intensional« treatment is bound to remain “confused and vague” and at any rate inferior to the extensional treatment as invented by Boole.35 As Leibniz never got tired of stressing, the logical relations between concepts can alternatively be treated in an extensional or in an »intensional« way. Thus in a fragment of August 1690, the transition from the extensional to the »intensional« point of view (“ab individuis ad ideas”) was explained as follows: And the method of notions is contrary to the method of individuals, just as all men are part of all animals, or all men are contained in all animals, so conversely the notion of animal is contained in the notion of man. And just like there are more animals besides the men, so something must be added to the idea of animal in order to get the idea of man. For by augmenting the conditions, the number decreases.36

Similarly, in the New Essays on Human Understanding the equivalence between the two points of view was defended as follows:

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137

The common manner of statement concerns individuals, whereas Aristotle’s refers rather to ideas or universals. For when I say Every man is an animal I mean that all the men are included among all the animals; but at the same time I mean that the idea of animal is included in the idea of man. “Animal” comprises more individuals than “man” does, but “man” comprises more ideas or more attributes: one has more instances, the other more degrees of reality; one has the greater extension, the other the greater intension.37

In sections 3–6 below, it will be shown how Leibniz’s algebra of concepts (i.e., as it were, the »intensional« counterpart of the extensional algebra of sets) gradually evolves from the traditional theory of the syllogism in four steps. First, by distilling an abstract operator of conceptual containment out of the informal “Every A is B.” Second, by inventing (or better: by just finding) the operator of conceptual conjunction inherent in the operation of juxtaposition of concepts like “rational animal.” Third, by a thoroughgoing elaboration of the laws of conceptual negation, which goes hand-in-hand, fourth, with the invention of the operator of possibility, or self-consistency, of concepts.

3. Distilling the operator of conceptual containment By the end of the 1670s, Leibniz has come to realize that, in the traditional formulation of the UA , the informal quantifier expression “every” is basically superfluous. Instead of “Every A is B” one may simply say “A is B” or, equivalently, “A contains B.” Thus, in the “Specimen Calculi Universalis” of 1679, he sets out to explain: (1) A universal affirmative proposition will be expressed here as follows: A is B, or (every) man is an animal. We shall, therefore, always understand the sign of universality to be prefixed.38

The logical properties of the containment-relation are easily determined. Already in “De Elementis cogitandi” of 1676, Leibniz had put forward the “absolute identical proposition A is A” together with the “hypothetical identical proposition: If A is B, and B is C, then A is C.”39 Hence the containment-relation is both reflexive and transitive. In what follows we formalize the containment-relation by the symbol A∈B

“A is B”; “A contains B.”40

The above-quoted laws then take the form

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The Aftermath of Syllogism

Cont 1

A∈A

Cont 2

A∈B ∧ B∈C ⇒ A∈C.

Leibniz soon recognizes that the identity or coincidence of concepts may be defined as mutual containment. Thus in “Elementa ad calculum condendum” of around 1678 he notes that “If A is B and B is A, then one can be substituted for the other salva veritate,” where a few lines later he defines that “A and B are the same, if one can everywhere be substituted for the other.”41 With the help of the symbol “=,” the former definition may be rendered as Iden 1

A = B ⇔ A∈B ∧ B∈A.

Furthermore the famous »Leibniz law of identity« (i.e. the principle of the substitutivity of identicals) can be formalized by the following inference scheme (where α is an arbitrary proposition): Iden 2

If A = B, then α[A] ⇔ α[B].

By means of these two basic principles, the subsequent corollaries, according to which the identity-relation is reflexive, transitive, and symmetric, can easily be derived: Iden 3

A=A

Iden 4

A=B∧B=C⇒A=C

Iden 5

A = B ⇒ B = A.42

4. Inventing the operator of conceptual conjunction Before we consider the conjunction of two concepts A and B, let us have a brief look at the conjunction of two propositions α and β! Leibniz never really cared about the connective “and,” nor was this a serious topic for medieval logicians who otherwise took great pains to develop the laws for the propositional connectives.43 As E. J. Ashworth remarked in her exposition of post-medieval logic: There is not much to be said about the conjunction, which was viewed as a purely truth-functional connective. Everyone agreed that a conjunction was true if and only if all its parts were true.44

As a matter of fact, (α∧β) can either be characterized semantically by the trivial truth-table

An Algebra of Concepts α

β

α∧β

T

T

T

T

F

F

F

T

F

F

F

F

139

Or (α∧β) can be characterized syntactically (i.e. proof-theoretically) by three inference rules according to which the conjunction (α∧β) may be inferred from the two premises α and β, while conversely from (α∧β) one may infer both α and β. Thus at the beginning of the sixteenth century Hieronymus of St. Mark pointed out: “From the truth of a conjunction to the truth of either part there is a valid consequence.”45 At first sight, the conjunction of concepts also doesn’t seem to require a separate logical investigation. As a matter of fact, the corresponding »operator« remains rather hidden (e.g. when the concepts “animal” and “rational” are conjoined to “rational animal”) or when, more generally, two concepts A and B are combined by mere juxtaposition into AB. Anyway, as Leibniz points out in an early draft of a logical calculus, it follows from the very meaning of conjunctive juxtaposition that AB contains A (and similarly AB contains B) because “AB wants to express just this, namely that which is A and which also is B”46: Conj 1

AB∈A

Conj 2

AB∈B.

In the “Addenda to the specimen of the Universal Calculus” of 1679, Leibniz pointed out that the operation of conceptual conjunction is both symmetric and idempotent: It must also be noted that it makes no difference whether you say AB or BA, for it makes no difference whether you say “rational animal” or “animal rational.” The repetition of some letter in the same term is superfluous, and it is enough for it to be retained once; e.g. AA or “man man.”47

In our symbolism these laws take the form: Conj 3

AB = BA

Conj 4

AA = A

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The Aftermath of Syllogism

Leibniz further recognized that in addition to principles Conj 1, 2 which show that a “compound predicate can be divided into several,” also conversely: Different predicates can be joined into one; thus if it is agreed that A is B, and (for some other reason) that A is C, then it can be said that A is BC. For example, if man is an animal, and if man is rational, then man will be a rational animal.48

Hence one gets as another law of conjunction: Conj 5

A∈B ∧ A∈C ⇒ A∈BC.

In Leibniz’s riper calculi this law will usually be strengthened into an equivalence: “That A contains B and A contains C is the same as that A contains BC.”49 Conj 6

A∈B ∧ A∈C ⇔ A∈BC.

Once the operator of conceptual conjunction is available, one can expand the logic of the identity operator e.g. by the following law: Iden 6

A = B ⇒ AC = BC.

This inference, of course, cannot be converted. Similarly, the additional law for the operator of conceptual containment “If B is C, then AB will be AC (i.e. if man is an animal, it follows that a wise man is a wise animal)” holds only in the form of a one-way inference: Conj 7

A∈B ⇒ AC∈BC.50

To conclude this section, let it be pointed out that just as (according to Iden 1) the identity operator can be defined by “∈,” so conversely the ∈-operator might be defined (with the additional help of the operator of conceptual conjunction) by “=,” namely according to the law: Cont 3

A∈B ⇔ (A = AB).

This important principle was put forward by Leibniz (e.g., in § 83 of the “General Inquiries”) and it admits a very elegant formalization of the four categorical forms, to wit: (UA ) A = AB

A = A∼B (UN )

(PA ) A ≠ A∼B

A ≠ AB (PN ).51

In the sophisticated essays of August 1690 devoted to the determination of the “Primary Bases of the Logical Calculus,” Leibniz preferred to work with “=” rather than with “∈” as a primitive operator. This approach seduced him into

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141

trying desperately to derive certain basic principles like that of contraposition from the laws of identity. As has been shown elsewhere, it was Leibniz’s unwillingness to accept the crucial principles as improvable axioms which in the end prevented him from proving the theory of the syllogism within his much stronger »Universal Calculus«.52

5. Elaborating the laws for conceptual negation Leibniz always used one and the same word, “not” (i.e. in Latin “non”), to designate the negation either of a proposition or of a concept. As was explained in section 1, however, here we want to use two distinct symbols, namely “¬” for the negation of a proposition, and “∼” for the negation of a concept. The logic of the propositional connective is quite straightforward. If one defines the negation, or the »contradictory«, of a proposition in the traditional way such that these “two propositions neither can be together true, nor can be together false,” one obtains the following truth-conditions: If the affirmation is true, then the negation is false; if the negation is true, then the affirmation is false [. . .] If it is true that it is false, or if it is false that it is true, then it is false; if it is true that it is true, and if it is false that it is false, then it is true. All these are usually subsumed under the name of the Principle of contradiction.53

This characterization is equivalent to the familiar truth-table which entails, in particular, the validity of the law of double negation, ¬(¬α) ⇔ α. α

¬α

¬¬α

T

F

T

F

T

F

While Leibniz had an absolute clear understanding of the logic of propositional negation, during his research into the laws for conceptual negation he encountered serious problems. From the tradition, he knew little more than the law of double negation, “Not-not-A = A”:54 Neg 1

∼(∼A) = A.

Also, it was not really difficult for Leibniz to transform the informal principle of contraposition into an appropriate law of the »Universal calculus«, viz.:

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Neg 2

The Aftermath of Syllogism

A∈B ⇔ ∼B∈∼A.55

Furthermore Leibniz happened to discover the following variants of the law of consistency where the symbols “≠” and “∉,” of course, are meant to abbreviate the negation of identity and the negation of conceptual containment, respectively: Neg 3

A ≠ ∼A

Neg 4

A = B ⇒ A ≠ ∼B.

Neg 5*

A∉∼A

Neg 6*

A∈B ⇒ A∉∼B.56

Principles Neg 5, 6 have been marked with a “*” in order to indicate that these laws are not absolutely valid. As will be explained in the next section, they have to be restricted to self-consistent terms. The cardinal mistake of Leibniz’s theory of negation, however, consists in the frequent assumption that the one-way implication Neg 6 might be strengthened into an equivalence so that “A isn’t B” would be “the same” as “A is not-B”: Neg 7*

A∉B ⇔ A∈∼B.57

This error is a bit surprising because in general Leibniz was well aware of the fact that, in his logical system, the formula “A∈B” expresses the universal affirmative proposition while, on the background of principle Obv 1, “A∈∼B” formally represents the universal negative proposition. In view of the traditional theory of opposition, the negated formulae “A∉B” and “A∉∼B” therefore represent the particular negative and the particular affirmative proposition, respectively: (UA ) A∈B

A∈∼B (UN )

(PA ) A∉∼B

A∉B (PN ).

Hence the (basically but not entirely) correct principle Neg 6* is nothing but the formal counterpart of the law of subalternation, Sub 1, and this inference clearly must never be converted! Thus, e.g., in § 92 of the “General Inquiries,” Leibniz emphasized that the inference from A∉∼B to A∈B (or, similarly, from A∉B to A∈∼B) is invalid.58 On the other hand, a little bit earlier, namely in § 82, he had maintained that “ ‘A isn’t B’ is the same [!] as ‘A is not-B’ ,” and this error was repeated again and again in many other fragments.59 The root of Leibniz’s notorious problems with the insufficient distinction between “A∉B” and “A∈∼B” is closely connected with the distinction between singular and general terms! If A is the name of some individual, or, as one could

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also say, if A is an individual-concept, then the two propositions ¬(A est B) and (A est ∼B), though being syntactically different, are semantically equivalent because one may assume that for each individual x, x has the negative property ∼B if x fails to have the positive property B. Thus already Ockham pointed out in his Summa Logicae: The inference from an affirmative proposition with an infinite predicate to a negative proposition with a finite predicate is valid [. . . and conversely] thus it follows “Socrates is not white, therefore Socrates is not-white.”60

Similarly in the “Calculi universalis investigationes,” Leibniz explained: Two terms are contradictory if one is positive and the other the negation of this positive, as “man” and “not man.” About these the following rule must be observed: If there are two propositions with exactly the same singular subject of which the first has the one and the second the other of the contradictory terms as predicate, then necessarily one proposition is true and the other false. But I say: exactly the same [singular] subject, for instance if I say “Apostle Peter was a Roman bishop” and “Apostle Peter was not a Roman bishop.”61

The crucial law Neg 7* is indeed valid for the special case where the subject A is an individual concept. Unfortunately, Leibniz failed to realize with sufficient clarity that this principle may not be generalized to the case where A is an arbitrary concept. Thus, after the just quoted passage, he temporarily considered that, out of the pair of propositions “Omnis homo est doctus,” “Omnis homo est non doctus,” exactly one would be true and the other false, but soon afterwards he noticed this error and remarked that the generalized rule is wrong.62 However, a few lines later he considered the rule again in a more abstract way (omitting the informal quantifier expression “omne”) and then he repeated the mistake of postulating not only the (basically) correct principle Neg 6: “I If the proposition “A is B” is true, then the proposition “A is not B” is false,” but also the incorrect conversion: “III If the proposition “A is B” is false, then the proposition “A is not B” is true.”63

6. The operator of conceptual possibility: An ingenious invention Fortunately, the partial confusions and errors of Leibniz’s theory of negation (as described in the previous section) are highly compensated by an ingenious discovery, namely the invention of the operator of possibility or self-consistency of concepts. This operator shall here be symbolized by:

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P(A)

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“A is possible.”

Leibniz himself used many different locutions to express the self-consistency of a concept. Instead of “A is possible” he often says “A is a thing” (“A est res”), or “A is being” (“A est ens”) or simply “A is” (“A est”). In the opposite case of an impossible concept, he sometimes also calls A a »false term«. Now in Leibniz’s »Universal calculus«, one can consider, in particular, the inconsistent concept A∼A (“A Not-A”); therefore one may define that a concept B is possible if and only if B doesn’t contain a contradiction like A∼A: Poss 1

P(B) =df (B∉A∼A).64

In order to get a clearer understanding of the truth-condition of the proposition P(B), let it be noted that the extension of a negative concept ∼A must always be conceived as the set-theoretical complement of the extension of A, because an object x has the negative property ∼A just in case x fails to have property A. Furthermore, the extension of a conjunctive concept BC generally is the intersection of the extension of B and the extension of C, because x has the property BC if and only if x has both properties. From these conditions it follows that the extension of A∼A is the intersection of Ext(A) and its own complement (i.e. the empty set)! Hence a concept B is possible if and only if its extension is not contained in the empty set, which in turn means that Ext(B) itself is not empty! At first sight, this requirement appears inadequate, because there are certain concepts—such as that of a unicorn—which happen to be empty but which may nevertheless be regarded as possible (i.e. not involving a contradiction). However, as Leibniz explained in a paper on “Some logical difficulties,” the universe of discourse underlying the extensional interpretation of his logic should not be taken to consist of actually existing objects only, but instead to comprise all possible individuals.65 Therefore the non-emptiness of Ext(B) is both necessary and sufficient for guaranteeing the self-consistency of B. Clearly, if B is possible, then there must be at least one possible individual x that falls under concept B. The following two laws describe some characteristic relations between the possibility-operator P and other operators of the algebra of concepts: Poss 2

A∈B ∧ P(A) ⇒ P(B)

Poss 3

A∈B ⇔ ¬P(A∼B).

Leibniz’s own formulation of principle Poss 2: “If A contains B and A is true, B also is true” prima facie sounds a bit strange, but he goes on to explain:

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By a false letter I understand either a false term (i.e. one which is impossible, or not-being) or a false proposition. And in the same way by [a true letter] I understand either a possible term or a true proposition.66

Hence, if the term (or concept) A contains B and if A is »true« (i.e. possible) then B must also be possible. This law, incidentally, might be proved as follows. Assume that A∈B and that P(A); then P(B) must hold, too, because otherwise B would contain a contradiction like C∼C. But from A∈B and B∈(C∼C) it would follow by Cont 2 that A∈(C∼C) which contradicts the assumption P(A). The important law Poss 3, in contrast, cannot be derived from the remaining laws for containment, negation, and conjunction, but it must be adopted as a fundamental axiom of the algebra of concepts.67 The systematic importance of Poss 3 is evidenced by the fact that in “General Inquiries” Leibniz stated no fewer than six different versions of this law. Leibniz hit upon this crucial axiom by his investigation of propositions “secundi adjecti” vs. “tertii adjecti” which culminated in the discovery: (151) We have, therefore, propositions tertii adjecti reduced as follows to propositions secundi adjecti: “Some A are B” gives “AB is a thing” “Some A are not B” gives “A not-B is a thing” “Every A is B” gives “A not-B is not a thing” “No A is B” gives “AB is not a thing.”

Hence the four categorical forms can be formally represented by the following schema: (UA ) ¬P(A∼B)

¬P(AB) (UN )

(PA ) P(AB)

P(A∼B) (PN ).68

With the help of the possibility operator, P, the two (almost valid) laws of consistency Neg 5* and Neg 6* may now be amended as follows: Neg 5

P(A) ⊃ A∉∼A

Neg 6

P(A) ⊃ (A∈B ⇒ A∉∼B).

As Neg 6 shows, the validity of the principle of subalternation (i.e. the inference from the UA “A∈B” to the PA “A∉∼B”) only presupposes that the subject term A is self-consistent (and hence has a non-empty extension within the set of all possible individuals). Note also that the axioms Poss 2, Poss 3 admit a proof of the following counterpart of what in propositional logic is called “ex contradictorio quodlibet”:

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Neg 8

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A(∼A)∈B.69

Just as the contradictory proposition α∧¬α entails any other proposition β, so the contradictory concept A(∼A) contains any other concept B!70 It has often been noted that Leibniz’s logic of concepts lacks the operator of conceptual disjunction. Although this is by and large correct, it doesn’t imply any defect or any incompleteness of his algebra of logic because the »missing« operator might simply be introduced by definition: Disj 1

A∨B = df ∼(∼A∼B).71

On the background of the above axioms of negation, the characteristic laws of disjunction, Disj 2

A∈(A∨B)

Disj 3

B∈(A∨B)

Disj 4

A∈C ∧ B∈C → (A∨B)∈C,

can easily be derived from corresponding laws of conjunction. More generally, Leibniz’s »intensional« logic of concepts turns out to be provably equivalent, or isomorphic, to the extensional (or »Boolean«) algebra of sets, and in this sense, more than 150 years before Boole, Leibniz managed to transform the theory of the syllogism into a complete and sound algebra of concepts.72

7. Some steps beyond the algebra of concepts To conclude, let it be pointed out that the full »system« of Leibniz’s logic has much more to offer than »only« the algebra of concepts.73 For reasons of space, just two major ideas shall be sketched here. First, Leibniz discovered a brilliant method to transform the algebra of concepts into an algebra of propositions. The core of this method consists in the strict parallel between the containment relation among concepts and the implication relation among propositions. Just as “A is B” is true,“when the predicate is contained in the subject,” so a conditional proposition “If α, then β“ is true “when the consequent is contained in the antecedent.”74 In later works Leibniz compressed this idea into formulations like “a proposition is true whose predicate is contained in the subject or more generally whose consequent is contained in the antecedent.”75 Since, according to Leibniz, the logical laws for the negation and conjunction of propositions also mirror the laws for the negation and conjunction of concepts, one obtains the

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following mapping of the primitive formulas of the algebra of concepts into formulas of the algebra of propositions: A∈B

α⇒β

A=B

α⇔β

∼A

¬α

AB

α∧β

P(A)

◊α.

In this way, e.g., the fundamental law Poss 3, A∈B ⇔ ¬P(A∼B), may be »translated« into the formula (α⇒β) ⇔ ¬◊(α∧¬β) which shows that the resulting “⇒“-relation between propositions is not a material but a strict implication. As Leibniz put it in the paper Analysis Particularum: Thus if I say “If α is true it follows that β is true,” this means that one cannot suppose at the same time that α is true and that β is false. This is the true analysis of the words “if ” and “it follows.”76

Another important extension of the algebra of concepts consists in the introduction of so-called indefinite concepts X, Y, . . ., which in Leibniz’s system function as quantifiers ranging over concepts! Thus in the “General Inquiries” Leibniz explained: (16) An affirmative proposition is “A is B” or “A contains B” [. . .]. That is, if we substitute the value for A, one obtains “A coincides with BY”[. . .] For by the sign “Y” I mean something undetermined, so that “BY” is the same as “Some B” [. . .] or “a certain animal.” So “A is B” is the same as “A coincides with some B,” i.e. “A = BY.”77

With the help of the modern symbol for the existential quantifier, the latter law can be expressed more precisely as follows: Cont 4

A∈B ⇔ ∃Y(A = BY).

Next consider a draft of a calculus where Leibniz tried to prove the (not entirely valid) principle: Neg 9*

A∉B ⇔ ∃Y(YA∈∼B).

On the one hand, it is interesting to see that after first formulating the condition on the right hand side of the equivalence, »as usual«, in the elliptic way “YA is Not-B,” Leibniz later paraphrased it by means of the explicit quantifier expression

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“there exists a Y such that YA is Not-B.” On the other hand, Leibniz discovered that Neg 9* has to be improved by requiring more exactly that there exists a Y such that YA contains ∼B and YA is possible, i.e. Y is compatible with A: Neg 9

A∉B ↔ ∃Y(P(YA) ∧ YA∈∼B).

Leibniz’s own proof is quite remarkable: (18) [. . .] to say “A isn’t B” is the same as to say “there exists a Y such that YA is Not-B.” If “A is B” is false, then “A Not-B” is possible by [Poss 3]. “Not-B” shall be called “Y.” Hence YA is possible. Hence YA is Not-B. Therefore we have shown that, if it is false that A is B, then YA is Not-B. Conversely, let us show that if YA is Not-B, “A is B” is false. For if “A is B” would be true, “B” could be substituted for “A” and we would obtain “YB is Not-B” which is absurd.78

To conclude the sketch of Leibniz’s quantifier logic, let us consider some of the rare passages where an indefinite concept functions as a universal quantifier. In the above quoted paper “Specimina Calculi rationalis,” Leibniz put forward principle “(15) ‘A is B’ is the same as ‘If L is A, it follows that L is B’ . ” This law clearly has to be understood in the sense of: Cont 5

A∈B ⇔ ∀Y(Y∈A ⇒ Y∈B).79

Furthermore, in § 32 of the “General Inquiries,” Leibniz at least vaguely recognized that just as (according to Cont 4) A∈B is equivalent to ∃Y(A = YB), so the negative condition A∉B means that, for any indefinite concept Y, A ≠ BY: Cont 6

A∉B ⇔ ∀Y(A ≠ YB).

Anyway, with the help of “∀,” one can formalize Leibniz’s conception of individual concepts as maximally-consistent concepts in the following way: Ind 1

Ind(A) ⇔df P(A) ∧ ∀Y(P(AY) ⇒ A∈Y).

Thus A is an individual concept if and only if A is self-consistent and A contains every concept Y which is compatible with A. The underlying idea of the completeness of individual concepts had been formulated in § 72 of the “General Inquiries” as follows: So if BY is [»being«], and if the indefinite term Y is superfluous, i.e., in the way that “a certain Alexander the Great” and “Alexander the Great” are the same, then B is an individual. If the term BA is [»being«] and if B is an individual, then A will be superfluous; or if BA=C, then B=C.80

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Now it is not difficult to see that Ind 1 might be simplified by requiring that, for each concept Y, A either contains Y or contains ∼Y: Ind 2

Ind(A) ⇔ ∀Y(A∈∼Y ⇔ A∉Y).

As a corollary it follows that the invalid principle Neg 7*, which Leibniz again and again had considered as generally valid, in fact holds only for individual concepts: Neg 7

Ind(A) ⇒ (A∉B ⇔ A∈∼B).

Notes 1 Cf. the preface to the second edition of Immanuel Kant, Kritik der reinen Vernunft (Riga, 1787), B VIII –IX . 2 Cf. Ernest A. Moody, Truth and Consequence in Medieval Logic (Amsterdam, 1953) and Earline Jennifer Ashworth, Language and Logic in the Post-Medieval Period (Dordrecht, 1974). 3 For an overview of the development of syllogistic logic in the Middle Ages cf. Henrik Lagerlund, “Medieval Theories of the Syllogism,” in Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy (Spring 2016 edition). 4 I am using three different kinds of inverted comma here: single ones (‘ ’) in order to mention the linguistic expression; double (“”) for quotations; and French (»«) to indicate that the expression is taken in an unusual or queer way. 5 In second order predicate logic one may introduce predicate variables Φ, Ψ, . . . and another type of quantifiers ∀Φ (“for every property Φ”), ƎΦ (“for at least one property Φ”); these will be briefly discussed in section 7 below in connection with Leibniz’s theory of »indefinite concepts«. 6 The subsequent sketch leans a bit on section 2 of Wolfgang Lenzen, “Precis of the history of logic from the point of view of the Leibnitian calculus,” in Estudios de Historia de la Logica, Actas del II Simposio de Historia de la Logica, eds. Ignatio Angelelli and Angel d’Ors (Pamplona, 1990), 321–340. 7 The former may be formalized either by ¬(p ∧ ¬p) or by the modal formula ¬◊(p ∧ ¬p); the latter similarly by (p ∨ ¬p) or by □(p ∨ ¬p). For Aristotle’s version cf. William and Martha Kneale, The Development of Logic (Oxford, 1962), 46–47. 8 Kneale, The Development of Logic, 41. Aristotle himself speaks of “transposing arguments.” 9 Cf. Wolfgang Lenzen, “Ockham’s Calculus of Strict Implication,” in Medieval Logic, Logica Universalis, eds. G. Hamelin and R. Guerizoli, Special Volume 9 (2015):

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10

11

12

13 14 15

16 17 18

19

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181–191. According to Kneale The Development of Logic, 270, Ockham’s Summa Logicae was finished in 1325 (i.e. almost 700 years before C. I. Lewis). For a much more detailed account of the history of the PC cf. Jan Łukasiewicz, “Zur Geschichte der Aussagenlogik,” Erkenntnis, 5 (1935): 111–131. Cf. George Boole, Mathematical Analysis of Logic (Cambridge, 1847); and An Investigation of the Laws of Thought on which are Founded the Mathematical Theories of Logic and Probability (London, 1854). Cf. Gottlob Frege, Begriffsschrift—Eine der arithmetischen nachgebildete Formelsprache des reinen Denkens (Halle, 1879), and Clarence I. Lewis, A Survey of Symbolic Logic (Berkeley, 1918). According to the contemporary interpretation of these propositions, SaP (i.e. Vx(Sx ⊃ Px)) entails SiP (i.e. Vx(Sx ∧ Px)) only under the additional premise that the subject S is not empty: Vx(Sx). This issue will be further discussed in section 6. Cf. Joseph M. Bocheński, Formale Logik (Freiburg, 1956), 161–162. Cf. the passage from Petrus Hispanus, Summulae Logicales, ed. J. M. Bocheński (Turin, 1947) as quoted in Bocheński, Formale Logik, 246. This point has already been discussed by Aristotle who, however, only accepted the inference from SaP to Se∼P but not conversely. Cf. Kneale, The Development of Logic, 57; cf. also Bocheński, Formale Logik, 69–70. Kneale, The Development of Logic, 57. Cf. Gottlob Frege, Grundgesetze der Arithmetik, begriffsschriftlich abgeleitet, 2 vols (Jena 1893, 1903). Cf. Nicholas Rescher, Leibniz—An Introduction to his Philosophy (Lanham MD, 1986), 2; and cf. Louis Couturat, La logique de Leibniz (Paris, 1901; repr. Hildesheim, 1985), 8. Cf. Johannes Hospinianus, Non esse tantum 36 bonos malosque categorici syllogismi modos, ut Aristotle cum interpretibus docuisse videtur, sed 512, quorum quidem probentur 36, reliqui omnes rejiciantur (Basel, 1560); Leibniz also mentions Hospinianus’ other work, Controversias dialecticas (Basel, 1576). In his Compendium Universalium seu Metaphysicae Euclideae (The Hague, 1660), Johann-Christoph Sturm had put forward several unorthodox inferences which seemingly violated the traditional rules “Ex puris negativis nihil sequitur” and “Conclusio sequitur qualitatem debilioris ex praemissis.” The text of Leibniz’s Dissertatio may be found in vol. 4 of C. I. Gerhardt (ed.), G. W. Leibniz—Die philosophischen Schriften, esp. 46–50 and 55–56. The fragment was first published in Opuscules et fragments inédits de Leibniz, ed. Louis Couturat (Paris, 1903), 330; a text-critical edition may be found in vol. 4 of the Academy-edition of Leibniz’s philosophical writings, i.e. Gottfried Wilhelm Leibniz, Sämtliche Schriften und Briefe, hrg. von der Berlin-Brandenburgischen Akademie der Wissenschaften und der Akademie der Wissenschaften in Göttingen, Sechste Reihe, Vierter Band (Berlin, 1999), 427.

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21 The fact that “Joh. Suisset” refers to the author of Liber calculationum (Padua, 1477) (i.e. Richard Swineshead) has been pointed out by the editors of the Academy edition. 22 The main work of Joachim Jungius, Logica Hamburgensis, first appeared in (Hamburg, 1638); Leibniz particularly studied the second (posthumous) edition of 1681 prepared by Vagetius. Cf. Leibniz, Sämtliche Schriften und Briefe, vol. 4, 1059–1084; 1085–1090; 1211–1306. 23 Cf. “Tabula Autorum” in Leibniz, Sämtliche Schriften und Briefe, vol. 4, 108. Leibniz must have studied Fabry’s work quite intensively since he devoted a long marginal note to it in “De formis syllogismorum mathematice definiendis” (in Leibniz, Sämtliche Schriften und Briefe, vol. 4, 503–505). The full title of Fabry’s book is Philosophiae Tomus primus qui complectitur scientiarum Methodum sex libris explicatam: Logicam Analyticam, duedeccim Libris explicatam, et aliquot Controversias logicas, breviter disputatas (Lyon, 1646). 24 Cf. Antoine Arnauld et Pierre Nicole, La Logique ou l’Art de Penser (Paris, 1662); quotes are here taken from the fifth edition (repr. 1992). 25 Cf. Leibniz, Sämtliche Schriften und Briefe, vol. 4, 108 and 505. 26 Cf. Leibniz, Sämtliche Schriften und Briefe, vol. 4, 591. Furthermore, in a marginal note to “Paraenesis de scientia Generali,” Arnauld is listed together with Jungius, Claubergius and Fabrius as the most important logicians; cf. Leibniz, Sämtliche Schriften und Briefe, vol. 4, 971. 27 The laws, of course, are not formalized as above but only put forward in a quite informal way. Cf. Arnauld-Nicole, La Logique ou l’Art de Penser, 172, where, e.g., the principle of subalternation is formulated as follows: “Les propositions particulières sont enfermés dans les générales de même nature, et non les générales dans les particulières, I dans A, et O dans E, et non A dans I, ni E dans O.” 28 Cf. Arnauld-Nicole, La Logique ou l’Art de Penser, 172–173, “Regle I” and “Regle II .” 29 Cf. Opuscules et fragments inédits de Leibniz, ed. Couturat, 193–206. What it means to prove the »completeness« of the theory of the syllogism is explained in Wolfgang Lenzen, “On Leibniz’s essay Mathesis rationis,” Topoi, 9 (1990): 29–59. 30 Cf. Arnauld-Nicole, La Logique ou l’Art de penser, 51–52. The translation is from The Port-Royal Logic, ed. Thomas Spencer Baynes (Edinburgh, 1861). 31 More precisely, the intension may be defined as a function Ф which assigns to each proposition α (relatively to a world w from a set W of possible worlds) a truth-value Ф(α,w) and to each unary predicate F (relatively to w) a set of objects Ф(F,w) from the underlying universe of discourse, U. The set Ф(F,w) then corresponds to the extension of F in world w, and Ф(F,w1) and Ф(F,w2) can strongly vary from w1 to w2. 32 The characterization of the intension of a concept F as the set of attributes G which are contained in F (where F contains G if and only if every object x which has property F eo ipso has property G, Λx(Fx ⊃Gx)) is meant only heuristically. A

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33 34 35

36 37 38 39 40

41 42

43

44 45

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The Aftermath of Syllogism

formally correct definition was developed in Wolfgang Lenzen, “Zur extensionalen und »intensionalen« Interpretation der Leibnizschen Logik,” Studia Leibnitiana, 15 (1983): 129–148. Cf. Opuscules et fragments inédits de Leibniz, ed. Couturat, 53; the English translation is taken from Leibniz Logical Papers, ed. G. H. R. Parkinson (Oxford, 1966), 20–21. Cf. Willard v. O. Quine, From a Logical Point of View (New York, 1953), 21. Cf. Couturat, La Logique de Leibniz: “L’échec final de son système est donc extrêmement instructif, car il prouve que la Logique algorithmique (c’est-à-dire en somme la Logique exacte et rigoureuse) ne peut pas être fondée sur la considération confuse et vague de la compréhension; elle n’a réussi à se constituer qu’avec Boole, parce qu’il l’a fait reposer sur la considération exclusive de l’extension, seule susceptible d’un traitement mathématique,” 387. Cf. Opuscules et fragments inédits de Leibniz, ed. Couturat, 235. Cf. Book IV, ch. XVII , § 8 of the Nouveaux Essais de l’Entendement (i.e. G. W. Leibniz—Die Philosophischen Schriften, ed. C.I. Gerhardt, vol. 5, 469). Leibniz Logical Papers, ed. Parkinson, 33. For the sake of uniformity, Leibniz’s small letters “a,” “b” have been replaced by capitals “A,” “B.” Cf. Leibniz, Sämtliche Schriften und Briefe, Series 6 Philosophische Schriften, vol. 3, 506. Only in one fragment of around 1678, Leibniz himself considered to formalize the relation of conceptual containment, namely by the mathematical symbol “Γ” which he otherwise used in mathematical works for the greater-relation. Cf. Leibniz, Sämtliche Schriften und Briefe, Series 6 Philosophische Schriften, vol. 4, 143: “(2) Nota Γ aut vox est (ex. grat. e Γ d vel 30 Γ 6, homo est animal) significat in locum e vel 30 substitui posse d vel 6 vel animal.” Cf. Leibniz, Sämtliche Schriften und Briefe, Series 6 Philosophische Schriften, vol. 4, 154. Leibniz stated these laws especially in the “General Inquiries” of 1686. Cf. Leibniz, Sämtliche Schriften und Briefe, Series 6 Philosophische Schriften, vol. 4, 751: “Propositio per se vera est A coincidit ipsi A;” 750: “(6) Si A coincidit ipsi B, B coincidit ipsi A [. . .] (8) Si A coincidit ipsi B, et B coincidit ipsi C, etiam A coincidit ipsi B.” Łukasiewicz, “Zur Geschichte der Aussagenlogik,” 116 points out that already Stoic logicians like Sextus Empiricus interpreted conjunction as the truth-function “which is true if and only if both members are true; otherwise it is false.” Cf. Ashworth, Language and Logic in the Post-Medieval Period, 127. Cf. Hieronymus of St. Mark, Compendium preclarum quod parva logica seu summule dicitur ad introductionem juvenum in facultate logices (Cologne, 1507), quoted in Ashworth, Language and Logic in the Post-Medieval Period, 127. Cf. Leibniz, Sämtliche Schriften und Briefe, Series 6 Philosophische Schriften, vol. 4, 148: “AB est A pendet a significatione huiusmodi compositionis literarum. Hoc

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47 48 49

50

51

52

53

54 55

56

57

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ipsum enim vult AB, nempe id quod est A, itemque B.” Cf. also the related fragment “Elementa ad calculum condendum” of around 1678/79 (o.c., 150–155), where the law Conj 1 is characterized as the “newest fundamental proposition” of his calculus: “Si A est BC, etiam A est B, quia BC est B quae novissima est propositio hujus characteristicae.” Leibniz Logical Papers, ed. Parkinson, 40. Cf. ibid. Cf. Leibniz Logical Papers, ed. Parkinson, 58, fn. 4. In the earlier fragment “De Varietatibus Enuntiationum . . . ” (in Leibniz, Sämtliche Schriften und Briefe, Series 6 Philosophische Schriften, vol. 4, 125–133) the fundamental law Conj 4 had been put forward for the special case where the subject term A denotes an individual: “A est B et D [ex. gr.] Deus est justus et felix [. . .] resolvi potest in duas A est B et A est D, nempe Deus est justus et Deus est felix.” Note that Leibniz here uses the conjunction “et” not only to combine two propositions but also to conjoin two concepts B and D to “B et D”! Note further that in his drafts of the so-called Plus-Minus-Calculus, Leibniz denoted the conjunction by means of the addition-symbol “+.” Cf. Leibniz, Sämtliche Schriften und Briefe, Series 6 Philosophische Schriften, vol. 4, 291: “Si B est C, tunc AB erit AC [. . .] Retrorsum autem non colligi potest: AB est AC, ergo B est C.” Cf. Opuscules et fragments inédits de Leibniz, ed. Couturat, 236: “Sed videamus an haec sola sufficiant: Univ. Aff. A ∞ AB, Part. Neg. A non ∞ AB, Univ. Neg. A ∞ A non B, Part. Aff. A non ∞ A non B.” Cf. Wolfgang Lenzen, “Two Days in the Life of a Genius,” forthcoming in From Arithmetic to Metaphysics—A Path through Philosophical Logic—Studies in Honour of Sergio Galvan, eds. C. De Florio and A. Giordani (Milano, 2016). The first quotation is from an essay of April 1679, the second from a fragment of around 1686; cf. Leibniz, Sämtliche Schriften und Briefe, Series 6 Philosophische Schriften, vol. 4, 248 and 804. Cf. § 96 of the “General Inquiries,” i.e. Leibniz, Sämtliche Schriften und Briefe, Series 6 Philosophische Schriften, vol. 4, 767. Cf. § 77 of the “General Inquiries,” i.e. Leibniz, Sämtliche Schriften und Briefe, Series 6 Philosophische Schriften, vol. 4, 764: “Generaliter A esse B idem est quod non-B est non-A.” In the “General Inquiries,” these principles are formulated as follows: “A proposition false in itself is ‘A coincides with not-A’ ” (§ 11); “If A = B, then A ≠ not-B” (§ 171, Seventh); “It is false that B contains not-B (i.e. B doesn’t contain not-B”) (§ 43); and “A is B, therefore A isn’t not-B” (§ 91). Cf. Leibniz, Sämtliche Schriften und Briefe, Series 6 Philosophische Schriften, vol. 4, 751, 783, 755, and 766. Cf. Leibniz, Textes inédits, ed. Gaston Grua (Paris, 1948), 536: “A non est B, et A est non B esse idem.”

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58 Cf. Leibniz, Sämtliche Schriften und Briefe, Series 6 Philosophische Schriften, vol. 4, 766: “Non valet consequentia: Si A non est non-B, tunc A est B, seu Omne animal esse non hominem falsum est, quidem; sed tamen hinc non sequitur Omne animal esse hominem.” 59 Cf., e.g. § 21 of “Specimina calculi rationalis” in Leibniz, Sämtliche Schriften und Briefe, Series 6 Philosophische Schriften, vol. 4, 813: “A non est B idem est quod A est non B.” Further occurrences of this mistake have been gathered in Wolfgang Lenzen, “ ‘Non est’ non est ‘est non’—Zu Leibnizens Theorie der Negation,” Studia Leibnitiana, 18 (1986): 1–37. 60 Cf. W. v. Ockham, Summa Logicae (St. Bonaventure, N.Y., 1954), Pars II , Tractatus Tertius (De Consequentiis), Cap. 9, 625–626. 61 Cf. Leibniz, Sämtliche Schriften und Briefe, Series 6 Philosophische Schriften, vol. 4, 218; the quoted example of Apostle Peter only appears in the critical apparatus; Leibniz later replaced it by the less fortunate example “this piece of gold is a metal” vs. “this piece of gold is a not-metal.” 62 Cf. Leibniz, Sämtliche Schriften und Briefe, Series 6 Philosophische Schriften, vol. 4, 218, critical apparatus, variant (d): “Imo hic patet me errasse, neque enim procedit regula.” 63 Cf. Leibniz, Sämtliche Schriften und Briefe, Series 6 Philosophische Schriften, vol. 4, 218; in order to avoid confusion, I have interchanged Leibniz’s symbolic letters “B” and “A.” 64 Cf. Leibniz, Sämtliche Schriften und Briefe, Series 6 Philosophische Schriften, vol. 4, 749, fn 8: “A non-A contradictorium est. Possibile est quod non continet contradictorium seu A non-A. Possibile est quod non est Y, non-Y.” 65 Cf. Leibniz Logical Papers, ed. Parkinson, 115–121. 66 Cf. § 55 of the “General Inquiries,” Leibniz, Sämtliche Schriften und Briefe, Series 6 Philosophische Schriften, vol. 4, 757, or the English translation in Leibniz Logical Papers, ed. Parkinson, 60. 67 More exactly, this holds only for the implication ¬P(A∼B) ⇒ A∈B, while the converse A∈B ⇒ ¬P(A∼B) is easily proven: If A∈B, then (by Cont 3) A = AB, hence (by Iden 6) A∼B = AB∼B, and thus (A∼B)∈(B∼B), i.e. ¬P(A∼B). Cf. Leibniz, Sämtliche Schriften und Briefe, Series 6 Philosophische Schriften, vol. 4, 863: “Vera propositio categorica affirmativa universalis est: A est B, si A et AB coincidat et A sit possibile, et B sit possibile. Hinc sequitur, si A est B, vera propositio est, A non-B implicare contradictionem, nam pro A substituendo aequivalens AB fit AB non-B quod manifeste est contradictorium.” 68 Cf. also § 199 of the “General Inquiries,” i.e. Leibniz, Sämtliche Schriften und Briefe, Series 6 Philosophische Schriften, vol. 4, 787: “Propositio particularis affirmativa, AB est. Particularis negativa A non-B est. [. . .] Universalis affirmativa A non-B non est. Universalis negativa: AB non est.”

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69 Consider the complex concept A(∼A(∼B)) which contains A(∼A). Since A∼A is contradictory, it follows by Poss 2 that A(∼A(∼B)) also is impossible; but ¬P(A(∼A(∼B))) immediately entails by Poss 3 that A(∼A)∈B! 70 The inference from a contradictory pair of premises, α, ¬α to an arbitrary conclusion β was well known in Medieval logic, but Leibniz wasn’t convinced of its validity. In his excerpts from Caramuel’s Leptatos (in Leibniz, Sämtliche Schriften und Briefe, Series 6 Philosophische Schriften, vol. 4, 1334–1343) he considered the “argumentatio curiose” by means of which, e.g., the conclusion “Circulus habet 4 angulos” is derived from the premises “Petrus currit” and “Petrus non currit.” Although the deduction is based on two impeccable formal principles: (i) from α to infer (α∨β); (ii) from (α∨β) and ¬α to infer β, Leibniz annotated “Videtur esse sophisma.” 71 From the tradition Leibniz knew quite well that the corresponding propositional connective (α∨β) can similarly be defined as ¬(¬α ∧¬β). For a closer discussion cf. Lenzen, “Zur extensionalen und »intensionalen« Interpretation der Leibnizschen Logik,” esp. 132–133. 72 Cf. Wolfgang Lenzen, “Leibniz und die Boolesche Algebra,” Studia Leibnitiana, 16 (1984): 187–203. 73 This system has been reconstructed in Wolfgang Lenzen, Das System der Leibnizschen Logik (Berlin, 1990). 74 Cf. Leibniz, Sämtliche Schriften und Briefe, Series 6 Philosophische Schriften, vol. 4, 551. 75 Cf. Leibniz, Sämtliche Schriften und Briefe, Series 6 Philosophische Schriften, vol. 4, 671. 76 Cf. Leibniz, Sämtliche Schriften und Briefe, Series 6 Philosophische Schriften, vol. 4, 656. Leibniz’s symbols “L” and “M” have been replaced by “α” and “β.” For a more comprehensive investigation of Leibniz’s “Calculus of Strict Implication” (which covers also his possible-worlds-semantics) cf. Wolfgang Lenzen, Calculus Universalis— Studien zur Logik von G. W. Leibniz (Paderborn, 2004), ch. 11–13. 77 Cf. Leibniz, Sämtliche Schriften und Briefe, Series 6 Philosophische Schriften, vol. 4, 751. 78 Cf. Leibniz, Sämtliche Schriften und Briefe, Series 6 Philosophische Schriften, vol. 4, 809–810. 79 Cf. Leibniz, Sämtliche Schriften und Briefe, Series 6 Philosophische Schriften, vol. 4, 808. 80 Cf. Leibniz Logical Papers, ed. Parkinson, 65, § 72 + fn. 1. For a closer investigation cf. Wolfgang Lenzen, “Logical Criteria for Individual(concept)s,” in M. Carrara, A. M. Nunziante and G. Tomasi (eds), Individuals, Minds, and Bodies: Themes from Leibniz (Stuttgart, 2004) 87–107.

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Kant’s False Subtlety of the Four Syllogistic Figures in its Intellectual Context Alberto Vanzo University of Warwick

Kant’s only work in the field of formal logic (or, to use his terms, general pure logic1) is the short essay The False Subtlety of the Four Syllogistic Figures. Kant completed it in a “few hours”2 in 1762, shortly before completing three longer works, published in 1763 and 1764: The Only Possible Argument in Support of a Demonstration of the Existence of God, Attempt to Introduce the Concept of Negative Magnitudes into Philosophy, and Inquiry into the Distinctness of the Principles of Natural Theology and Morality.3 These four works outline a coherent set of doctrines, several of which are discussed in more than one work4 and differ significantly from Kant’s earlier and later views. In fact, two periods of silence separate the works of 1762–1764 from Kant’s other major publications. Kant only published minor, occasional writings from 1757 to 1761 and from 1765 to 1766.5 Among Kant’s works from the early 1760s, the False Subtlety has received the least attention from scholars. Most systematic studies focus on Kant’s views on syllogistic reduction. Interpreters diverge widely on what patterns of inference Kant allows,6 what reduction procedures he contemplates,7 and whether he intends them to apply to all valid forms of the second, third, and fourth figure.8 The few historical studies mostly focus on the relation between Kant’s claims on syllogism and the views that he developed in the Critical period.9 Little has been written on how the False Subtlety relates to the doctrines outlined in Kant’s other works from 1762–1764 and to the views of Kant’s contemporaries and immediate predecessors. It is especially unclear who Kant’s polemical targets were and to what extent Kant’s polemical aims shaped his views on syllogism. In the False Subtlety, Kant claims that second-, third-, and fourth-figure syllogisms are valid only insofar as they can be reduced to the first figure and he denies that logicians should dwell on the doctrine of modes and figures. By putting forward these views, does Kant intend 157

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to reject “Leibniz’s syllogistic logic,” as Silvestro Marcucci states,10 or is he “undoubtedly” using Leibniz as his source, as Adolfo León Gómez claims?11 Does Kant move “a small step” away from Christian Wolff ’s position, as Nicholas Rescher holds,12 or does he reject it altogether, as Michael Wolff suggests?13 This chapter discusses how Kant’s views on the foundations of syllogistic inference relate to their immediate intellectual context—the views of eighteenth-century German authors who wrote on syllogism—and to the conception of metaphysics that Kant develops in 1762–1764. We will see that Kant’s positions are, on the whole, rather original, even though they lack the marked independence from the intellectual context that one can find in Kant’s Critical works.14 Despite Kant’s polemical tone, his views on syllogism are not mainly motivated by polemical purposes. Instead, Kant’s views on the foundations of syllogism bear an interesting relation to his views on metaphysics, as they reflect the role that Kant assigns to syllogism in the process of metaphysical inquiry. This is in keeping with Kant’s later works, where several aspects of his formal logic are influenced by transcendental logic. I will focus on the relation of the False Subtlety with the views of Christian Wolff and some of his German successors. However, I do not intend to suggest that Kant was only influenced by these authors.15 I will not attempt to identify all influences on Kant’s conception of syllogism, nor will I survey all German writings on syllogism of the period “from Wolff to Kant.” I will only chart a representative sample of positions. This is sufficient to shed light on the degree of originality of the False Subtlety, to assess competing claims on the putative influences of Leibniz and Wolff on Kant, and to give the reader a sense of what questions were discussed, what the main points of disagreement were, and on which issues views were so fragmented that advancing a new view was itself a conventional move. Having outlined the positions of Kant’s immediate predecessors (§ 1), I will illustrate Kant’s views on the foundations of syllogisms and on the status of the second, third, and fourth figure (§ 2). I will then turn to their relation with the views of Kant’s immediate predecessors (§ 3.1) and with Kant’s own views on the foundation of metaphysics (§ 3.2). I will only discuss categorical syllogisms, as opposed to hypothetical and disjunctive syllogisms, because they are the only type of syllogism that the False Subtlety takes into account.

1. Kant’s immediate predecessors on syllogism Kant’s immediate predecessors generally agreed that, out of the 64 possible syllogistic moods and 256 syllogistic forms, 10 moods and 19 forms are valid.16

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They also agreed that all valid syllogisms in the second, third, and fourth figure can be reduced to the first figure.17 However, they disagreed on two questions: on what grounds we should accept those moods and forms as valid and whether second-, third-, and fourth-figure syllogisms are useful and should be studied. Kant’s answers to these questions are just two among a varied array of views that were upheld by his predecessors and contemporaries.

1.1 The foundations of syllogistic inference Kant’s immediate predecessors resorted to two methods to establish the validity of the 19 syllogistic forms. They are the method of principles and the reductive method.18 The method of principles amounts to formulating a series of rules to which all valid syllogisms must conform and excluding the forms which violate them, until one is left with the 19 valid forms. For instance, EAA and EAI violate the rule that, if one of the premises is negative, the conclusion must be negative. The reductive method amounts to establishing the validity of a privileged class of syllogisms (typically, those of the first figure) and reducing all other syllogisms to them. Kant does this by arguing that their conclusions can be inferred from the premises by means of a syllogism of the privileged class, in combination with non-syllogistic inferences.19 Martin Knutzen, a rather independent Wolffian20 who was Kant’s university teacher, preferred the method of principles.21 He held that prior attempts to employ the reductive method failed: Some learned men tried, with little success, to bring the entire doctrine of syllogisms under a single formula and a very general rule. Those who expressed the foundation of affirmative and negative syllogisms by means of two very general rules [as Kant would do in the False Subtlety] were not more successful.22

Most other authors privileged the reductive method. Among them was Christian Wolff, who was by far the most influential writer on logic in eighteenthcentury Germany. Wolff shares the then widespread distrust for the fourth figure, which he disregards entirely.23 He explains how second- and third-figure syllogisms can be reduced to the first figure.24 He adds that “the inferences that take place in the second and third figure can be accepted as valid [richtig] only because it is possible to reduce them to the first figure.”25 He even goes so far as to claim that second- and third-figure syllogisms are actually “cryptic first-figure syllogisms,”26 that is, first-figure syllogisms whose “authentic form is not apparent.”27 First-figure syllogisms, in turn, depend on the dictum de omni et

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nullo (henceforth simply “the dictum”), which is the conjunction of two principles: Dictum de omni: “Whatever can be affirmed of a whole genus or species is also affirmed of whatever is contained under that genus or species.”28 Dictum de nullo: “Whatever is denied of a whole genus or species must also be denied of whatever is contained under that genus or species.”29

Wolff characterizes genera and species extensionally, as classes, but also intensionally, as sets of shared features.30 Accordingly, the dictum can be read both extensionally, as in Wolff ’s German Logic, and intensionally, as in the works of his disciple Georg Friedrich Meier.31 On the extensional interpretation, the dictum states that whatever property can be truthfully ascribed or denied of all members of a class can be truthfully affirmed or denied of any of those members individually.32 On the intensional interpretation, the dictum states that whatever feature is part of the content of the concept of a genus or species is also part of the content of the concepts of its lower species or genera. In Wolff ’s view, two of the four forms of the first figure, Barbara (AAA-1) and Darii (AII-1), are “nothing else than the distinct application” of the dictum de omni. The other two forms, Celarent (EAE-1) and Ferio (EIO-1), are applications of the dictum de nullo.33 Since the dictum is the foundation of first-figure syllogisms and syllogisms in other figures can be reduced to them, the dictum is the “solid and unshaken foundation on which the entire doctrine of syllogism is to be erected.”34 It is a solid foundation because its truth is evident to whoever contemplates it. However, it is not a first principle, but an intermediate principle, because it can be proven on the basis of a more basic principle. According to Wolff, one can prove the dictum by showing that its negation involves a contradiction and, thus, is false.35 Being a reductio ad absurdum, this argument presupposes the validity of the law of excluded middle. Wolff regards it as a corollary of the law of contradiction,36 which is the first principle of his entire philosophy. In Wolff ’s eyes, then, the law of contradiction provides the ultimate basis of the reductive strategy for the foundation of syllogistic inference. Meier explains the rationale of this strategy with his usual clarity: By deriving the rules of syllogisms from the law of contradiction, we prove that they are not, as it were, arbitrary commands of philosophers, but absolutely necessary truths, and that the syllogisms which are formed in accordance with them have a necessarily correct form, on which we can rely with the most perfect trust.37

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Wolff ’s successors were generally sympathetic toward his attempt to reduce all syllogisms to an intermediate principle which, in turn, depends on one or more first principles of all philosophy. However, they disagreed on whether the dictum is a suitable intermediate principle. Joachim Georg Daries, whose logic displays some independence from Wolff, claimed that the dictum depends on the principium convenientiae: “the things that can be combined with the same third item can also be combined with each other under the same respect.”38 The Wolffian Hermann Samuel Reimarus agreed that a variant of the principium convenientiae is the foundation of all syllogisms, but he dispensed with the dictum altogether.39 Reimarus had two complaints against the dictum. It is not basic, because it depends on the laws of identity and contradiction. It cannot be straightforwardly applied to second-, third-, or fourth-figure syllogisms, because what “is affirmed or denied” by them “is not always predicated of the whole species of genus [. . .] Therefore, it was even more necessary” for him “to establish the validity [Richtigkeit] of all syllogisms by means of a more general rule” than the dictum,40 the principium convenientiae. While the limited applicability of the dictum led Reimarus to replace it with a different principle, it led others to complement it with other principles. Meier introduced three additional principles: “if the sufficient reason is true, its consequence too is true [. . .] if the consequence is false, its sufficient reason too is false;” “if one of [two] contradictory judgements is true, the other is false, and if it is false, the other is true;” “if a judgement is true, what has been derived from it through a truth-preserving logical combination must be true too.”41 For the anti-Wolffian Christian August Crusius,42 the dictum is just one (the sixteenth) of the 43 principles of valid syllogistic inferences. Each of those principles derives from the law of contradiction, the principle of sufficient reason, or both. In sum, most of Kant’s immediate predecessors shared the goal of establishing the validity of syllogistic inference through a reductive strategy. However, they disagreed on what principles should provide the basis for the reduction. Crusius, Daries, Meier, and Reimarus all made somewhat original proposals which disagreed with Wolff and one another. Nor would the practice of formulating new principles of syllogisms stop with the publication of the False Subtlety in 1762. Lambert, whose views on syllogism were antithetical to Kant’s, and Feder, who endorsed Kant’s central claims, formulated new principles of syllogisms in 1764 and 1774.43 Even the author of a very favourable review of the False Subtlety took the opportunity to correct Kant’s principles.44

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1.2 The status and usefulness of the second, third, and fourth figure Within Wolff ’s logic, the first figure has a privileged status for three reasons:

1. 2.

3.

It is the only figure to which all syllogisms of any other figure can be reduced. It is the only figure in which there are syllogisms with universal affirmative conclusions (in Barbara), particular affirmative conclusions (in Darii), universal negative conclusions (in Celarent), and particular negative conclusions (in Ferio).45 By contrast, second-figure syllogisms only have negative conclusions. Third-figure syllogisms only have particular conclusions. Fourth-figure syllogisms have negative conclusions and particular affirmative conclusions, but not universal affirmative conclusions. First-figure syllogisms are more natural than syllogisms in the other figures. This naturalness thesis might mean: (a) (natural1) people have a disposition to employ first-figure syllogisms more often than syllogisms in the other figures; (b) (natural2) formulating first-figure syllogisms is easier (takes up fewer cognitive resources) than formulating syllogisms in the other figures; and (c) (natural3) people typically formulate first-figure syllogisms more quickly than syllogisms in the other figures.

With his naturalness thesis, Wolff means at least natural1, because he holds that the naturalness of first-figure syllogisms derives from their proximity to the dictum.46 According to Wolff, we have an innate disposition to follow the laws of logic,47 some of them more than others. When we reason, we do not typically follow the inference schemata of the second, third, or fourth figure, but the dictum,48 of which the forms of first-figure syllogisms are paraphrases. Because of its primacy, Wolff calls the first figure “the perfect figure.”49 He claims that the first figure “is sufficient for reasoning” and that “we can be content with the first figure alone.”50 His discussion of the second and third figure in the Latin Logic provides reasons for dismissing them. He had done so in the shorter German Logic, which discusses only first-figure syllogisms.51 Of Wolff ’s reasons for privileging the first figure, (a) and (b) were not disputed.52 However, his claim that the first figure is the most natural was problematic. Not only did its justification invoke the dictum, that was controversial, but also, on all three readings, it is an empirical claim. Yet, Wolff provided no empirical evidence for it.

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One could challenge the naturalness thesis in two ways.53 First, one could hold a large-scale empirical inquiry of people’s reasoning patterns, which Kant’s predecessors did not carry out. Hence, there was no hard evidence to establish whether people reason mostly in the first figure, as Wolff held, or whether “the understanding thinks almost more often by means of the other syllogistic figures, especially the second and fourth, than [. . .] in the first,” as Crusius stated.54 Second, one could claim that syllogisms in the second or third figure are “extremely natural and simple,” whereas their reductions to the first figure are “very convoluted and forced.”55 Hollmann and Knutzen held this. An example that supports their view can be found in Johann Heinrich Lambert’s New Organon, which was published shortly after Kant’s False Subtlety.56 According to Lambert, when we are faced with the sentences: All circles are round. No rectangles are round.

we can infer “no rectangles are circles” straightaway. The inference with which we do so is a second-figure syllogism in Camestres (AEE-2). Alternatively, we can derive the conclusion from the premises with two immediate inferences and a first-figure syllogism:

(a) from “all circles are round” we can infer “whatever is not round is not a circle,” that is, “no non-round things are circles” through contraposition; (b) from “no rectangles are round” we can infer “all rectangles are non-round” through obversion; (c) we can use the conclusions of these inferences as the premises of a syllogism in Celarent (EAE-1): ● ● ●

No non-round things are circles. All rectangles are non-round. ∴ No rectangles are circles.

When Wolff ’s peers claimed that second- and third-figure syllogisms are more “natural and simple” than their “convoluted and forced” reductions to the first figure,57 they appear to have had examples like this in mind. They expected their readers to agree that formulating the second-figure syllogism is easier (contra natural2) and faster (contra natural3) than formulating their reductions.58 If this is true, if the example can be generalized, and if people have a disposition to employ easier and faster inferences more often than harder and slower ones, there might be a reason to reject natural1 too.

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However things may be with regard to the naturalness thesis, Crusius highlighted another reason why one should not be content with the first figure, as Wolff had suggested. All syllogistic forms should be discussed because the aim of logic is to explain all formally valid inference forms. Crusius makes this clear when he criticizes those who “did not want to admit any figures and moods that can be reduced to moods that do not belong to the first figure.”59 With this convoluted expression, Crusius might be referring to those syllogistic forms, like Disamis (IAI-3), which can only be reduced to the first figure by first being reduced to the third or fourth figure.60 The complexity of their reduction provides no reason to disregard them because: if the understanding can form syllogisms in various ways and if logic must explain its manifold operations, it is not superfluous to learn those forms too [. . .]61

Crusius’ tendency toward comprehensiveness contrasts sharply with Kant’s view that “logic” should only focus on the “simplest mode of cognition,”62 to which other modes of cognition (like second-, third-, and fourth-figure syllogisms) can be reduced. Given these divergences, what constituted a “false [i.e. useless] subtlety” was far from agreed. Those who stressed the preeminence of the first figure, like Wolff, noted that the other figures can be reduced to it and held that discussing them thoroughly is a useless subtlety. Those who advocated the usefulness of three or all four figures, like Hollmann and Knutzen, often refrained from “annoying readers” by “dwelling on the reduction principles with which Scholastics filled the memory of their young pupils.”63 If Knutzen, who wrote these words in 1751, had lived long enough to read the False Subtlety, he might well have regarded Kant’s reduction principles as the truly useless subtlety in the doctrine of syllogism.

2. Kant’s view of syllogism in the False Subtlety In this context, Kant’s False Subtlety puts forward a very clear-cut view. The only portion of the doctrine of syllogism that logic should be concerned with is that regarding the first figure. Although “valid inferences may be drawn in all [. . .] four figures,”64 there is no need to dwell on the second, third, or fourth figure, the “rules peculiar” to each of them, or the list of valid forms which are found in each figure.65 This is because the aim of logic is “reducing everything to the simplest mode of cognition”66 and syllogisms in the second, third, and fourth

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figure can be reduced to combinations of first-figure syllogisms and immediate inferences. Kant defends these views by putting forward an account of the function of syllogism, two new principles of syllogisms, a sketch of the procedures for reducing the second, third, and fourth figure to the first, and the claim that people ordinarily follow those procedures when making inferences.

2.1 Background: Marks, judgements, and syllogisms Kant discusses the foundations of syllogistic inference in the first two sections of the False Subtlety. There, he introduces two first principles of all syllogisms, building on his notion of mark and his definitions of judgement and syllogism. Kant holds that the content of some concepts is simple and unanalyzable. Other concepts derive from the combination of further concepts, which can be identified through a process of analysis. An example is provided in Figure 9.1. Sometimes, Kant calls mark [Merkmal, nota] a concept that composes another concept: for instance, when he mentions “a mark of a mark.”67 Other times, he calls mark a property of a thing (“a mark of the thing itself”68). I will call the former marksc and the latter marksp.69

Figure 9.1 The content of a concept

“To compare something as a mark with a thing is to judge.”70 The result of this comparison is a mental content, a judgement, which combines a subject concept with a predicate concept. The subject concept designates the “thing,” broadly understood,71 that is the subject of predication. The predicate concept designates a feature (“a mark of some thing or other”72). The copula unaccompanied by negation expresses the belonging of the markp to the subject of predication. The copula accompanied by negation expresses the non-belonging of the markp to the subject of predication.73 “That which is a mark of a mark of a thing is called a mediate mark of that thing.”74 More precisely, assuming that an object a has properties P and Q,

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if the concept of P is a component of the concept of Q, then P is a mediate mark of a.75 Consider, for instance, the concept of bachelor, as represented in Figure 9.1. That concept has some first-level components (the concepts of male, adult, and unmarried), which have, in turn, other components.76 Being a male and being a living being are both properties (marksp) of bachelors and the concept of a living being is a component (a markc) of the concept of being male. Hence, being a living being is a mediate mark of a bachelor. By contrast, the properties corresponding to first-level components of the concept of bachelor (being male, adult, and unmarried) are immediate marks of the concept of bachelor. Kant’s predecessors and, in the 1780s, Kant himself distinguished between two ways of formulating syllogisms or chains of syllogisms. We may entertain the premises and infer the conclusion from them, employing syllogism as a tool for discovering truths that we had not previously thought of. Alternatively, we may start from the conclusion and seek its justification, that is, a reason for asserting the belonging or non-belonging of the mediate markp expressed by the predicate to the item(s) referred to by the subject. In this case, we look for a middle term which we can combine with the subject and the predicate, so as to formulate two sentences which we take to be true and from which we can derive the conclusion.77 In the False Subtlety, Kant regards syllogism as a tool for justification, rather than discovery. He defines a syllogism as a “judgement which is made by means of a mediate mark.” “In other words, a syllogism is the comparison of a mark with a thing by means of an intermediate mark.”78 The comparison presupposes that the conclusion is being thought and it aims to establish its truth. It should lead us “clearly to recognise the relation of the mark [the predicate of the conclusion] to the thing [its subject].”79 If the conclusion is an affirmative judgement, the relation that it expresses is that the predicate belongs to the subject.80 We should look for an intermediate mark (a middle term) that gives us reason to believe that the predicate belongs to the subject.81 More specifically, we should look for a markc of the subject concept, of which the predicate is in turn a markc: In order clearly to recognise the relation of the mark to the thing in the judgement: the human soul is a mind, I employ the intermediate mark rational, so that, by its means, I regard being a mind as a mediate mark of the human soul. In this case, three judgements must necessarily occur:

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Being a mind is a mark of that which is rational; Rational is a mark of the human soul; Being a mind is a mark of the human soul.

[. . .] Cast in the form of judgements, the three operations would run: all that is rational is a mind; the soul of man is rational; therefore, the soul of man is a mind.82

If, instead, we want to establish a negative conclusion, we should look for a markc of its subject, which is incompatible with a markc of the predicate. If the premises of the resulting syllogism contain mediate marksc of the subjects, they can be established through further syllogisms. If they contain immediate marks, ideally, we will recognize their truth through experience or intuition.83 Readers may wonder why the process could not unfold the other way round: start from judgements established through experience or intuition and deduce new conclusions from them. The False Subtlety does not answer this question. It leaves the reader wondering why Kant does not echo Daries’ view that “syllogisms are a means of invention,”84 but portrays them solely as tools for justifying propositions by seeking suitable middle terms.85

2.2 The foundations of syllogistic inference We have seen that Kant identifies syllogism with the activity of asserting that some marks belong or do not belong to things, on the ground that they belong, or are incompatible with, some of their other marks. Kant’s principles of syllogisms explain why we are entitled to make these assertions: [T]he first general rule of all affirmative syllogisms [i.e. syllogisms whose conclusion is an affirmative sentence] is this: A mark of a mark is a mark of the thing itself (nota notae est etiam nota rei ipsius). And the first general rule of all negative syllogisms is this: that which contradicts the mark of a thing, contradicts the thing itself (repugnans notae repugnat rei ipsi).86

Kant goes on to explain that his principles state the reasons for the truth of the dictum de omni et nullo. He formulates the dictum de omni as: “that which is universally affirmed of a concept, is also affirmed of everything that falls under that concept.”87 What is affirmed of a concept is a mark. It can be affirmed of the things that fall under the concept because, as the nota notae principle states, a mark of a mark of a concept is a mark of the things that fall under it.88 The same applies, mutatis mutandis, to the dictum de nullo. Kant also claims that his principles are first principles as they cannot be proven from more basic principles.

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This is because “a proof is only possible by means of one or more syllogisms” and any syllogisms presuppose the truth of his principles.89 Kant’s nota notae and repugnans notae principles cannot be found in the works of his immediate predecessors.90 Aristotle stated the nota notae principle in the Prior Analytics,91 but I have found no evidence that Kant was aware of this. The view that the nota notae and repugnans notae principles provide the foundation of the dictum is not found in Aristotle either. It probably was an original claim of Kant. However, Kant grossly overstates his originality when he claims that the dictum de omni and the dictum de nullo are “the principles which all logicians have hitherto regarded as the first rules of all syllogisms.”92 On the one hand, those who regarded them as principles of syllogisms, like Wolff, did not regard them as first principles. They took them to derive from the law of contradiction. On the other hand, in putting forward new principles of syllogisms, Kant was not departing from “all logicians.” He was following on the footsteps of Crusius, Daries, Meier, and Reimarus, all of whom had proposed new principles of syllogisms.93 It is hard to believe that Kant’s overstatement was unintentional. Kant had read the texts in which they propose those new principles.94 He also commented on Meier’s discussions of syllogism more than ten times in the logic courses that he held before 1762.95 Worse still, one of the reasons why Reimarus and, in all likelihood, Meier rejected the dictum as the foundation of syllogisms spells trouble for Kant’s new principles. Meier would not have complemented the dictum with three other principles if he thought that it alone provides the foundation of all syllogisms. Reimarus openly complained that the dictum applies only to first-figure syllogisms.96 Kant’s new principles do not apply to all syllogisms either. They fail to apply to some second-, third-, and fourth-figure syllogisms.97 Consider, for instance, an affirmative syllogism of the third figure (in Disamis, IAI-3): Some painters are creative. All painters are visual artists. ∴ Some visual artists are creative.

In Kant’s terms, the syllogism ascribes a mark (creativity) to certain things (some visual artists). If the syllogism conformed to Kant’s nota notae principle, it would ascribe creativity to some visual artists on the ground that they have another mark, which is expressed by the middle term (being a painter). Yet, the syllogism does not state that some visual artists are painters. It states the opposite, namely, that all painters are visual artists.98 It follows that the syllogism, as it is, does not conform to Kant’s principle.

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As an example of a negative syllogism, consider a second-figure syllogism in Baroco (AOO-2): All good historians have good memory. Some academics do not have good memory. ∴ Some academics are not good historians.

The syllogism concerns some academics. It denies that they have the mark of being good historians. If the syllogism conformed to Kant’s repugnans notae principle, it would deny that they have that mark on the ground that it is incompatible with another mark of theirs. Yet, the syllogism does not deny that some academics are good historians because this is incompatible with a mark that they have, but because it entails having a feature (good memory) that they lack.99 It may seem surprising that, even though he had read Meier’s and Reimarus’ texts, Kant proposed principles that fail to apply to all second-, third-, and fourth-figure syllogisms. Kant was aware that his principles relate specifically to the first figure. He writes that “the supreme rules governing all syllogisms lead directly to that order of concepts which is called the first figure.”100 To appreciate Kant’s motivation for focusing on first-figure syllogisms, we must turn to his views on the status and usefulness of the other figures.

2.3 The status and usefulness of the second, third, and fourth figure The reason why Kant regards the principle of the first figure as the principle of all syllogisms is that, like Wolff, he subordinates the other figures to the first. He does not go as far as to claim that all valid second-, third-, or fourth-figure syllogisms are actually “cryptic first-figure syllogisms.”101 However, he does claim that they are valid only insofar as they can be reduced to the first figure. More precisely, he claims that they are valid only if their conclusion can be derived by carrying out immediate inferences on one or both premises and formulating a first-figure syllogism.102 An example of this procedure is the reduction of a second-figure syllogism in Camestres (AEE-2) to a first-figure syllogism in Celarent (EAE-1) that we encountered in Section  1.2. The nota notae and repugnans notae principles ground the validity of first-figure syllogisms and these, along with immediate inferences, ground the validity of all other syllogisms.103 Hence, the nota notae and repugnans notae principles ground, directly or indirectly, the validity of all syllogisms.

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Kant’s claim is not just that the reduction of non-first-figure syllogisms to the first figure provides a reason for regarding them as valid. Kant claims that they are valid only insofar as they can be reduced to the first figure. They should be called mixed or hybrid syllogisms because they are “only possible by combining more than three judgements,”104 the fourth (and, in some cases, fifth) judgement being obtained through an immediate inference from one of the premises. By contrast, first-figure syllogisms are not mixed, but pure because they do not require that “there must be inserted between” the premises “some immediate inference which has been drawn from one or other of them, if the argument is to be valid [bündig].”105 This and similar statements106 imply that the validity of non-first-figure syllogisms depends on the possibility of deriving their conclusion from the premises by means of immediate inferences and a first-figure syllogism. As we saw above, valid syllogisms can be established through the method of principles, without reducing them to a privileged class. One can formulate a series of rules to which all valid syllogisms must conform and exclude the forms which violate them. Kant was aware of the possibility of employing this method. He could find it applied, inter alia, in Knutzen’s logic manual. He used it in a personal note from the 1750s.107 Although Kant knew that valid syllogisms can be established through the method of principles, he did not explain why he privileged the reductive method in the False Subtlety. Just two years after the publication of the False Subtlety, Lambert would put forward proof of the validity of syllogisms in each figure which do not rely on their reduction to any other figure. He took this to show the mistake of those who were misled to go as far as to regard the last three figures as indirect and capable only of a mediate proof, and to reject them as entirely unnatural, even though they admitted the validity of inferences in those figures.108

Kant’s view in the False Subtlety fits this description. Lambert’s proofs would put pressure on those who rely on the reductive method to make the reasons for this choice explicit in a way that Kant did not do. Kant’s claim that any other syllogistic forms are valid only insofar as they can be reduced to the first figure entails that the forms which do not satisfy this constraint should be rejected. In fact, Kant denies the legitimacy of the syllogisms whose conclusion, to his mind, cannot be derived from the premises through immediate inferences and first-figure syllogisms. These are the affirmative forms of the fourth figure (Bamalip and Dimatis), which, however, are both valid.109

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Instead of calling them invalid,110 Kant states, rather vaguely, that they are “not possible [. . .] at all.”111 He provides a second reason for rejecting them, besides the fact that they cannot be reduced to the first figure with his favored method. The reason is that their premises do not state the ground in virtue of which, if they are true, the conclusion too is true.112 Since Kant does not spell out the relevant notion of ground or the reason why syllogistic premises should provide such a ground, his brief remark is hardly convincing as it stands. Kant does not only state that the validity of syllogisms should be established through a reductive method, but he also claims that people follow it in their reasoning. He states that, when people infer the conclusion of a mixed syllogism from their premises (or, on Michael Wolff ’s reading, when they do so by running through all the required inferential steps113) they employ immediate inferences and a first-figure syllogism. In other words, ordinary people retrace the process that the Kantian philosopher employs to justify the validity of syllogisms. Kant highlights this in a series of incidental remarks. For instance, he writes that the “power to establish a conclusion [Schlußkraft]” of a mixed syllogism “depends upon the tacit addition” of an “immediate inference, which has to be present if only in thought.”114 Kant’s psychological claim raises a worry for those who, like him, are concerned with the naturalness of inferential processes. Kant’s concern with naturalness is most apparent when he complains that “[t]he mode of inference” in the fourth figure “is highly unnatural and depends upon a large number of intermediate inferences, which have to be supposed to be interpolated.”115 The reductions proposed by Kant for second- and third-figure syllogisms too require the interpolation of immediate inferences. For that reason, one could complain that they are harder and slower to carry out (less natural2 and natural3) than the original syllogisms. This is what Lambert claimed with regard to the example in Section  1.2. Even Feder, who agreed with Kant’s views on how we derive the conclusions of second-, third-, and fourth-figure syllogisms, held that some of them are more natural than the corresponding combinations of immediate inferences and first-figure syllogisms.116 If we have a disposition to make easier and faster inferences, rather than more complex and slower ones, we are more likely to infer the conclusions of second-, third-, or fourth-figure syllogisms directly from their premises than to employ Kant’s reduction procedure. Presumably, Kant held that his favored reduction procedure can be applied easily and quickly enough not to raise any concerns about unnaturalness. He states that his procedure lacks the “futile tediousness” of other procedures and claims that, given the conclusion and the middle term, one can employ his

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favored reductions “instantly.”117 Yet, as Lambert might reply, whether the reduction outlined in Section  1.2 is performed instantly is by no means uncontroversial. In this section, we have seen that the False Subtlety portrays syllogisms as tools for justification, as opposed to invention. Kant does not provide any reasons for disregarding invention. He puts forward two principles of syllogisms which are original, if compared with those proposed by his peers, even though formulating new principles of syllogisms was itself a conventional move. Kant’s principles directly apply to first-figure syllogisms. They ground other syllogisms in virtue of their reducibility to the first figure. Kant’s emphasis on a specific kind of reduction, carried out through immediate inferences and first-figure syllogisms, is rather original. However, he does not explain why we should only rely on reductions, as opposed to the method of principles, in order to ground the validity of syllogisms. Kant does not provide any clear, persuasive reasons for dismissing the syllogistic forms that, in his view, do not suit his reductive strategy (Bamalip and Dimatis). His claims on the psychological primacy of the first figure and on the employment of syllogistic reductions raise concerns about their naturalness, which Kant does not address. In conclusion, the False Subtlety does not provide sufficient justification for Kant’s silence on whether syllogisms can aid invention, the primacy that he assigns to the first figure, and his choice of privileging the reductive method, while disregarding the method of principles.

3. The False Subtlety, Kant’s immediate predecessors, and Kant’s works from 1762–1764 One might hope to explain Kant’s silence on whether syllogisms can aid invention, the primacy that he assigned to the first figure, and his choice of privileging the reductive method by looking at the works of his peers and immediate predecessors. Kant might have followed some of them closely, implicitly accepting their justification for certain views. If he strongly opposed other authors, this opposition might help explain why he took certain stances. Alternatively, one might seek an explanation for Kant’s views on syllogism by looking at the doctrines that he endorsed in his other works from the early 1760s. This section examines the relation between Kant’s views in the False Subtlety, those of his immediate predecessors, and the doctrines outlined in Kant’s other works from 1762–1764.

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3.1 The False Subtlety and Kant’s immediate predecessors Traditionally, Kant’s pre-Critical works have been read in the light of a familiar developmental story. Before becoming a Critical philosopher, Kant is said to have been first a Leibniz-Wolffian rationalist and, later, a Lockean or Humean empiricist.118 It is tempting to interpret the False Subtlety in the light of this evolutionary schema, focusing especially on its relation to Leibniz and Wolff. The False Subtlety has been said to be influenced by Leibniz, Wolff, or opposed to their views. Contrary to Silvestro Marcucci’s suggestion, the False Subtlety makes no explicit effort to criticize “Leibniz’s syllogistic logic.”119 Leibniz is not mentioned in the False Subtlety and was not often mentioned in discussions of syllogism by Wolff, Crusius, Reimarus, and Kant’s other contemporaries or immediate predecessors. Adolfo León Gómez holds that, nevertheless, Leibniz influenced Kant’s views both (a) directly, through his reading of the New Essays, and (b) indirectly, through Wolff ’s influence.120 We can safely rule out (a), at least with regard to the False Subtlety, because it was published in 1762, three years before the New Essays. As for (b), there are two reasons to doubt that Leibniz’s views on the foundation of syllogism influenced Kant via Wolff. First, Leibniz does not figure prominently in Wolff ’s discussions of syllogism.121 Second, the distinctive, “contra-traditionary”122 aspect of Leibniz’s discussion of syllogism in the New Essays is his preference for indirect reductions, which employ reductio ad absurdum. In the False Subtlety, Kant puts forward a different strategy, based on immediate inferences. He does not mention or criticize Leibniz’s strategy.123 According to Michael Wolff, Kant’s claim that only first-figure syllogisms are pure is directed against Christian Wolff ’s view that syllogisms of all figures are pure.124 However, as we saw in Section 1, Christian Wolff, too, gave pride of place to the first figure. Like Kant, he claimed that “the inferences that take place in the second and third figure can be accepted as valid only because it is possible to reduce them to the first figure.”125 Wolff and Kant also agreed that the first figure is the most natural, that people privilege it in their ordinary reasoning, and that any other syllogisms should be accepted because they can be reduced to the first figure.126 Rather than to Wolff ’s views, Kant’s views on syllogism are opposed to those of Crusius, who held that logic should discuss all four figures and that we sometimes reason more quickly and easily (hence, more naturally) by employing second-, third-, and fourth-figure syllogisms than first-figure syllogisms. However, Kant does not outline his views on the foundations of syllogistic

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inference by contrasting them with Crusius’ views. He criticizes him only in passing, for his discussion of the fourth figure.127 This is surprising, given that Kant was keen to criticize Crusius whenever he had a chance in the early 1760s.128 Moreover, Kant’s views are as far from Crusius’ views as they are from those of the Wolffian Martin Knutzen, who privileged the method of principles and dismissed syllogistic reductions as useless. Hence, it would be wrong to read the False Subtlety through the lens of the dichotomy of Wolffianism and anti-Wolffianism. In his other works from the 1760s, Kant outlines several doctrines by criticizing other authors. For instance, he introduces his theory of existence by contrasting it with Baumgarten’s, Wolff ’s, and Crusius’ theories.129 He develops his account of the principles of metaphysics by engaging with Crusius’ account.130 By contrast, the False Subtlety does not contain any explicit, extended engagement with the views of other authors. References not only to Crusius, but also to any other authors are scarce and sometimes imprecise. Kant unfairly classifies all earlier logicians as upholders of the view that all four figures are on a par. He mistakenly claims that they all endorsed the dictum, even though the texts he had read, such as Reimarus’ Vernunftlehre, prove otherwise.131 All this indicates, first, that the False Subtlety is not mainly the result of Kant’s endorsement of the views of his immediate predecessors. Despite some affinities with the views of Wolff and others,132 the principles of syllogisms and the reduction strategy that the False Subtlety puts forward are not found among Kant’s immediate predecessors. Second, the False Subtlety is not mainly the result of Kant’s polemical engagement with the views of specific authors. We cannot explain Kant’s silence on whether syllogisms can aid invention, the primacy that he assigned to the first figure, and his choice of privileging the reductive method by looking at the relation between his views and those of his peers.

3.2 The False Subtlety and Kant’s works from the early 1760s Kant’s texts from the early 1760s do not provide solid reasons for his focus on syllogism as a tool for justification, his focus on the first figure, and his employment of the reductive method. However, they allow us to see why Kant found these choices attractive. This is because they fit in closely with the theory of the method of metaphysics that Kant developed in his other works from 1762–1764, especially the Inquiry into the Distinctness of the Principles of Natural Theology and Morality. Kant’s concern with the method of metaphysics in the early 1760s derives from his bleak assessment of the status of philosophy in general and metaphysics

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in particular. “Claims to philosophical cognition generally enjoy the fate of opinions and are like the meteors, the brilliance of which is no guarantee of their endurance.”133 Metaphysics is a “dark and shoreless ocean” and all attempts to develop metaphysical systems had failed.134 In Kant’s eyes, the failure of Wolff ’s metaphysics depends largely on his employment of a mathematical method.135 Conversely, Kant’s hopes of success in this discipline rely on his belief that he had identified the true method of metaphysics.136 The method advocated by Kant is based on intuition and conceptual analysis. Metaphysical inquiries address questions such as what time is and whether bodies are made up of simple substances.137 The concepts of the objects of metaphysics, such as those of time and body, are given to us before we raise those questions, but only “confusedly or in an insufficiently determinate fashion.”138 To answer a metaphysical question, we should analyse the relevant concepts in all kinds of relation [. . .]: different marks which have been abstracted have to be combined together to see whether they yield an adequate concept; they have to be collated with each other to see whether one mark does not partly include another within itself.139

In doing so, we should bear in mind that not all concepts can be analyzed. Some are unanalyzable because they have no marks, others because our cognitive limits prevent us from identifying them.140 Given an analyzable concept, we should identify its immediate and mediate marks. This process unfolds through acts of judgement, because “a distinct concept [that is, a concept of which we can enumerate some marks] is possible only by means of a judgement.”141 Every true judgement that identifies a markc of a concept (and the corresponding markp of the things that fall under that concept) is true in virtue of the law of identity: “to every subject there belongs a predicate which is identical with it.”142 Every true judgement that denies a mark of a concept is true in virtue of the law of contradiction: “to no subject does there belong a predicate which contradicts it.”143 As we saw in Section 2.1, marks are either mediate or immediate. According to Kant, we become aware that an immediate mark is part of the content of a concept through an act of intuition. Intuition makes us aware of an “identity” or “contradiction” that “is to be found immediately in the concepts” and “cannot or may not be understood through analysis by means of intermediate marks.”144 The belonging of a mediate mark B to a concept a is not revealed by intuition. It must be established through a syllogism. We must look for a mark of a of which B is in turn a mark, so that we can apply the nota notae principle: “A mark

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of a mark is a mark of the thing itself.”145 For instance, in order to establish that divisibility is a mark of bodies, we can employ the intermediate mark “compound.” The judgements “bodies are compound” and “what is compound is divisible” ascribe immediate marks to their subjects and we can be intuitively aware of their truth. They provide the premises of a first-figure syllogism whose conclusion is “bodies are divisible.”146 The cognitions that we establish in this way are to be organized in a system. Intuition warrants the truth of its basic or, in Kant’s terms, indemonstrable propositions. Syllogisms warrant the truth of demonstrable propositions, which we deduce from indemonstrable propositions and previously proven propositions. The nota notae and repugnans notae principles ensure the validity of the syllogisms employed. The ensuing metaphysical system aims to represent the basic structure of the world. “To use the terminology of school-philosophers, at that time” Kant conceived of the world itself as “a system of species and genera, subordinated to one another according to the law of identity.”147 Kant’s account of syllogism in the False Subtlety is in keeping with the functions that he assigns to syllogisms within the method of metaphysics. To begin with, Kant holds that we derive metaphysical truths by analyzing concepts that are “given” to us “confusedly.”148 Syllogisms must justify those truths by deducing them from indemonstrable propositions and from previously proven propositions. Accordingly, the False Subtlety portrays syllogism as a tool for justification, not for invention. In the second place, Kant’s method of metaphysics employs syllogisms to justify the ascription or denial of mediate marks to things, based on the ascription or denial of immediate marks to them. The two principles introduced in the False Subtlety, the nota notae and repugnans notae principles, spell out the rationale of these ascriptions more clearly than the dictum. The syllogisms which are used for these ascriptions are first-figure syllogisms. To be sure, second-, third-, and fourth-figure syllogisms may be helpful for Kant’s purposes. As Lambert would note in his New Organon, one can employ the second figure to “prove differences between things, the third” to “prove examples and exceptions,” and “the fourth” to “rule out” relations between species and kinds.149 All of these actions can be useful to build the kind of metaphysical system that Kant was contemplating in the early 1760s. Nevertheless, Kant’s method of metaphysics focuses on the identification of relations of inclusion and exclusion between concepts, which are established primarily through firstfigure syllogisms. Their central role within Kant’s theory of metaphysics parallels the pride of place that they have within the False Subtlety.

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Finally, Kant’s foundation of the second, third, and fourth figure through a reductive method fits in nicely with the architectonic structure of his philosophy. If Kant had followed the method of principles, he would have identified numerous principles, which he would have employed to reduce the number of valid syllogistic forms from 256 to 19. By following the reductive method, Kant can put forward just two principles of all syllogisms, which parallel the principles of judgements. On the one hand, Kant admits two principles of true judgements, the laws of identity and contradiction. He claims that all truths depend on them. He relates them respectively to affirmative and negative truths. On the other hand, Kant admits two principles of valid syllogisms, the nota notae and repugnans notae principles. He claims that the validity of all syllogisms depends on them. He relates them respectively to affirmative and negative syllogisms. It is well known that Kant paid much attention to architectonic considerations, as the structure of his Critical works makes apparent.Architectonic considerations alone cannot warrant Kant’s claims on the principles of syllogisms. Nevertheless, they explain why Kant found it attractive to claim that all valid syllogistic forms are grounded on the nota notae and repugnans notae principles. We have seen that Kant’s theory of the method of metaphysics fits in closely with his focus on syllogism as a tool for justification, on the first figure, and his employment of the reductive method. There are two reasons why this fit helps explain Kant’s views on syllogism. To begin with, Kant held that identifying the method of metaphysics is crucial for its success. Kant wrote in 1763 that he had meditated on this topic for years.150 Although he was duty-bound to teach logic semester after semester, Kant did not think that the theory of syllogism was nearly as important as the methodology of metaphysics. He took the doctrine of moods and figures to be useless151 and he called the False Subtlety “the labour of a few hours.”152 It is understandable that his views in an occasional work on a topic of secondary importance were influenced by the ideas which he was spending much time and many efforts on. Moreover, it is well known that the Critical Kant was keen to map central notions and distinctions of his epistemology-cum-metaphysics onto formallogical notions and distinctions. This tendency is not confined to Kant’s Critical works. In the early 1760s, Kant draws several parallels between logical and metaphysical notions: logical ground and real ground,153 logical opposition and real opposition,154 logical necessity and real necessity,155 formal principles and material principles.156 Kant’s endorsement of a doctrine of syllogism that reflects the role of syllogism within metaphysics is yet another expression of his tendency to relate formal-logical views to epistemological and metaphysical views.

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This chapter has examined the relation of the False Subtlety with its intellectual context, including the works of Kant’s immediate predecessors and Kant’s other works from the early 1760s. This examination supports two conclusions. First, the False Subtlety is a moderately original work. The principles of syllogisms and the reduction strategy that Kant puts forward are original with respect to his intellectual context. However, the False Subtlety is far from displaying the level of innovation and autonomy from Kant’s cultural environment that can be found in his later, Critical works. Kant’s choice of putting forward new principles of syllogism was a rather conventional one, having been pursued by Crusius, Daries, Meier and Reimarus, among others. His claims on the primacy and naturalness of the first figure recall similar claims by Wolff. At any rate, the False Subtlety was not mainly the result of Kant’s endorsement or rejection of the views of his predecessors. Second, the False Subtlety has some puzzling features, for which Kant provides little or no reason. These are his focus on syllogism as a tool for justification, his focus on the first figure, and his employment of the reductive method for the foundation of syllogisms. These features of the False Subtlety can be explained by considering the relation between Kant’s logical and metaphysical views. Kant endorses a view of syllogism that is in line with, and influenced by, his conception of the method of metaphysics. Thus, the study of the False Subtlety confirms the usefulness of reading Kant’s formal logic and his epistemology-cum-metaphysics in the light of one another.

Notes 1 Kant rarely uses the expression “formal logic” (A131/B170). However, he often stresses the formal character of general pure logic (e.g. in A55/B79, A59–60/B84–85). References to the Critique of Pure Reason appeal to the first and second edition pagination (A and B). Otherwise, the pagination to which I refer in Kant’s texts is from his Gesammelte Schriften, ed. Königlich Preußische (Deutsche) Akademie der Wissenschaften (Berlin, 1900–). I use the following abbreviations: Beweisgrund = Der einzig mögliche Beweisgrund zu einer Demonstration des Daseins Gottes; Deutl. = Untersuchung über die Deutlichkeit der Grundsätze der natürlichen Theologie und der Moral; M. Herder = Metaphysik Herder; Größen = Versuch den Begriff der negativen Größen in die Weltweisheit einzuführen; Spitzf. = Die falsche Spitzfindigkeit der vier syllogistischen Figuren. Translations are from The Cambridge Edition of the Works of Immanuel Kant, ed. Paul Guyer and Allen W. Wood (Cambridge, 1992). I have replaced American spelling with British spelling and “characteristic mark” with “mark” as a translation of “Merkmal.”

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2 Spitzf., 2:57. 3 I have listed these works in the order of composition, which differs from the order of publication. It was established on the basis of philological criteria after several controversies. See Mariano Campo, La genesi del criticismo kantiano (Varese, 1953), 249–251. 4 For instance, the theory of formal and material principles of truth outlined in Deutl., 2:293–296 expands on ideas sketched in Spitzf., 2:60–61. The distinction between logical and real opposition is first introduced in Beweisgrund, 2:85–87 and then explained in Größen. The mistake of starting philosophical inquiries with definitions is criticized first in Beweisgrund, 2:66 and then in Deutl., 2:281–282, 283, 284, 285, 288–289, 292–293. 5 They are the announcement of his lectures on physical geography (1757); New Doctrine of Motion and Rest (1758); An Attempt at Some Reflections on Optimism (1759); Thoughts on the Occasion of Mr. Johann Friedrich von Funk’s Untimely Death (1760); and the announcement of Kant’s lectures for the winter semester 1765–1766. 6 On whether Kant admits contraposition and obversion, see Kirk D. Wilson, “The Mistaken Simplicity of Kant’s Enthymematic Treatment of the Second and Third Figures,” Kant-Studien, 66 (1975): 404–417, 413; Mirella Capozzi, “Osservazioni sulla riduzione delle figure sillogistiche in Kant”, Annali della Facoltà di Lettere e Filosofia dell’Università di Siena, 1 (1980): 79–98, 88–91; Theodor Ebert, “Michael Wolff über Syllogismen bei Aristoteles und Vernunftschlüsse bei Kant,” Journal for General Philosophy of Science, 40 (2009): 357–372, 367–368. On whether Kant admits the transposition of premises, see Capozzi, “Osservazioni sulla riduzione delle figure sillogistiche in Kant,” 87, 89; Lorenzo Pozzi, Da Ramus a Kant: Il dibattito sulla sillogistica (Milan, 1981), 98; Johan Arnt Myrstad, “Kant’s Treatment of the Bocardo and Barocco Syllogisms,” in Recht und Frieden in der Philosophie Kants: Akten des X. Internationalen Kant-Kongresses. 4–9. Sept. 2005 in São Paulo, ed. Valerio Rohden et al. (Berlin, 2008), vol. 5, 163–174, 164n3. 7 See Capozzi’s and Myrstad’s criticisms of Wilson and the debate between Theodor Ebert and Michael Wolff, respectively in Capozzi, “Osservazioni sulla riduzione delle figure sillogistiche in Kant”; Myrstad, “Kant’s Treatment of the Bocardo and Barocco Syllogisms”; Ebert, “Michael Wolff über Syllogismen bei Aristoteles und Vernunftschlüsse bei Kant”; Michael Wolff, “Volkommene Syllogismen und reine Vernunftschlüsse: Aristoteles und Kant,” Journal for General Philosophy of Science, 40 (2009): 341–355; Michael Wolff, “Vollkommene Syllogismen und reine Vernunftschlüsse: Aristoteles und Kant: Eine Stellungnahme zu Theodor Eberts Gegeneinwänden. Teil 2,” Journal for General Philosophy of Science, 41 (2010): 359–371; Theodor Ebert, “Michael Wolff über Kant als Logiker: Eine Stellungnahme zu Wolffs Metakritik,” Journal for General Philosophy of Science, 41 (2010): 373–382.

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8 Spitzf., 2:58 might suggest that this is the case. Pozzi (Da Ramus a Kant, 100) and Myrstad (“Kant’s Treatment of the Bocardo and Barocco Syllogisms,” 172) deny it. 9 See esp. Wolfgang Malzkorn, “Kants Kritik an der traditionellen Syllogistik,” History and Philosophy of Logic, 16 (1995): 75–88; Marco Sgarbi, Logica e metafisica nel Kant precritico: L’ambiente intellettuale di Königsberg e la formazione della filosofia kantiana (Frankfurt a. M., 2010), 185–218. 10 Silvestro Marcucci, “Introduzione,” in Immanuel Kant, La falsa sottigliezza delle quattro figure sillogistiche, ed. Silvestro Marcucci (Pisa, 2001), 9–18, 17, see 16. 11 Adolfo León Gómez, “La silogística en Leibniz y Kant, y su parentesco,” Ideas y Valores, 92–93 (1993): 41–46, 43. 12 Nicholas Rescher, Galen and the Syllogism: An Examination of the Thesis That Galen Originated the Fourth Figure of the Syllogism in the Light of New Data from Arabic Sources (Pittsburgh, Penn., 1966), 37. 13 Michael Wolff, “Volkommene Syllogismen und reine Vernunftschlüsse,” 354–355. 14 This is in line with Giorgio Tonelli’s overall assessment of Kant’s stance between 1745 and 1768. See his Elementi metodologici e metafisici in Kant dal 1745 al 1768: Saggio di sociologia della conoscenza (Turin, 1959), 209. This is one of the most detailed studies of the relation of Kant’s views with those of his peers. Tonelli’s discussion of the False Subtlety (204–208) is unusually cursory. 15 For a broader discussion of the influences on the False Subtlety, that complements this chapter, see Sgarbi, Logica e metafisica nel Kant precritico, 185–218. 16 See e.g. Joachim Georg Daries, Introductio in artem inveniendi seu logicam theoreticopracticam (Jena, 1742), Analytica § 257. Categorical syllogisms are composed of three propositions, each of which can be universal affirmative (A), universal negative (E), particular affirmative (I) or particular negative (O), for a total of 64 possible combinations (AAA, AAE, AEE, . . . OOO). Each combination is called a mood. Besides the form of the propositions that compose it, syllogisms are identified by the position of the middle term (which is the term that appears in the premises, but not in the conclusion). For instance, the middle term of a syllogism of mood EAE can be the subject of the major premise and the predicate of the minor premise (no mammals are plants; all humans are mammals; no humans are plants). It can also be the predicate of the minor and major premise (no humans are plants; all roses are plants; no roses are humans). The position of the middle term determines the figure of the syllogism. In the first figure, the middle term is the subject of the major premise and the predicate of the minor premise. In the second figure, the middle term is the predicate of both premises. In the third figure, the middle term is the subject of both premises. In the fourth figure, the middle term is the predicate of the major premise and the subject of the minor premise. The form of a syllogism (EAE-1, EAE-2, etc.) is determined by its mood and figure. Unlike current-day authors, Kant and his predecessors accepted the inference of I- and O-sentences

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from A- and E-sentences by subalternation. If this inference is rejected, the valid forms will be 15, not 19. See Irwing M. Copi et al., Introduction to Logic, 14th edn (Harlow, UK , 2014), 244. See e.g. Daries, Introductio in artem inveniendi, Analytica §§ 274–275; Christian August Crusius, Weg zur Gewißheit und Zuverlässigkeit der menschlichen Erkenntniß (Leipzig, 1747, repr. 1965), §§ 333–335; Hermann Samuel Reimarus, Die Vernunftlehre, als eine Anweisung zum richtigen Gebrauche der Vernunft in der Erkenntniß der Wahrheit (Hamburg, 1756), §§ 142, 148. Paul Thom mentions a third method, the method of counterexamples. As far as I am aware, Kant and his immediate predecessors did not rely on it. See Paul Thom, “Syllogismus; Syllogistik,” in Historisches Wörterbuch der Philosophie, eds. Joachim Ritter et al. (Basel, 1971–2007), vol. 10, 687–707, 690. Non-syllogistic inferences may be accepted as valid independently from syllogisms (Spitzf., 2:50). Alternatively, they may be regarded as enthymematic hypothetical syllogisms which can be reduced to syllogisms of the privileged class (Christian Wolff, Philosophia rationalis sive Logica, 3rd revised edn (Frankfurt a.M., 1740), repr. with notes and an index by Jean École in Christian Wolff, Gesammelte Werke (Olms, 1962–), sect. 2, vol. 1, §§ 413, 415, 460). Several passages of his logic manual stress the importance of sensibility as the “basis and principle of all our cognitions” (Martin Knutzen, Elementa philosophiae rationalis seu logicae (Königsberg, 1747, repr. 1991), § 27; see §§ 64, 289n). They recall passages by anti-Wolffians like Crusius more than Wolff ’s works. See, e.g., Christian August Crusius, Entwurf der nothwendigen Vernunft-Wahrheiten, wiefern sie den zufälligen entgegen gesetzet werden (Leipzig, 1745, repr. 1964), §§ 45, 56; Crusius, Weg zur Gewißheit, § 53. Knutzen’s preference for the method of principles over the reductive method is a point of divergence between him and Wolff. Knutzen, Elementa philosophiae rationalis, §§ 444–446. Knutzen, Elementa philosophiae rationalis, § 443. Knutzen criticizes two such putative principles, including Joachim Georg Daries’ principium convenientiae, and he notes that the dictum de omni et nullo (endorsed by Wolff ) is disputed. Like Knutzen, Samuel Christian Hollmann has no time for syllogistic reductions. See his Philosophia rationalis, quae logica vulgo dicitur, multum aucta et emendata (Göttingen, 1746), § 474. Among earlier texts, the widely read Port-Royal Logic employed the method of principles. See Antoine Arnauld and Pierre Nicole, The Port-Royal Logic, ed. Thomas Spencer Baynes (Edinburgh, 1861), 190–191. The same attitude toward the fourth figure can be found among Wolff ’s disciples. His faithful follower, Friedrich Christian Baumeister, explains what the fourth figure is, but he only provides rules for the first three figures and he only mentions their moods. See his Institutiones philosophiae rationalis (Wittenberg, 1735), repr. in Wolff, Gesammelte Werke, sect. 3, vol. 24, §§ 260, 269–278, 281; Hollmann, Philosophia

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rationalis, §§ 455–474. For an overview of early modern attitudes toward the fourth figure, see Rescher, Galen and the Syllogism, 34–38. Wolff, Philosophia rationalis, §§ 384, 389, 396. Wolff ’s German Logic focuses only on first-figure syllogisms. See Christian Wolff, Vernünftige Gedancken von den Kräfften des menschlichen Verstandes und ihrem richtigen Gebrauche in Erkäntniß der Wahrheit, ed. Hans Werner Arndt, in Wolff, Gesammelte Werke, sect. 1, vol. 1 (Hildesheim, 1962 [1754]), Ch. 4. Christian Wolff, Ausführliche Nachricht von seinen eigenen Schrifften, die er in deutscher Sprache [. . .] heraus gegeben, 2nd enlarged edn (Frankfurt a.M., 1733), repr. in Wolff, Gesammelte Werke, sect. 2, vol. 9, p. 201. Wolff, Philosophia rationalis, §§ 385, 397. Wolff, Philosophia rationalis, § 365. Wolff, Philosophia rationalis, § 346. Wolff, Philosophia rationalis, § 347. Christian Wolff (§ 402) ascribes the thesis that the dictum is the foundation of syllogisms to Aristotle. However, this is controversial. See, e.g., Ebert, “Michael Wolff über Syllogismen bei Aristoteles und Vernunftschlüsse bei Kant,” 357–365; Michael Wolff, “Vollkommene Syllogismen und reine Vernunftschlüsse: Aristoteles und Kant: Eine Stellungnahme zu Theodor Eberts Gegeneinwänden. Teil 1,” Journal for General Philosophy of Science, 41 (2010): 199–213, 208–212. Wolff, Philosophia rationalis, §§ 44–45. See Wolff, Gedancken von den Kräfften, Ch. 4, §§ 2, 4; Georg Friedrich Meier, Vernunftlehre, ed. Günter Schenk (Halle/Saale, 1997 [1752]), § 401; Georg Friedrich Meier, Auszug aus der Vernunftlehre, in Kant, Gesammelte Schriften, vol. 16, § 363. Crusius clearly explains this interpretation of the dictum in his Weg zur Gewißheit, § 282. Wolff, Philosophia rationalis, § 380n. Wolff, Philosophia rationalis, § 353n. Additionally, Wolff formulates foundational principles for second- and third-figure syllogisms (Philosophia rationalis, §§ 381, 389). The principle of second-figure syllogisms is a corollary of the dictum. The principle of third-figure syllogisms is a procedure to obtain them from first-figure syllogisms. Wolff, Philosophia rationalis, §§ 347n, 348n; Gedancken von den Kräfften, Ch. 4, § 5. As Matt Hettche notes, “a proposition could be known immediately one way and yet, in another way, follow as a conclusion of a sound deductive argument” (“Christian Wolff,” in The Stanford Encyclopedia of Philosophy, ed. Edward N. Zalta, Winter 2016 edition. Archived at https://perma.cc/2HCJ-G9PV. Available at: http://plato.stanford. edu/archives/win2016/entries/wolff-christian/, § 6). According to Wolff, this is the case for the dictum. See Christian Wolff, Philosophia prima sive ontologia (Frankfurt a.M., 1736), repr. in Wolff, Gesammelte Werke, sect. 1, vol. 3, § 54.

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Meier, Vernunftlehre, § 400. Daries, Introductio in artem inveniendi, Praecognita § 19n; Analytica §§ 252–253. Reimarus, Vernunftlehre, §§ 138–139. Reimarus, Vernunftlehre, § 139. Reimarus could employ the second- and third-figure syllogisms discussed in Section 2.2 as examples. Meier, Vernunftlehre, §§ 402–404; Auszug aus der Vernunftlehre, §§ 364–366. According to Meier, these principles follow from the law of contradiction (Vernunftlehre, § 400). Crusius, Weg zur Gewißheit, §§ 273–296. See Johann Heinrich Lambert, Neues Organon oder Gedanken über die Erforschung und Bezeichnung des Wahren und dessen Unterscheidung vom Irrthum und Schein (Leipzig, 1764), vol. 1, 142–143; Johann Georg Heinrich Feder, Logik und Metaphysik, 4th edn (Göttingen, 1774), § 43. Feder’s references indicate that he regarded his new principle as equivalent both to the dictum and to the principles of the False Subtlety. The first edition of Feder’s Logik und Metaphysik, which I could not access, was published in 1769. Anon., review of Immanuel Kant, Die falsche Spitzfindigkeit der vier syllogistischen Figuren, Briefe, die Neueste Litteratur betreffend, 22 (1765): 147–158, 150–151. Tonelli, following Erich Adickes, states that the author of this review was Moses Mendelssohn. See Tonelli, Elementi metodologici e metafisici in Kant dal 1745 al 1768, 208. Steve Naragon, Kant in the Classroom states that the author was Friedrich Gabriel Resewitz. Available at http://users.manchester.edu/FacStaff/SSNaragon/Kant/ Helps/writings.htm archived at https://perma.cc/H6DZ-LHRS. Wolff, Philosophia rationalis, § 378; Gedancken von den Kräfften, Ch. 4, § 14. Wolff, Philosophia rationalis, § 380: “First-figure syllogisms are the most natural, that is, they are the closest to the dictum de omni et nullo.” Wolff, Gedancken von den Kräfften, Ch. 16, § 3. Logic as a discipline (logica artificialis docens) illustrates the principles that we spontaneously follow in our ordinary reasoning, called “natural logic” (Philosophia rationalis, § 11). “When we reason within natural logic, we do not pay attention to anything else than the dictum de omni et nullo” (§ 280). Wolff, Philosophia rationalis, § 401. See § 400: “a figure in which all propositions can be inferred is called a perfect figure.” Wolff, Philosophia rationalis, § 379. Ludwig Philipp Thümmig’s manual of Wolffian logic too discusses only the first figure. See his Institutiones philosophiæ Wolfianæ, in usus academicos adornatæ (Frankfurt a.M., 1725–1726), repr. in Wolff, Gesammelte Werke, sect. 3, vol. 19, part 1, §§ 33–50. Reimarus (Vernunftlehre, 143) agrees that it is not necessary to discuss any other figure besides the first. However, he states that using the other figures may be useful in dialectical contexts, to refute one’s opponent. Although Kant agrees, he

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prefers to “pass over in silence” this “academic athleticism” because “it does not contribute greatly to the advancement of truth” (Spitzf., 2:57). Several authors stated (b), e.g. Crusius, Weg zur Gewißheit, §§ 333–335; Knutzen, Elementa philosophiae rationalis, § 456; Reimarus, Vernunftlehre, §§ 142, 148. Rescher (Galen and the Syllogism, 42) noted this. Crusius, Weg zur Gewißheit, § 332. Crusius’ suggestion that “one can find” this “in experience” would have hardly convinced Wolff. Hollmann, Philosophia rationalis, § 474; see Knutzen, Elementa philosophiae rationalis, § 457. Lambert, Neues Organon, vol. 1, 139–140. I have modified Lambert’s original example, which appears to mistake a fourth-figure syllogism in non-canonical form for a first-figure syllogism. Hollmann, Philosophia rationalis, § 474. Lambert (Neues Organon, vol. 1, 139) argues against natural2. He states that the reduction of his example involves an immediate inference, and a proposition derived through an immediate inference “is definitely not always as evident as the proposition from which we derived it.” Crusius (Weg zur Gewißheit, § 332) argues against natural3. He notes that the propositions from which we can infer a conclusion may come to mind in a different order from that of the first figure, as in Lambert’s example. In this case, we can infer the conclusion more quickly by employing a second-figure syllogism than immediate inferences and a first-figure syllogism. Crusius, Weg zur Gewißheit, § 331. A syllogism in Disamis can be reduced to Darii (AII-1) in two ways. One can transform it into Datisi (AII-3) through transposition of the premises, and transform the latter into Darii (AII-1) through simple conversion of the minor premise (Capozzi, “Osservazioni sulla riduzione delle figure sillogistiche in Kant,” 86). Alternatively, one can transform Disamis into Dimatis (IAI-4) and this into Darii (AII-1) through simple conversion of the major premise, transposition of the premises, and simple conversion of the conclusion (Myrstad, “Kant’s Treatment of the Bocardo and Barocco Syllogisms,” 166–168). Crusius, Weg zur Gewißheit, § 331. For a similar point, see Rogelio Rovira, “¿Es una ‘falsa sutileza’ la division lógica de las figuras del silogismo? Sobre la crítica de Kant a la doctrina aristotélica del silogismo categórico,” Teorema, 29 (2010): 5–21, 19. Spitzf., 2:56. Knutzen, Elementa philosophiae rationalis, § 457. Spitzf., 2:55. Spitzf., 2:56. This claim relates to the practical purpose of the False Subtlety (2:57). Kant published it together with the announcement of his logic lectures to explain why they covered syllogistic moods and figures only briefly. Unfortunately, we cannot check this statement against the transcripts of Kant’s lectures from those

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years. The earliest logic transcripts that are available to us, the Logik Blomberg and Logik Philippi, are based on lectures from the 1770s. Spitzf., 2:56. Accordingly, the “four modes of inference ought to be simple, unmixed and free from concealed supplementary inferences” (2:56). As we shall see, in Kant’s view, only one of the four figures satisfies this requirement. Spitzf., 2:49. Such a mark is a concept, rather than a property, because Kant calls it “the middle principal concept” of a syllogism (2:48). Spitzf., 2:49. On this distinction, see Houston Smit, “Kant on Marks and the Immediacy of Intuition,” Philosophical Review, 109 (2000): 235–266, 248–251. Kant’s ambiguous use of “mark” might lead to the suspicion that he confuses the “properties of things which fall under” a concept with the “characteristics which make up the concept” (Gottlob Frege, Die Grundlagen der Arithmetik: Eine logisch mathematische Untersuchung über den Begriff der Zahl, ed. Christian Thiel (Hamburg, 1988 [1884]); trans. The Foundations of Arithmetic: A Logico-Mathematical Enquiry into the Concept of Number, ed. J. L. Austin (Oxford, 1974), § 53). Related objections against Kant’s principle of syllogisms are discussed in Michael Wolff, “Volkommene Syllogismen und reine Vernunftschlüsse,” 348–350; Ebert, “Michael Wolff über Syllogismen bei Aristoteles und Vernunftschlüsse bei Kant,” 365–366. Spitzf., 2:47. I argue that Kant uses a broad notion of object, which includes non-existent items, in “Kant on Existential Import,” Kantian Review, 19 (2014): 207–232, 221–223. Spitzf., 2:47. Kant uses stronger terms than “non-belonging” to designate the relation between subject and predicate in negative judgements: “contraposed,” “contradicts,” “contrasting” [entgegen gesetzt, widespricht, widerstreitend] (Spitzf., 2:47). These and other expressions may suggest that for Kant, ca.1762, all truths are analytic. Charles Nussbaum, among others, holds this. See his “Critical and Pre-Critical Phases in Kant’s Philosophy of Logic,” Kant-Studien, 83 (1992): 280–293, 280, 284. I do not take a stand on this issue. Spitzf., 2:47. Further, for every object a and every property P, that belongs to a, P is a mediate mark of a if and only if a has a property Q, such that the concept of P is a component of the concept of Q. I set aside the possibility that they may be simple, unanalysable concepts for the sake of simplicity. Hollmann, Philosophia rationalis, § 447; Reimarus, Vernunftlehre, § 150; Lambert, Neues Organon, vol. 1, 154–155; A331/B387–388. Spitzf., 2:48. Spitzf., 2:48.

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80 More precisely, it states that the mark expressed by the predicate belongs to the item(s) referred to by the subject. I omit the italicized expressions for the sake of simplicity. 81 Traditional logic provided a set of rules, called pons asinorum, for finding suitable middle terms. Andreas Rüdiger formulated a new version of those rules. Kant mentions them neither in the False Subtlety nor, as far as I am aware, elsewhere. See Heinrich Schepers, “Eselsbrücke,” in Historisches Wörterbuch der Philosophie, vol. 2, 743–745. 82 Spitzf., 2:48. Kant provides a similar example for negative judgements. 83 For Kant’s views on intuition as a source of justification, see Section 3.2. 84 Daries, Introductio in artem inveniendi, Praecognita § 128n. 85 In 1781 too, Kant regards logic as a tool not for generating cognitions, but only for assessing them (A60/B84, A796/B824). This does not shed light on why the False Subtlety, which was published 19 years earlier, is silent on whether we can use syllogisms for invention. 86 Spitzf., 2:49. 87 Spitzf., 2:49, trans. modified. 88 Kant combines this explanation with the claims that lower concepts are abstracted from things and higher concepts are abstracted from lower concepts. Kant’s explanation is independent from those claims. 89 Spitzf., 2:49. 90 They are similar, but not identical to the principles of judgements of Kant’s New Elucidation of 1755. Cf. Sgarbi, Logica e metafisica nel Kant precritico, 208. 91 Rovira, “¿Es una ‘falsa sutileza’ la division lógica de las figuras del silogismo?,” 15. 92 Spitzf., 2:49. 93 Other aspects of the False Subtlety are not particularly original. (1) Kant’s conception of the role of syllogism is similar to Reimarus’ characterization of syllogism as a way of establishing the agreement or contrast between the subject and predicate of “judgements of mediate insight” (Vernunftlehre, §§ 137–138). It also recalls earlier definitions of syllogism, e.g. by Baumeister, Institutiones philosophiae rationalis, § 237, and Hollmann, Philosophia rationalis, § 446, besides the passages of the Port-Royal Logic and Segner’s De syllogismo which are mentioned in Mirella Capozzi and Gino Roncaglia, “Logic and Philosophy of Logic from Humanism to Kant,” in The Development of Modern Logic, ed. Leila Haaparanta (New York, 2009), 78–158, 102, and in Sgarbi, Logica e metafisica nel Kant precritico, 208. See also a passage by Johann Heinrich Lambert, whose date of composition is unknown (in his Logische und philosophische Abhandlungen, ed. Johann Bernoulli (Berlin 1782), vol. 1, 230), and the passages by Sulzer and ’s Gravesande quoted in Sgarbi, Logica e metafisica nel Kant precritico, 208. (2) Reimarus mentioned that syllogisms can serve for discovery besides justification. Yet, his account of syllogism, like Kant’s, focuses on the search for premises to

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justify conclusions. For a well-known precedent, see Arnauld and Nicole, The Port-Royal Logic, 191: “the conclusion is supposed before we make the syllogism to prove it.” (3) Before Kant, Meier and Reimarus had used the term “Vernunftschluß” to designate syllogisms. See Meier, Vernunftlehre, § 390; Meier, Auszug aus der Vernunftlehre, § 354; Reimarus, Vernunftlehre, §§ 134, 354. The only possible exception is Daries’ Introductio in artem inveniendi. Crusius was one of Kant’s main philosophical influences in the 1750s and 1760s. Kant refers to a passage of his Weg zur Gewißheit in Spitzf., 2:54n, 55. Kant used Meier’s Auszug and, possibly, his Vernunftlehre as textbooks for his logic lectures since the 1750s. Kant owned and read Reimarus’ Vernunftlehre. See Arthur Warda, Immanuel Kants Bücher: Mit einer getreuten Nachbildung des bisher einzigen bekannten Abzuges des Versteigerungskataloges der Bibliothek Kants (Berlin, 1922), 53; Größen, 2:191. Reimarus’ Vernunftlehre is the likely source of several of Kant’s views. See J. Bergmann, “Zur Lehre Kants von den logischen Grundsätzen,” Kant-Studien, 2 (1898): 323–348, 330; Norbert Hinske, “Reimarus zwischen Wolff und Kant: Zur Quellen- und Wirkungsgeschichte der ‘Vernunftlehre’ von Hermann Samuel Reimarus,” in Logik im Zeitalter der Aufklärung: Studien zur “Vernunftlehre” von Hermann Samuel Reimarus, eds. Wolfgang Walter and Ludwig Borinski (Göttingen, 1980), 9–32; Michael Oberhausen, Das neue Apriori: Kants Lehre von einer ursprünglicher Erwerbung apriorischer Vorstellungen (Stuttgart, 1997), 99–112. Kant held 13 lecture courses on logic between the beginning of his teaching and the winter semester 1761/1762. He might have used Baumeister’s textbook during some of the earlier courses. See Steve Naragon, Kant in the Classroom Available at: http:// users.manchester.edu/FacStaff/SSNaragon/Kant/Lectures/lecturesListDiscipline. htm#logic, archived at https://perma.cc/HMH4-LESV. Reimarus, Vernunftlehre, § 139. As I note in the text section, Kant proposes a method to transform them into syllogisms which conform to his principles. However, by Kant’s own admission, this method cannot be applied to the affirmative forms of the fourth figure (Bamalip and Dimatis). If we replaced “all painters are visual artists” with “some visual artists are painters,” which we can infer from it by conversion, we would obtain an invalid syllogism with form III-1. As an example of a fourth-figure syllogism that does not conform to Kant’s principles, consider the following syllogism in Baralip (AAI-4): all phones are artefacts; all artefacts are material objects; some material objects are phones. If the syllogism conformed to the nota notae principle, it would predicate being a phone of some material objects on the ground that being a phone is a mark of one of their marks. Yet, the syllogism does not ascribe any other marks to material objects, besides being a phone. Hence, the syllogism does not conform to the nota notae principle. Spitzf., 2:57–58.

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101 Wolff, Philosophia rationalis, §§ 385, 397. 102 See Spitzf., 2:58: “all other transpositions of the middle term [of second-, third-, and fourth-figure syllogisms] only yield valid inferences if, by means of easy and immediate inferences, they lead to such propositions as are connected in the simple order of the first figure.” Some of the reductions to which Kant refers also require the transposition of the premises. Kant accepts and employs it, but he denies that it is an immediate inference. See Capozzi, “Osservazioni sulla riduzione delle figure sillogistiche in Kant,” 87–89. 103 For Kant, “immediate inferences” are “not [enthymematic] syllogisms” (Spitzf., 2:50). 104 Spitzf., 2:50, italics added. 105 Spitzf., 2:51, italics added. 106 If a syllogism is mixed, then “the conclusion is valid [eine richtige Folge] only as a result of my” being able to carry out certain logical operations on the premises (2:51, italics added). Kant makes similar statements for third-figure syllogisms and negative fourth-figure syllogisms (2:53). 107 Refl. 3256, 16:740–742. 108 Lambert, Neues Organon, vol. 1, 135. 109 Bamalip is not valid if one rejects inferences by subalternation, but Kant and his peers accepted it. The negative forms (Calemes, Fesapo, Fresinom) can be reduced to the first figure by means of Kant’s rules, but only in a convoluted and “unnatural” way (Spitzf., 2:53) because they require immediate inferences to be carried out on not just one, but both premises. 110 Kant does not make this claim, pace David Walford’s remark in Immanuel Kant, Theoretical Philosophy, 1755–1770, ed. David Walford and Ralf Meerbote (Cambridge, 1992), 427n32. 111 Spitzf., 2:53. 112 For instance, in “Every mind is simple; Everything simple is imperishable; Therefore, some of what is imperishable is a mind,” “I cannot say that some of what is imperishable is a mind because it is simple; for it is not the case that something is a mind simply in virtue of its being simple” (Spitzf., 2:54, italics added). 113 See Michael Wolff ’s remarks on Kant’s use of the verb “to follow” [fließen] in “Vollkommene Syllogismen und reine Vernunftschlüsse: Aristoteles und Kant,” 367. 114 Spitzf., 2:51, italics added. On second-figure syllogisms, see 2:52: “[t]his conversion must [. . .] be tacitly [geheim] thought in making the inference, for otherwise my propositions do not conclude [schließen]” (trans. modified). I set aside the issue of what, exactly, “schließen” may mean in this sentence. On fourth-figure syllogisms, see 2:53: “[t]he negative syllogism in this figure, the form in which it must be really thought, takes the following form: [. . .].” 115 Spitzf., 2:53.

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116 Feder, Logik und Metaphysik, § 45. 117 Spitzf., 2:58. 118 An influential version of this account can be found in Friedrich Paulsen, Versuch einer Entwicklungsgeschichte der Kantischen Erkenntnisstheorie (Leipzig, 1875). 119 Marcucci, “Introduzione,” 17. 120 Gómez, “La silogística en Leibniz y Kant, y su parentesco,” 43. 121 Nevertheless, see Sgarbi, Logica e metafisica nel Kant precritico, 192 for a likely Leibnizian influence on Wolff ’s views on syllogism. 122 Rescher, Galen and the Syllogism, 43. 123 Gottfried Wilhelm Leibniz, Nouveaux Essais sur l’entendment humain par l’auteur du système de l’harmonie préétablie, in Sämtliche Schriften und Briefe, 6th series, vol. 6; (Berlin, 1962 [1704–1705]), trans. New Essays on Human Understanding, ed. Peter Remnant and Jonathan Bennett (Cambridge, 1981), Part 4, Ch. 2. Kant’s wariness toward indirect proofs influenced his late discussions of syllogism. See Capozzi, “Osservazioni sulla riduzione delle figure sillogistiche in Kant,” 96–98. 124 Michael Wolff, “Volkommene Syllogismen und reine Vernunftschlüsse,” 354–355. 125 Wolff, Ausführliche Nachricht von seinen eigenen Schrifften, p. 201. 126 There are also some differences between Wolff ’s and Kant’s views on syllogism. Wolff disregards the fourth figure. Kant discusses it explicitly, if only to dismiss it. Wolff states and Kant denies that immediate inferences are enthymematic syllogisms. 127 Spitzf., 2:54n, 2:55. Kant also alludes to Crusius in a passage on judgements, not syllogisms (2:61). 128 See, e.g., Beweisgrund, 2:76; Deutl., 2:169, 295; M. Herder, 28:10. 129 Beweisgrund, 2:72–73. 130 Deutl., 2:293–296. 131 Spitzf., 2:49. 132 See note 93 above. 133 Deutl., 2:283. 134 Beweisgrund, 2:66. See Deutl., 2:283. 135 Beweisgrund, 2:71; Größen, 2:167; Deutl., 2:283. 136 Kant claims that Newtonian physics owes its success to its method (Deutl., 2:275). Kant takes himself to be applying Newton’s method to metaphysics (Deutl., 2:286). 137 Deutl., 2:279, 283–284. 138 Deutl., 2:276. 139 Deutl., 2:277. 140 Deutl., 2:280. 141 Spitzf., 2:58. 142 Deutl., 2:294; see Spitzf., 2:60; M. Herder, 28:8. 143 Deutl., 2:294; see Spitzf., 2:60; M. Herder, 28:8.

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144 Deutl., 2:294. 145 Spitzf., 2:49. 146 Deutl., 2:294. As Adickes noted, the Critical Kant regards “bodies are divisible” as a synthetic judgement. See Adickes, “Beiträge zur Entwicklungsgeschichte der Kantischen Erkenntnistheorie,” in his Kant-Studien (Kiel, 1895), 1–164, 85. 147 Giorgio Tonelli, “Die Umwälzung von 1769 bei Kant,” Kant-Studien, 54 (1963): 369–375, 370. 148 Deutl., 2:276. 149 Lambert, Neues Organon, vol. 1, 140–141, see 142–143, echoed in Feder, Logik und Metaphysik, § 45. 150 Letter to Johann Heinrich Samuel Formey of 28 June 1763, 10:41. 151 Spitzf., 2:56. 152 Spitzf., 2:57. 153 Größen, 2:202. 154 Größen, 2:171. 155 Beweisgrund, 2:82. 156 Deutl., 2:294–296.

10

“Everything Rational is a Syllogism” Hegel’s Logic of Inference Georg Sans, SJ Hochschule für Philosophie, München

Hegel’s Science of Logic is notorious, especially among Aristotelians, for its awkward identity claims, such as “being and nothing are the same,” “freedom is the truth of necessity,” or “the particular is the universal.” From a formal point of view, one might urge a careful distinction between identification (“being is numerically identical with nothingness”), classification (“being is a species of nothingness”), and predication (“being has the quality of being nothing”). However, as it turns out, Hegel’s very conception of what it is to be a concept goes against such a rigid separation. The Hegelian Concept1 can be characterized by the three moments of being a general quality (the universal) as well as the species of a genus (the particular) as well as an individual (the singular). Each and every moment of the Concept is both the whole and one of its aspects. It is thanks to this kind of internal differentiation that the Concept can unite with itself in the form of a syllogism (sich mit sich zusammenschließen). When stating that “everything rational is a syllogism” (90; 588),2 Hegel above all tells us something about the speculative Concept. No matter whether what has been said so far is intelligible or not, it should be clear from the outset that Hegel’s conception of concepts and syllogisms is worlds apart from classical syllogistic. To start with, Hegel’s view of deductive reasoning is not limited to the consideration of merely extensional relations. Whereas ordinary syllogisms are founded on quantified judgments, expressing relations of inclusion between sets or classes (“all As are B,” “some Cs are D”), Hegel seems to nominalize quantifiers, so as to make “the universal,” “the particular” and “the singular” the three terms of syllogism. Furthermore, he is not much concerned with the formal principles of reasoning, as opposed to their 191

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application in various fields of inquiry. Hegel’s Logic rather deals with the semantic aspects of inference. Universality, particularity and singularity are interpreted not only as indicating different ranges, but as standing for various ways of conceiving the functioning of concepts. This peculiar methodology is meant to allow for achieving philosophical insight about concepts and their relation to reality in an a priori fashion.3 Notwithstanding these dissimilarities, if Hegel’s doctrine of syllogism is assessed by its outer appearance, it presents itself as an odd mixture of traditional formal logic with specifically Kantian architectonic devices. Hegel’s treatment of syllogistic figures and induction, for instance, is reminiscent of the former. To the latter the chapter on syllogism owes its structure, which partially follows Kant’s table of judgments and categories. As depicted in Figure  10.1, Hegel distinguishes between several genera of inferences, namely qualitative syllogism or syllogism of existence, syllogism of reflection, and syllogism of necessity. These genera correspond to Kant’s titles of quality, relation and modality. As each Kantian class contains three categories, every genus of syllogism in Hegel’s Logic comprises three species. The first set encompasses the three figures known from Aristotelian syllogistic, whereas the second and third sets include other types of inferences, like induction, analogy, hypothetical and disjunctive syllogism.

Figure 10.1

Hegel undertakes the discussion of all those forms of reasoning in order to offer an elaborate doctrine of conceptual thinking. Yet, he does not confine himself to dealing with abstract formulas or merely subjective operations. Instead, he considers the question of how the constitutive structures of reason are instantiated in reality. This is why the “Doctrine of the Concept” that makes up the second part of Hegel’s Science of Logic, besides covering the traditional themes of formal logic such as judgment and syllogism, encloses chapters on topics like mechanism, chemism, teleology, life, the true and the good. What connects them among each other and with the issue of inferential reasoning is Hegel’s conviction that conceptual relations as such are real. By an argument founded on the nature of syllogism and associated with the ontological proof for

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the existence of God, Hegel maintains to establish the objectivity of the Concept. If the transition is sound, the argument leads to the twofold conclusion that, on the one hand, objectivity is to a certain extent conceptually structured and on the other hand, the Concept itself is a specific kind of object. In what follows, I will initially give an overview of the three genera and nine species of syllogism distinguished by Hegel. The first genus comprises the Aristotelian figures of syllogism which, according to Hegel, form a circle of mutually justifying inferences (1). The second and third genera serve to disclose the ontological implications of inference. At this stage of the argument, it becomes indispensable to differentiate between concepts representing properties, concepts representing classes of things, and concepts representing metaphysical kinds. While the Hegelian Concept is conceived of as being all the three of them, its main feature is that of a really existing, objective universal (2). The paradigmatic case of an objective universal which can be described in syllogistic terms, is the solar system. A careful reading of the respective texts demonstrates that Hegel’s doctrine of syllogism is essentially concerned with the different perspectives from which a complex whole may be considered. Each aspect is made explicit by a syllogism, the terms of which stand for the various moments of the systematic whole. The single syllogisms combine into a circle by the permutation of their middle terms (3). In the Encyclopedia, several triads of syllogisms are used for explaining the organization of objective universals, such as the state, or philosophy itself. For Hegel, syllogistic reasoning after all is concomitant with proving our conception of something to be rational (4).

1. The circle of the three syllogistic figures Hegel starts his discussion by declaring that “the syllogism in its immediate form has for its moments the determinations of the concept as immediate” (92; 590). This statement requires clarification. With the moments of the syllogism Hegel does not mean its premises and conclusion, but its three terms. These terms are identified as the determinations of the concept (i.e. the universal (U), the particular (P), and the singular (S)). Such an interpretation of the syllogism seems to suggest an extensional reading, taking the determinations to be quantifiers. It is worth noting, though, that these quantifiers are not the traditional “all,” “no,” “some” and “some not.” On the one hand, Hegel does not mention negative premises, so as to exclude two thirds of the 24 Aristotelian moods. On the other hand, the third moment of the Hegelian syllogism, appears to

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be a singular term, whereas Aristotle’s syllogisms contain exclusively general terms. If we replace, for example, the determination of universality with “mortals,” particularity with “humans” and singularity with “Gaius,” we will obtain the following inference: “All humans are mortal. Gaius is a human. Therefore Gaius is mortal.” Notwithstanding Hegel’s moan about the boredom by which one is seized when hearing the spiel (95; 593), the three judgments make up a correct syllogism. The subject and predicate of the conclusion, which constitute the extremes of the syllogism, are mediated by a third term which functions as subject in the major and as predicate in the minor premise. Quoting just the three terms, we obtain “Gaius—human—mortal,” or schematically “S—P—U,” Hegel’s formula for the first figure syllogism.4 One might still wonder about the exact meaning of Hegel’s schema. In classical formal logic the variables stand for any concept. If the propositions “all As are B” and “all Bs are C” are true of a triple of concepts, then so will be “all As are C.” The same relations can be expressed set theoretically by saying that set A is included in set B which in turn is included in set C. Consequently, it may be claimed that C is “the universal” in proportion to A and to B. But what applies to a syllogism of the form Barbara, obviously does neither hold for Celarent nor for Darii. If “all Ds are E,” and “no E is F,” then F cannot be considered “the universal” with respect to D and to E. Likewise, if “some Gs are H,” and “all Hs are J,” then G may or may not be more “universal” than H and J.5 Even less evident is the way in which Hegel uses the other two determinations of the concept. In the syllogism Barbara, B is “the particular” in proportion to C, but A is also “the particular” in proportion to B and to C. Furthermore, according to Hegel’s schema, A has to be “the singular,” which rules out all minor premises as well as conclusions with a plural subject. Only by strictly limiting the discussion to modus Barbara and to syllogisms with a singular premise, like in the example cited above, it seems plausible to identify the three terms with the determinations of universality, particularity, and singularity. Hegel describes the function of a syllogism fundamentally as mediating between two concepts, namely between the subject and the predicate of a judgment. The judgment demands for mediation in the sense that it lacks justification. The middle term of the syllogism founds its conclusion. If Gaius is actually mortal, then this is because he is human. Hence the syllogism is not so much a series of three propositions, as a judgment supplemented by its conceptual foundation. In Hegel’s schema, the middle term—figuratively speaking—replaces the copula. Subject and predicate of the conclusion are linked in virtue of an

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additional concept. In Hegel’s words: “Singularity connects [schließt sich zusammen]6 with universality through particularity” (93; 590). In the Encyclopedia Logic, Hegel specifies that “a subject as individual is joined together [zusammengeschlossen], through a quality, with some universal determinacy” (§ 183; 256). By asserting that Gaius is mortal, the singular subject Gaius is connected with the universal determination of mortality by means of the feature of being human. Gaius’ mortality is thus justified by its humanity insofar as all humans are mortal (first premise) and Gaius is a human (second premise). The nexus between conceptual mediation and justification is already present in Hegel’s lessons of philosophical propaedeutic taught at the Gymnasium in Nuremberg, where he states that the syllogism “contains, as such, the judgment with its ground.”7 The grounding function of the middle term has been a widely accepted idea for a long time and indeed goes back to Aristotle’s Posterior Analytics.8 In the Enlightenment philosopher Ernst Platner’s Aphorisms, used by Fichte as a textbook for his Jena lectures, the syllogism is defined as “a judgment with an added reason.” The reason is “that by which it is understood why the—affirmative or negative—predicate belongs to the subject.”9 Similarly, for Hegel, the difference between a mere judgment and the conclusion of an inference lies in the foundation on which the latter “as the mediated connection” (94; 592) is grounded. While the conclusion of a syllogism is justified by its premises, the premises as such are immediate judgments and in need of further justification. Although the inference is necessary, the conclusion of a qualitative syllogism is only hypothetically true: If all humans are mortal, and if Gaius is a human, then Gaius is mortal. However, even if not all humans were mortal, the inference as such would still remain valid, without Gaius being necessarily mortal. For this reason scientific explanation is usually an open-ended process. Since a conclusion is no better than its premises, the search for justification continues with the mediation of uncertain premises. For traditional formal logic all this does not constitute a major issue, because logical inquiry is limited to the study of the abstract rules of reasoning. The empirical sciences, on the other hand, look for experiential evidence on which to base their knowledge claims. Hegelian speculative reason on its part cannot settle for the former and is barred from the latter. The Science of Logic strives to provide new insights by developing pure thought-determinations, one of which is syllogism as the form of conceptual mediation. Hegel consequently is wondering how complete mediation is possible in pure thinking. As we have seen so far, in the syllogism of the first figure, the conclusion is based on two unfounded premises. In order to mediate also these premises, two additional inferences would be needed, one to found the first premise, the other to found

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the second premise. But this move obviously cannot improve the situation. On the contrary, now there are four premises that lack justification instead of previously two. Schematically the problem may be depicted as shown below in Figure 10.2. The attempt of complete mediation appears to lead to an infinite progression of proofs.

Figure 10.2

To avoid such a progress to infinity, Hegel introduces yet another way of mediating the premises, namely by means of the respective third term. The premise S—P is thus justified by the universal U, the premise P—U is justified by the singular S. In this way the second and third figures of the syllogism are derived from the first as presuppositions of its premises. The second figure (P—S—U) combines the three determinations of the concept in a different order from the first, in that the subject of the conclusion of the latter has become the middle term of the former. The third figure (S—U—P) represents still another combination of the same three moments, with the remaining determination at the center. Hence the premises of each species of syllogism are founded on the other two inferences, while the three figures as a whole are based on the permutation of terms as illustrated in Figure 10.3. The process of mediation thus results in a “circle of reciprocal presupposing” (105; 603) formed by the three types of qualitative syllogism.10 From a methodological stance, the replacement of an infinite progress with a circle does not make a big difference, because either argument seems aporetic. According to Hegel, however, another consequence can be drawn which has both a negative and a positive side. On the negative side, Hegel polemicizes against the formalism of syllogistic reasoning. He rightly observes that syllogisms of the second and third figures do not lead to much insight into their subject matter. Since they rest on either negative or particular judgments as premises, their conclusions are of limited range.11 As long as the form of syllogism is understood in an abstract way, “only totally empty results are produced” (108; 607). Alluding to Kant’s essay on The False Subtlety of the Four Syllogistic Figures and chastising the standard textbook accounts of logic, Hegel remarks that one

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Figure 10.3

should not be surprised if the Aristotelian figures “have later been treated as an empty formalism” (§ 187; 259). Nevertheless, the statement of formalism is only one side of the coin. The other side is “the positive result, namely that mediation occurs, not through any single qualitative determinateness of form, but through the concrete identity of the determinacies” (106; 604). Complete mediation can only be achieved if all three moments of the concept function one by one as middle term. The circle of the three syllogistic figures for Hegel has a profound sense which “rests upon the necessity that each moment as a determination of the concept becomes itself the whole and the mediating ground” (§ 187; 259).

2. Ontological implications of inference At first glance, Hegel’s development of the syllogism of existence is a failure. Although by connecting the three figures he obtains complete mediation of all premises, the result appears to be an empty formalism. This state of affairs makes it difficult even to imagine how the transition to further types of inference will be brought about. After exhausting the method of permutation, another sort of consideration is needed. As in all chapters in the Science of Logic, Hegel presents the development of different forms as a dialectical movement in the course of which categories are determined step by step. His method, in a nutshell, consists of introducing new categories or forms that express the conceptual content more adequately than their respective predecessors.12 This procedure leads to a

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semantic enrichment, as can be easily seen from the structure of the book. Categories such as “judgment,” “mechanism” or “life” (Doctrine of the Concept) are more complex than “ground” or “appearance” (Doctrine of Essence), which in turn are richer than “existence” or “quantity” (Doctrine of Being). Regarding qualitative syllogism, Hegel initially takes the three figures to be a mere aggregate of distinct forms. As long as no further specification is supplied, there is just a set of syllogisms, each with a different middle term. Syllogism as a genus can be characterized by enumerating the various figures, though without pretending completeness of the list. From there the transition to still another form of inference is motivated by the concern that if the true nature of syllogism amounts to nothing more than being a set of inferential forms, then it will be represented best in terms of inductive reasoning. To claim something about the syllogism in general means first to indicate the three figures with the determinations of universality (U), particularity (P), and singularity (S) as middle terms, and second to highlight their common trait of being a mediated connection of concepts. Hegel thus describes induction as “the syllogism of experience—of the subjective gathering together of singulars in the genus, and of the conjoining of the genus with a universal determinateness on the ground that the latter is found in all singulars” (114; 612 f.). While it may seem obvious that an empirical conception of inference is not applicable to formal reasoning nor to speculative logic, Hegel calls into question even its everyday use and scientific worth. Indeed, a contingent list of premises cannot be guaranteed to be complete, nor can the occurrence of counterinstances be excluded for certain. The fact that all the many swans observed so far have been white, neither implies that no other swans exist, nor does it mean that you will never find a black swan. But if the syllogism of induction, Hegel continues to wonder, just gathers the singular instances in a class, it remains unclear what makes them members of the same genus. This doubt ushers in the next form of inference, namely the syllogism of analogy. Hegel’s example of a syllogism of analogy is the erroneous reasoning: “The earth has inhabitants. The moon is an earth. Therefore the moon has inhabitants” (115; 614).13 To underscore the superficiality of the analogy, Hegel argues that inferring something’s having inhabitants from its being an earth calls for clarification of the nature of the middle term. If the syllogism is supposed to work, the concept “earth” cannot simply refer to something concrete, but must be taken likewise as a “universal nature” (117; 615). Only if having inhabitants constitutes an essential attribute of a heavenly body’s being an earth, the analogy yields its conclusion. In this case, however, we are already beyond the stage of

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induction and analogy or, as Hegel calls it, the syllogism of reflection. The validity of the conclusion no longer depends on the singular items, nor on the similarities existing between them, but on their essence or nature. The standard example of the categorical syllogism quoted above has the advantage of being grounded precisely in a middle term that expresses “the objective universal, the genus” (117; 616). The word “human” is used both as an adjective and as a noun. In the first case the term seems to signify a universal property, in the second case it denotes a singular subject or substance. The two are made possible by the fact that humanity as a natural kind possesses a certain set of attributes which necessarily belong to every individual of the genus. Gaius is mortal not just because he has the feature of being human, nor because all humans happen to be mortal, but because mortality is an essential note of humanity. What I have called a semantic enrichment thus reveals itself to be an ontological commitment. Inferential reasoning as such requires an essentialist perspective on the middle term. If the syllogism is founded either on abstract qualities or on sets of things, no conceptual insights will be obtained so that our knowledge remains strictly limited to the realm of empirical facts. In the chapter on syllogism Hegel makes a clear case for an essentialist conception of concepts. A true concept expresses the nature of the things falling under it in that they necessarily instantiate the essential attributes comprehended in the concept. Without a similar ontological commitment it would be impossible to gain knowledge through concepts. A similar reading of the syllogism chapter finds further confirmation in the fact that Hegel’s list of syllogisms otherwise would contain three identical items. The first figure of the qualitative syllogism, the syllogism of allness, and the categorical syllogism all actually have the same form. If there were no semantic differences, they would also agree in content. But even though Hegel’s system of syllogisms shows obvious reminiscences to Kant’s tables of judgments and categories, its order should not be simply dismissed as artificial. The distinction between three classes, corresponding to Kant’s titles, rather points to various ways of interpreting the middle term. In the syllogism of existence, mediation is thought to be realized by a particular quality, in the syllogism of reflection by a set of singular things, in the syllogism of necessity by the universality of genus. As it turns out, only the last interpretation of the middle term actually makes it possible to acquire inferential knowledge. Only if the conclusion is grounded not on observation, or any other empirical evidence, but on a genus concept, singular objects can be said to necessarily possess certain attributes. This means that only the third of the aforementioned species of syllogism is more than a blank formalism, because its middle term bears conceptual content.

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Hegel’s argument in the Science of Logic doctrine of syllogism thus boils down to establishing the categorical syllogism as the true form of inferential reasoning. There are, however, two shortcomings in this reconstruction. The first is that two other forms of inference still follow, namely hypothetical and disjunctive syllogism. The second difficulty is that so far we have been talking about ordinary concepts (e.g. the concept of humanity), whereas Hegel is concerned with the concept of the Concept. His “Doctrine of the Concept” is not so much an investigation of whether and why “humanity” warrants Gaius’ mortality, as a study on the determinations of the speculative Concept and their interrelations. Hegel’s overall aim is to prove that the three moments of universality, particularity, and singularity constitute an objective whole, or genus. The remaining two forms of syllogism serve the purpose to make explicit what kind of concept is presupposed by the categorical syllogism. Hegel, more specifically, intends to establish the real nature of the middle term. The final step of his argument, which comprises the hypothetical and disjunctive syllogism, reveals the genus or objective universality as something existing. Hegel’s consideration is roughly the following: If the genus concept is to ground the conclusion, there has to be a necessary relation between a singular object’s being a member of the genus (Gaius’ being human) and its possession of certain essential properties (Gaius’ being mortal). This relation, as Hegel sees it, is expressed by a syllogism of the form: “If A is, so is B. But A is. Therefore B is” (121; 620). This move is rather bewildering, since the hypothetical in contrast to the categorical syllogism comprises only two terms which are so to speak extremes without a middle.14 Moreover, the premises in the formula above are existential instead of predicative judgments. As Hegel sees it, the hypothetical syllogism adds the “immediacy of being” (ibid.). These irregularities notwithstanding one may still see the hypothetical syllogism as expressing exactly the function fulfilled by the middle term of the categorical syllogism. The latter provides conceptual knowledge on the condition that every specimen of the genus possesses a certain essential quality. In other words: whenever there is an instance of A (for example, being human), there is also an instance of B (being mortal). The expression “an instance of ” disguises the difference between the classification in a genus and the predication of an attribute. Although this may seem formally incorrect, it does not cause any trouble, as long as the Hegelian Concept is thought of as something which is universal in the sense of both genus and attribute. The hypothetical syllogism then does not change the perspective of the

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preceding passages, namely to make explicit the necessity to interpret the middle term of the categorical syllogism as objective universality. This line of argument is completed in the section dedicated to the disjunctive syllogism. Whereas Hegel’s hypothetical syllogism tallies with the traditional modus ponens, his disjunctive syllogism is equivalent to modus tollendo ponens, obeying to the following rule: “A is either B or C or D. But A is B. Therefore A is neither C nor D” (124; 622). By the subject term A Hegel now means the objective universal.15 The predicates B, C, D can be seen as species which form the genus A. This explains why A’s being B necessarily implies it not being C nor D. It is characteristic for objective universality to realize itself in several forms which constitute a whole by reciprocally excluding each other. This analysis explains the apparent oddity that the formula for Hegel’s disjunctive syllogism consists of four instead of three terms. The discrepancy is unavoidable whenever various subsets are said to belong to the same class. By claiming, for instance, that all cycles are either pedal-powered or motor-powered, one uses three terms for defining two different species of two-wheelers. The same applies for the “mediating means” (Vermittelnde) in the Hegelian syllogism: it is “the universal sphere of its particularizations” and at the same time “is determined as a singular” (124; 623). Thereby it should be clear that the “middle” (Mitte) here does not denote an alleged central term of the disjunctive syllogism but rather that concept which could serve as mediator in the categorical syllogism, and the constitution of which is made explicit by the disjunctive syllogism. From the perspective of speculative logic, the term A thus has to be regarded as the Concept, with B, C and D representing the three moments of universality, particularity and singularity. The main feature of the Concept as objective universal is its being both particularized and determined as a singular. The singularity, for Hegel, is instantiated through the negative relation holding between each moment and the others. Since the disjunctive syllogism is emblematic for “the unity of the mediator and the mediated” (124; 623), Hegel finally declares that “the form of the syllogism, which consisted in the difference of the middle term over against its extremes, has thereby sublated itself ” (125; 624). As a result of the “sublation of the mediation” (126; 624), the conceptual scheme of formal logic—judgment and syllogism—does not any longer suffice for expressing the true nature of the Concept. Hegel introduces the category of “objectivity” for further determining pure thought. He labels this step the “realization of the concept,” comparing it with Anselm’s as well as Descartes’ ontological argument for the existence of God (§ 193; 265–268). Like the idea of

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the most perfect being implies its existence, the concept of the Concept suggests a really existing, objective universal.

3. The paradigmatic case of the solar system The syllogism chapter aims at establishing the Concept as something objective, to wit really existing. In the subsequent section of the Science of Logic, Hegel explains the specific “objectivity” of the Concept with the help of the categories of mechanism, chemism, and teleology. The corresponding chapters always struck readers as odd because of the difficulty of avoiding the impression that after dealing with mental activities such as judging and reasoning, the author now passes to the treatment of physical objects in space and time. In such a case, Hegel would have to be blamed for merging the sphere of pure logical thinking with the realm of nature. It is worthy of note, though, that a similar objection could already be leveled against interpreting logical subjectivity as something mental, thus assigning judgment and syllogism to the philosophy of mind. Hegel clearly refused both interpretations. Subjectivity as well as objectivity are determinations of the Concept as such and do not refer directly either to mind or to nature. The neutral stance becomes evident when Hegel describes mechanism, chemism, and teleology themselves as syllogisms. For the sake of brevity I will engage only with “absolute mechanism” which is arguably the most elaborate case of syllogistic reasoning in Hegel’s Logic. Hegel distinguishes several types of logical mechanism depending on which kind of forces are thought to act on a body. The simplest case of moving force is pressure or impact, as exemplified by one billiard ball colliding with another. Such a mechanism is far from being absolute because the pushing body usually receives its drive from a third one, and so forth. Whether a ball hits the next mainly depends on the forces which act on them. The mechanical process of action and reaction is triggered by external factors which leave the object as such intact. After rejecting its depiction in terms of matter and form, or as a thing with properties, Hegel deploys the moments of universality, particularity, and singularity for further clarification. When one body interacts with another, communicating kinetic energy to it, “their identical universality is posited.” This universal form yet does not sublate the particularity of each object. On the contrary, the universality “particularizes itself only in their diversity,” in that one body is acting, the other is reacting. What occurs here is “a reciprocal repulsion of the impulse.” By repelling the impact, the mechanical object for Hegel

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demonstrates its self-subsistence. When mechanically speaking action “passes over into rest,” logically speaking the particular object “returns to singularity” (138 f.; 636 f.). In summarizing the process delineated so far, Hegel puts his considerations in syllogistic form: “Immediately, the object is presupposed as a singular; then as a particular as against another particular; but finally as indifferent towards its particularity, as universal. The product is the totality of the concept previously presupposed but now posited. It is the conclusion [Schlußsatz] in which the communicated universal is united [zusammengeschlossen] with singularity through the particularity of the object” (139; 637). One and the same physical body hence combines in itself all three moments constitutive of the concept. Abstractly considered, it is just a singular thing; seen in connection with another body acting on it, the object becomes something particular; from the perspective of the equality of action and reaction, it is universally determined. Finally Hegel associates the product of the mechanical process with the logical scheme S–P–U of the syllogism. Even if the object is in rest, it receives its determination by the mediation of another body. The foregoing statement of the unity of self-subsistence and mediation is merely formal. It applies indistinctively to any mechanical object. Physical bodies characteristically do not possess internal determinations but are only externally interrelated. In kinematics they are idealized as moving point masses. Hegel’s story, however, does not finish here. Despite their apparent independence, the manifold objects form a complex whole called absolute mechanism. The unity of the whole for Hegel is represented by the center (Zentrum) or central body (Zentralkörper) towards which all the other objects strive (142 f.; 640 f.). The mechanism is absolute in the sense that the various bodies are in motion without being driven by an external force, as can be seen by the examples of objects falling to the Earth, or planets circling around the Sun. Neither free fall nor orbital motion is communicated by impact or pressure. They depend on the relation between falling or gravitating bodies and the said center. Hegel designates the latter “the individualized universality of the single objects and their mechanical process” as well as “the real middle term [reale Mitte]” through which the objects are united (zusammengeschlossen) in and for themselves (143; 641). Which then is the syllogism of which the center of absolute mechanism is the real middle? So far we have encountered only two terms, namely the single objects and the central body. Hegel yet introduces a further distinction between what, in celestial mechanics, are called planets and satellites respectively. A planet is an object both orbiting the central body and orbited on his part by other,

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smaller bodies. “These second centers and the non-self-subsistent objects are brought into unity [zusammengeschlossen] by the absolute middle term” (144; 642). The syllogistic structure of absolute mechanism may be exemplified, for instance, by the triad of Earth, Sun and Moon. The relation between Earth and Moon is intelligible on the basis of their common interaction with the Sun as the center of mass. It should be added immediately that the absolute mechanism, in contrast to the mechanical process considered above, is not encompassed in one single syllogism but in a circle of the three syllogisms. As sketched in the preceding chapter, the remaining figures evolve through the permutation of the middle term. Thus, Hegel explains, “the relative individual centers themselves also constitute the middle term of a second syllogism. This middle term is, on the one hand, subsumed under a higher extreme, the objective universality and power of the absolute center; on the other hand, it subsumes under it the non-selfsubsistent objects.” To complete the series, the third term also has to function as mediating means. “These non-self-subsistent objects are in turn the middle term of a third syllogism, the formal syllogism, for since the central individuality obtains through them the externality by virtue of which, in referring to itself, it also strives towards an absolute middle point, those non-self-subsistent objects are the link between absolute and relative central individuality” (ibid.).16 Passing through the circle of the three syllogistic figures for Hegel is first and foremost a mark of systematicity and, as a result, rationality. Since inferential knowledge is specific to reason, being brought into the form of a syllogism is tantamount to being rational. Complying with reason on the other hand means absoluteness, or independence, or self-sufficiency (Selbständigkeit). The planetary system is an absolute mechanism in that it is completely governed by the law of gravitation. No further inner qualities or external forces are needed for differentiating the objects or explaining the processes which make up the whole. While the development of Hegel’s speculative logic obviously has not yet reached its final stage, the category of mechanism already foreshadows the perfect unity between conceptual ideality and reality as well as between freedom and necessity. Hegel dubs the law of absolute mechanism paradoxically “free necessity” because “in the ideality of its difference it refers only to itself ” (146; 644). Besides the blatant reference to Spinoza’s metaphysics, the formula indicates a process of gradual self-differentiation that generates complex determinations without external impact. It is astonishing, to say the least, that the most extended application of inferential reasoning in Hegel’s system is found in the mechanism chapter of the

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Science of Logic. One reason may be the proximity to the doctrine of syllogism. With the three figures and genera still fresh to the mind, both author and reader will more easily grasp the hidden conceptual structures which determine the logical categories as well as the corresponding reality. The case of the planetary system then is paradigmatic because in accordance with the three syllogisms just as many kinds of moving forces can be distinguished. The first and most abstract sort of relation is represented by pressure and impact. Mechanical objects formally considered are indifferent with respect to the forces exercised by or upon them. On a second level, however, there is an essential difference between a celestial body that attracts smaller objects, and these objects falling towards the central body. The center defines the force field in which the objects lacking self-sufficiency are located. In the third and final type of mechanism, attraction and fall are replaced by gravity. Hegel portrays the latter as the “objective universality” which “persists self-identical in the particularization” (145; 643). One and the same law of gravitation determines all of the particular objects forming the system. The relation between several mechanical objects hence can be considered from a threefold perspective: as pressure and impact, as attraction and fall, or as gravitation. What makes the planetary system paradigmatic for inferential reasoning is the amalgamation of these three aspects, each correspondent to one of the syllogistic figures, with three types of celestial bodies, each correspondent to one of the terms. As we have already seen, apart from the absolute center (universality) and the non-self-subsistent objects (particularity), the absolute mechanism incorporates relative individual centers (singularity).17 Like the Earth that stands in the middle between the Moon and the Sun, the relative centers combine centrality, or self-sufficiency, with dependency. In sum, what makes up a system of syllogisms is the connect between a triad of terms with as many perspectives.

4. Other triads of syllogisms Although the category of mechanism has its paradigmatic application in the solar system, its use is not restricted to the realm of physics, or nature in general. In the Science of Logic, Hegel in fact coins the term “spiritual mechanism” and describes it as consisting in “the things connected in the spirit remaining external to one another and to spirit” (133; 631). When somebody recites a poem in a monotonous voice, devoid of any emotion, she may be relying on mechanical memory which connects the words externally without attaching a sense to them.

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Or when devout people perform their prayers and fulfill their rituals in a detached and uninvolved manner, they could be said to act mechanically (cf. § 195 Remark; 270 f.). In both cases the spirit seems to operate without considering the meaning and implications of what is said or done. As the “pervasive presence that is proper to spirit” is lacking (133; 631), spiritual mechanism is contrary to self-conscious freedom. Hegel’s talk of spiritual mechanism should not be taken in a reductionist sense, as if the human mind was reduced to a machine. Spirit certainly belongs to a higher domain of reality than the planetary system, and is far too complex to be explained in terms of mechanism. However, as always in Hegel’s system, with the advancing development of the Concept the earlier categories are not completely abandoned but sublated into the later ones. The concept of objectivity, for instance, takes up the previously explicated determinations of being, existence, actuality, and substantiality (cf. 130; 628). In a similar way, the idea of life supposes mechanical and chemical processes (cf. 189; 686). Likewise some operations of the human spirit can be described as mechanical, though spirit as such transcends mechanism. This is the reason why “in things spiritual the center, and the union with it, assume higher forms” (143; 641). The clearest example is the analogy drawn by Hegel between the solar system and the state. “The government, the individual citizens, and the needs or the external life of these—Hegel declares—are also three terms, of which each is the middle term of the other two.” (144 f.; 642) As the list makes evident, the three terms cannot be simply identified with various things, entities, or substances. Since all elements of the planetary system are celestial bodies with different masses, one might have expected the moments of the state to be the citizens with their respective social roles, such as for instance the three estates (clergy, nobility, commoners) in the Ancien Régime, or the three branches of government (legislative, executive, and judicial). Hegel yet draws a more complex picture of the social organism. The state is seen from different perspectives which are displayed by the triad of syllogisms. He briefly characterizes each of the three syllogisms, beginning with the moment of universality constituted by the government. It is “the absolute center in which the extreme of the singulars is united [zusammengeschlossen] with their external existence.” The middle term of the next syllogism is the individual citizens, who “incite that universal individual into external concrete existence and transpose their ethical essence into the extreme of actuality.” In the third and final syllogism “the singular citizens are tied by their needs and external existence to this universal absolute individuality” (145; 642).

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In a remark to the Encyclopedia Logic Hegel repeats the same considerations at greater length and in a slightly different order. Because of its pertinence to our topic, it is worth quoting the text in full before commenting on it: (1) The individual (the person) joins itself through its particularity (physical and spiritual needs, what becomes the civil society, once they have been further developed for themselves) with the universal (the society, justice, law, government). (2) The will, the activity of individuals, is the mediating factor which satisfies the needs in relation to society, the law, and so forth, just as it fulfils and realizes the society, the law, and so forth. (3) But the universal (state, government, law) is the substantial middle [term] in which the individuals and their satisfaction have and acquire their fulfilled reality, mediation, and subsistence. § 198 Remark; 273

These three phrases arguably constitute Hegel’s most explicit statement of syllogistic reasoning in the practical sphere. He concludes the remark with the declaration that “it is only through the nature of this joining together, through this triad of syllogisms with the same terminis, that a whole is truly understood in its organization” (ibid.). The state is seen not so much as the union of its citizens which like atoms compose a molecule, or like members form a body. The individuals’ specific contribution to the understanding of the social whole rather consists in their being subjects of self-conscious will and activity. The second stage of Hegel’s argument turns on the mediation between the particular interests and desires propelling people, on the one hand, and the universal norms governing social life, on the other. The adjustment between the two extremes depends on the citizens’ free self-determination. Pursuing both the satisfaction of their own needs and the actualization of common values, every singular person aims at reconciling particularity with universality. The mediating principle is the people’s willing and acting. The economic system as well as the socio-political institutions, for Hegel, are no impersonal processes or structures which escape human influence, but manifestations of our free will and activity. Like the planetary system, the triad of syllogisms originates in the permutation of terms so that “the mediation joins each of the determinations with the other extreme” (ibid.). Again, like physical mechanism, the three syllogisms represent several types or levels of mediation. Hegel, in other words, distinguishes three ways of conceiving social unity, namely in the first place as determined by economic requirements; in a second moment as facilitating personal selffulfillment; or finally as directed towards the implementation of universal

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norms.18 The first syllogism thus corresponds to the point of view of what Hegel calls the civil society, in which all individuals or singular families tend to achieve their respective physical and spiritual needs. The second syllogism stresses the volitional character of social organization and the active part citizens have to play in the construction of society. Without the third syllogism these considerations would ultimately amount to a liberalist conception of the state, with political institutions confined to a functional role either for the development of the economic sector or for the exercise of individual liberty. Hegel then adds the aspect of universality as represented by the political institutions and the constitution of the state as a whole. Fundamental ethical norms in a society are to be preserved through legislation, governance, and judicature. The third type of mediation is as essential as the preceding ones. If the convictions of a people are not brought into a constitutional order, they will remain literally ineffective. The different aspects of the three syllogisms, though, reveal the true nature of the social organism only if taken together. A society that does not satisfy its members’ material needs, or disregards their freedom of choice, would be equally defective as a community that does not give itself a political constitution in accordance with common ethical norms. Nevertheless, as Hegel sees it, the third syllogism performs the function of integrating the preceding moments into a complex whole exemplifying objective universality. In the realm of physics this results in the primacy of gravitation over impact and attraction, in the case of the state it leads to the supremacy of politics over economy. Hegel certainly subscribes to the claim that the common good takes precedence over private concerns, but the main issue here is that political institutions by their nature are meant to solve the tension between particular needs or singular wills, on the one hand, and a vision of the whole on the other hand. With Karl Popper in mind, it could be objected that the excesses of holism are still more harmful and dangerous than any kind of liberalism. In contrast, Hegel points out that, as the gravitational system is not just a set of bodies impacting one another, the constitution of the state is more than a mere mechanism of balancing interests. Without necessarily implying that political procedures should not be understood as a mechanism at all, Hegel deploys his syllogistic method to arrive at a more adequate conception of the state as a whole. Notwithstanding the succeeding chapters are scattered with syllogistic vocabulary like “premise,” “middle term,” “inference,” or “conclusion,” Hegel admittedly offers no further elaboration of his method. In the Science of Logic, he explicitly talks of three syllogisms which constitute the totality of chemism (cf. 152; 649).19 When dealing with teleology, he associates the means (Mittel) with

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the middle term (Mitte) of a formal syllogism (cf. 163; 660), mentioning again three syllogisms (cf. 171; 669).20 In the Encyclopedia Logic, Hegel denotes the idea of life as “the syllogism, whose moments are systems and syllogisms in themselves.” By the moments he means the mechanical, chemical, and teleological processes which conjointly make up living, understood as “the process of its coming to closure together with itself [Zusammenschließens mit sich selbst]” (§ 217; 288). In the Philosophy of Nature, Hegel characterizes his way of determining the notion of gravitation as the “syllogism of totality, which is in itself a system of three syllogisms.”21 A few paragraphs later, he remarks about the chemical process that its complete exposition would require “that it should be explicated as a triad of intimately interrelating syllogisms,” referring without much ado to the aforesaid section 198 of the Encyclopedia Logic.22 With regard to the animal organism, Hegel claims that it “passes syllogistically through its three determinations,” namely the formation of shape, the assimilation of stimuli and nutriment, and reproduction. Since the three processes concern one and the same animal, “each syllogism is implicitly the same totality of substantial unity, and [. . .] at the same time the transition into the others.”23 Even though the state in Hegel’s Logic is presented as a system of syllogistic inferences, neither his Philosophy of Right in general nor the section on the state in particular take up the alleged triad. To be sure, Hegel makes ample use of syllogistic discourse, but it is far from obvious which syllogisms, if any, form his system of right.24 In the Encyclopedia, it is not before the end of the section on absolute spirit that the pattern of interrelated syllogisms is again employed. After explaining the several moments of Christian religion, from God’s nature via the creation of the world and the incarnation of Christ to the effusion of the Holy Spirit, Hegel speaks of the revelation as “three syllogisms, which constitute the one syllogism of the absolute mediation of spirit with itself.”25 I have shown elsewhere that each syllogism stands for another aspect of religion, namely the history of salvation, the justification of man, and God’s essence as absolute spirit.26 Let me just repeat the crucial point that, according to Hegel, the three perspectives follow each other in ascending order. From a merely external representation of particular past events, religion proceeds to the conversion of the singular person culminating in the believers’ universal unity in God. In Hegel’s system, religion is surmounted by philosophy as conceptual knowledge of the absolute which manifests itself in pure thought, in nature and in spirit. Not surprisingly, Hegel takes the triad of syllogisms to be the best pattern for explaining the unity of these moments. The concluding syllogisms of the system are meant to show that logic, nature and spirit constitute one

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conceptually determined whole. In the last sections of the Encyclopedia, Hegel indicates the syllogisms, the first of which has “nature as the middle that joins [zusammenschließt] the spirit together with the logical” (§ 575), in the second syllogism spirit “is the mediator [Vermittelnde]” (§ 576), whereas the third “has self-knowing reason, the absolutely universal, for its middle [Mitte]” (§ 577).27 As in the other triads so far discussed, the permutation is not just a formalism but mirrors different senses of mediation. In the first instance the mediation has “the external form of transition,” the second syllogism relates to the standpoint of “subjective cognition,” whereas the third portrays philosophy as “self-knowing reason.”28 While the last syllogism includes the highest and speculatively true perspective, the others cannot be simply dispensed with. The permutation of terms rather exhibits the indissoluble unity of the three moments.29 This result is admittedly far away from inferences in the fashion of Aristotle’s modus Barbara. The Hegelian doctrine of syllogism is still centered on the middle term, but instead of being concerned with the conclusion as a proposition, the philosopher engages with the meaning of the three terms, emphasizing that their permutation leads to semantic enrichment. It is certainly in the latter sense that Hegel claimed that “everything rational is a syllogism” (90; 588). From a formal point of view, his method of syllogistic reasoning may appear unsatisfactory because he does not separate the logical form from material content. Furthermore it is not completely clear how Hegel himself arrives at the semantic determinations of his categories. Consequently, the Science of Logic is not an organon: it does not supply the reader with a toolkit of dialectical reasoning that could be schematically applied for deducing new concepts. For this reason, Hegel himself—in contrast to many of his followers and most of his critics—never considered the syllogistic presentation of his own system as concluded.

Notes 1 For convenience, I will use the capital when referring to the Hegelian speculative concept, and the lowercase when referring to concepts in the ordinary sense. 2 All parenthetical references in the text are to Hegel’s Logic. The Science of Logic is cited according to the pagination of the critical edition (Georg Wilhelm Friedrich Hegel, Wissenschaft der Logik; Zweiter Band: Die subjektive Logik, Hamburg, 1981), followed by the page number of the di Giovanni translation (Cambridge, 2010). The

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4 5

6 7 8 9 10 11

12

13

14 15

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Encyclopedia Logic is referred to by paragraph numbers, followed by the page number of the Brinkmann/Dahlstrom translation (Cambridge, 2010). On the speculative function of Hegel’s doctrine of syllogism see also Wolfgang Krohn, Die formale Logik in Hegels “Wissenschaft der Logik.” Untersuchungen zur Schlusslehre (München, 1972), 7–13. For grammatical reasons the order is inverse to Aristotle’s formulas since the Stagyrite writes “B belongs to every A” instead of “all As are B.” In “some philosophers are Kantians” the extension of the subject term is larger than the extension of the predicate term, whereas in “some philosophers are Germans” it is presumably not. The German verb “zusammenschließen” has the same root as the noun “Schluss” (syllogism or inference). Georg Wilhelm Friedrich Hegel, Nürnberger Gymnasialkurse und Gymnasialreden (Hamburg, 2006), 272; The Philosophical Propaedeutic (Oxford, 1986), 113. See Aristotle, Analytica Posteriora, I 6. Ernst Platner, Philosophische Aphorismen (Leipzig, 1793), 258 f. Since not the sequence of the extremes, but only the middle term is considered, there are not 3! = 6 combinations, but only 3. Consider for instance: “All humans are mortal. Some humans are philosophers. Therefore some philosophers are mortal” (mood Datisi), or: “No quadruped is human. All philosophers are human. Therefore no philosopher is a quadruped” (mood Camestres). It should be noted here that Hegel’s second figure corresponds to Aristotle’s third figure and the other way round. For more details see Georg Sans, Die Realisierung des Begriffs. Eine Untersuchung zu Hegels Schlusslehre (Berlin, 2004), 110–118. On Hegel’s dialectical method see Hans Friedrich Fulda, “Hegels Dialektik als Begriffsbewegung und Darstellungsweise,” in Seminar: Dialektik in der Philosophie Hegels ed. Rolf Peter Horstmann (Frankfurt, 1978), 124–174. The editor of the English translation (note 95) refers to a similar example in Antonio Genovesi’s Elementa artis logico-criticæ (Venice, 1749). The third part of Kant’s Universal Natural History and Theory of the Heavens (Königsberg, 1755) contains “an attempt to compare the inhabitants of the different planets on the basis of the analogies of nature” (Immanuel Kant, Natural Science, Cambridge, 2012, 294). On this issue see, for example, Immanuel Kant, Lectures on Logic (Cambridge, 1992), 623. On the following interpretation see Klaus Düsing, “Syllogistik und Dialektik in Hegels spekulativer Logik,” in Hegels Wissenschaft der Logik. Formation und Rekonstruktion, ed. Dieter Henrich (Stuttgart, 1986), 15–38, 29 ff. as well as Sans, Die Realisierung des Begriffs, 201–222.

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16 Although the mapping between the three kinds of celestial bodies and the moments of the concept is rather opaque, it may be conjectured that the absolute center is meant to represent universality, the non-self-sufficient objects particularity and the relative individual centers singularity. In this case the first syllogism corresponds to the figure S–U–P, the second to P–S–U, and the third to S–P–U. The order is apparently reverse with respect to the presentation of the three figures in the doctrine of syllogism. In § 198 of the Encyclopedia Logic, Hegel gives a schematic account of the triad which sticks more closely to the order of the figures in the syllogism chapter.—On the meaning of the three moments see also Nicolas Février, “Das syllogistische Bild des Sonnensystems in der absoluten Mechanik Hegels (1830),” in Jahrbuch für Hegelforschung 4–5 (1998–99): 143–170, 161–166, and La mécanique hegelienne. Commentaire des paragraphes 245 à 271 de l’Encyclopédie de Hegel (Louvain-La-Neuve-Paris, 2000), 113–119. 17 It should be noted that in § 198 of the Encyclopedia Logic, the meaning of the moments of particularity and singularity is inverted. 18 For an in-depth interpretation of these three tenets see Dieter Henrich, “Logische Form und reale Totalität. Über die Begriffsform von Hegels eigentlichem Staatsbegriff,” in Hegels Philosophie des Rechts. Die Theorie der Rechtsformen und ihre Logik, eds. Dieter Henrich, Rolf-Peter Horstmann (Stuttgart, 1982), 428–450; “Logical Form and Real Totality : The Authentic Conceptual Form of Hegel’s Concept of the State,” in Hegel on Ethics and Politics, eds. Robert B. Pippin; Otfried Höffe (Cambridge, 2004), 241–267. A more recent study is Nathan Ross, On Mechanism in Hegel’s Social and Political Philosophy (New York; London, 2008), 103–124. 19 For a syllogistic analysis of chemical processes see Georg Sans, “Weisen der Welterschließung. Zur Rolle des Chemismus in Hegels subjektiver Logik,” in Hegel-Studien 48 (2015), 37–63. 20 On the function of syllogism in teleological reasoning see Tommaso Pierini, Theorie der Freiheit. Der Begriff des Zwecks in Hegels Wissenschaft der Logik (München; Paderborn, 2006), 152–205. 21 Georg Wilhelm Friedrich Hegel, Philosophy of Nature (London, 1970), vol. I, 261. 22 Hegel, Philosophy of Nature, vol. II , 216. 23 Hegel, Philosophy of Nature, vol. III , 107. 24 The syllogistic structure of Hegel’s Elements of the Philosophy of Right is highlighted by Klaus Vieweg, Das Denken der Freiheit. Hegels Grundlinien der Philosophie des Rechts (München, 2012), esp. 366–433. See my review in Hegel-Studien 47 (2013), 227–231. 25 Georg Wilhelm Friedrich Hegel, Philosophy of Mind (Oxford, 2007), 265. 26 See Georg Sans, “Hegels Begriff der Offenbarung als Schluss von drei Schlüssen,” in L’assoluto e il divino. La teologia cristiana di Hegel, eds. Tommaso Pierini et al. (Pisa-Roma, 2011), 167–181.

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27 Hegel, Philosophy of Mind, 276. 28 Ibid. 29 The systematic meaning of the three final syllogisms is still contentious among Hegel scholars. The classic treatment is Hans Friedrich Fulda, Das Problem einer Einleitung in Hegels Wissenschaft der Logik (Frankfurt, 1965), 284–301. Recent interpretations include Stefano Fuselli, Forme del sillogismo e modelli di razionalità in Hegel (Trento, 2000), 206–230, Nicolas Füzesi, Hegels drei Schlüsse (Freiburg-München, 2004), and Angelica Nuzzo, “Hegels Auffassung der Philosophie als System und die drei Schlüsse der Enzyklopädie,” in Hegels enzyklopädisches System der Philosophie, eds. Hans-Christian Lucas; Burkhard Tuschling; Ulrich Vogel (Stuttgart-Bad Cannstatt, 2004), 459–480.

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Index a posteriori confirmation 6 a priori concepts/conclusions 78, 101 abstraction 39, 121 abstractive generalization of variables 6 absurd 148 ad hominem arguments 53 ad populum arguments 53 addition of explications 87 addition, or subtraction, of concepts 68, 85 al-Fārābi 17 alethic modalities 130 algebra of concepts 7, 133, 137 algebra of sets 137 analogy 42, 192, 198–9 analysis 63, 76, 105, 175 Anfang 105 Anselm 201 architectonic structure 192 Arnauld, A. and Nicole, P. 83–104, 134 artificial (meta-)language 39–40 Ashworth, E.J. 53, 138 Aversa 64 Avicenna 2 axioms (or maxims) 85–6, 88–9, 110, 121 Bacon, F. 105–6 Barnes, J. 119–20 Baumgarten, A.G. 174 Boethius 2 Boole 133, 136 Buridan 53 Buroker, J. 87–8 Cabero 64 categories 73 causal demonstration 5, 76 causes 76–8 certainty 62, 106, 112–13 Chrysippus 131 classic books (production and prints of) 51 classification 192

common sense 45, 64 completeness/incompleteness 101, 104, 148, 164 comprehension (or extension) and intension 5, 84, 86, 89, 90, 92, 94–6, 99–100, 160, 192 law of reciprocity of intension and extension 135 computation 68–9, 74, 78 concepts 192, 175, 200, 206 conceptual equation 63 conceptual mediation 195 maximally-consistent concepts 148 conceptual containment 7, 85, 96, 138 operator of conceptual containment 137 conclusive moods 89 conformation rules 6 contextualization 40–2 contextual determination of statements’ temporal duration: 13–14 conditions for c. 14 conversion/conversion rules: 15, 25–6, 83, 85, 116, 132 for temporally determined categorical propositions with existential import 16 of second and third figures 15 Copenhaver, B.P. 45 copulative theory of predication 12 Couturat, L. 136 Crusius, Ch.A. 161, 163–4, 168, 170, 173–4, 178 Daries, J.G. 161, 167–8, 178 Davidson, D. 49 de continente et contenuto rule 118 de dicto predication 21 de re predication 21 deductivism 108 definitions 77–8 degrees of reality 137

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216 demonstration: 60, 68, 76–7, 113, 176 demonstration of that 77–8 demonstration of why 77–8 Descartes and Cartesianism 62, 83–4, 99–100, 110, 119–20, 201 dialectic 37, 44, 46, 49, 52, 60, 108–9, 197, 209 dialectic determination 9 dictum de omni et de nullo 8, 90, 159–60, 167, 174 Diodorus Cronus 130–1 discovery 65, 76, 96, 109–10, 113, 166–7, 172, 174 dismissal of Aristotelian scientific results 61 dogmatism 120 Du Trieu, P. 118, 120 elenchus /ignoratio elenchi 41, 53 empiricism 78, 116, 195 enthymemes 88 epistemology 110, 177 epoché 105 essence: 2, 13–15, 18–20, 21–2, 25–6, 198–9, 209 essential attributes 135 essential statement 13 essentialism 199–200 Eudemus 26 existence: 202 e. in the divine intellect 23 existence and time 13, 18 existential assertions 2, 200 existential conditions 42 existential import assumption 24, 27, 75–6 hypothetical existence 2 in re existence 21, 24 mental existence/in intellectu e. 21, 23–4 necessity of existence 20, 193 experience 69, 167, 198 explanation 195 expositio 47 extension: see comprehension and intension Fabry, H. 134 factual and artificial confirmation 42

Index fallacy 99 Feder, J.G.H. 161, 171 Fichte 195 figures and moods of syllogisms 5, 8, 20, 67, 74–5, 83, 89–90, 157–9, 164, 177, 192–3, 205 first and second intention languages 45 formalism 3, 37, 44, 100, 192, 157, 197 formalization 7, 137 Forms 74, 92 Frege, G. 131, 133 generality 89 gnoseological natural order 121 God 2, 87, 201 Gomez, A.L. 158, 173 grammar 37, 44, 45 Green-Pedersen, N.J. 46 Hegius, Alexander 41 Heinlen, M. 52 Herbert of Cherbury 120 Hieronymous of St. Mark 139 Hispanus, P. 134 Hollman, S. Ch. 163–4 Horward, J. 51 Hospinianus, J. 134 humanistic literature 50 humanistic prejudice/humanist ideology 2, 35, 36, 49, 53 Iamblicus 26 ideas’ agreement 109, 111, 113, 120 identification 192, 197 identity operator 140 imagination 62 immediate inferences 170–1, 173, 195 impossibility 24, 171 impossibility of generlization 101 in itself (qua )/qua- attribution phrase 24, 25, 27–8 incunabula 51–2 individuals/individuality 87–8, 136–7, 148–9, 206 individual variables 130 induction/inductive cognitive order 7, 192, 198–9 inductivism 108 inferential (chains of) arguments 5, 59, 120

Index infinite regress 196 innatism/innateness 78, 109, 120 intellect 78, 116 intellectual negotiatio 60 intention 72–4 intuition 4, 60, 62, 109–11, 116, 120, 167, 175 inventio 46 John of Salisbury 41 judgement 165–6, 175–6, 194 Jungius, J. 134 justification 166–7, 172, 174, 176–8, 195 circle of permutative justification 193, 196, 204 Kant 106, 130, 157–90, 192, 196, 199 knowledge 84, 110, 113, 120–1 Knutzen, M. 159, 163–4, 170, 174 Lambert, J.H 161, 163, 170–2, 176 language: 68 stipulative character of l. 5, 71–2, 78 language-dependent reasoning 70 Latin language (use of) 42–4, 48 natural ordinary language 39–40, 44–5 oral vernacular(s) 43, 48 laws of negations 7, 137 laws of opposition 131 Leibniz 87, 106, 118, 120–1, 129–55, 158, 173 letters or symbols as variables 100 Lewis, C.I. 131 literal commentaries 11 loci argumentorum and natural reasoning 115, 117, 120 logic as axiomatic system 38, 119 logic text-books 3, 44, 50, 74, 83–4, 118, 129, 134, 170, 195 Logica Parva 43, 46, 48, 53 logical conjunctions 7 operator of conceptual conjunction 137, 139–40 logical inferences (consequentiae ) 38, 46 logicism (critique to) 108 Lowry, M. 50 Lullus, R. 134 Malebranche 111, 119 Marcucci, S. 158, 173

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mark (Merkmal ) 165–6, 168–9 (im)mediate mark 165–7, 175 matter of propositions 25 meaning (and lack of m.) 40, 44 mechanism 192, 202–3 mediating means (Vermittelnde ) 201 Meier, G.F. 160–1, 168–9, 178 memory 109 metaphysics 174–7 unavoidableness of metaphysics 20 method: 68, 76, 78, 105 m. of metaphysics 176–8 m. of principles 9, 159, 170, 172, 176 reductive m. 159, 172, 176, 178 middle term: 60, 74, 88, 91–2, 94–6, 101, 116–17, 133, 166–8, 171, 193–4, 196, 197–201, 206, 207 mediating action of the m. 203–4, 207, 210 permutation of m., 10, 197, 207 mistake (formal and material) 114 modality: 2, 25 and existence 19 and predicative relations 19 and time 13, 21, 27 modalized terms 22 modal operators 130 modal syllogistic 11 modes: see figures and moods modus cosgnoscendi 41 modus essendi 41 modus ponens 201 modus significandi 41 modus tollendo ponens 201 Molyneux, W. 119 “moments” of syllogism 9, 191–210 monadic predicates 131, 133 Moss, A. 52 mutually justifying inferences 193, 197 naturalness thesis 162–3, 171, 173 nature 202 Nauta, L. 45 necessity: 2, 24, 87 logical necessity 20, 160, 177 necessary and sufficient conditions 95 necessary, and possible, items 22–3 necessity of existence 20, 193

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Index

Nifo 60 nominalism 5, 71–2, 121 not-Euclidean geometrical demonstrations 63 objectivity 193, 201–2, 205–6 obligatio exercise 41 obversion inferences 133 Ockham 47 ontological commitment 199 ordering of being/chain of being 73–4, 121 ordo et connexio idearum 113 paradox 99 Pariente, S.J.-C. 86–7, 96–101 particularity 120–1, 191–5, 198, 201–3, 207 Paul of Pergola 52 Paul of Venice 52–3 pedagogical purpose 119 per accidens predications 19 per se /per accidens necessary propositions 15 perception 69, 78, 109, 113, 120 persuasion and argumentative techniques 38 Peter of Spain 53 Philo 131 Philoponus 26 philosophy 76, 193 Pico della Mirandola 43 Platner, E. 195 Plato 134 Popper, K. 208 possibility 24, 148 operator of possibility (or selfconsistency) of concepts 137 predicate logic 131 predication 109, 191 predicational versus quantified reading 21 premises: additional immediate premises 8 alternative premises 6 foundation of the premises 195 premises as perceptual intuitions 7 rearrangement of premises’ order 7, 117 simplyfication of premises 6 principles: 110

general principle for determining validity 93–100 nota notae p. 167, 168–9, 175–7 p. of affirmation 90 p. of contraposition 132, 141 p. of convenience (principium convenientiae ) 161 p. of excluded middle 130, 160 p. of fullness 118 p. of identity 109–10, 138, 161, 175–7 p. of negation 90 p. of non-contradiction 72, 109–10, 130, 160, 175, 177 p. of substitutivity of identicals 138 p. of sufficient reason 161 repugnans notae p. 167–9, 176–7 problem-solving techniques 64 Proclus 26 proof: 47, 112–14, 196 transparency of the p. 63, 65 propositions: 70, 84 containing and applicative propositions 94–6, 98–9 mental p. 112 verbal p. 112–13 propositional calculus 8, 129 propositional logic 129–31 proprietas terminorum 40 quantification and quantifiers 85–7, 89, 130, 147, 191 existential quantifier 147 indefinite concepts as quantifiers 8, 147–8 quiddities 2, 21, 24, 25 Quintilian 43, 46 Ramus, P. 134 rationality 193, 204 reason 64, 68, 74, 76, 92, 109, 111–14, 116–17, 120, 195, 210 reductio ad absurdum 160, 173 reduction to first figure syllogism 8, 9, 84, 88, 91–2, 157, 159, 161, 163–4, 170–3, 176, 178 referential and attributive use: of paronimous terms 14, 17 of predication 18, 27 of substantial terms 17, 28

Index reflexivity 137–8 Reimarus, W.H.S. 161, 168–9, 174, 178 Rescher, N. 158 rhetoric 37, 42, 45, 61 Rile, G. 46 Rummel, E. 52 Russel, B. 46 Saenger, P. 52 scholasticism 35, 36, 45, 49, 52, 65, 78, 119, 129, 131–2 Scholderer, V. 50 self-consistency 7, 148 (see also operator of possibility) self-differentiations 204 self-evidence 4, 61–2, 65, 109, 111, 121, 160 self-subsistence 203 self-sufficiency 204–5 semantic conventionality 5 semantic enrichment 199, 210 semantic inferences 192 signs (natural and arbitrary) 70 signs-references relations 8, 165–9 simmetry 138 singulars/singularity 191–5, 198–9, 201–3, 207 singular marks 70 skepticism 99 sophistry 2 sorites 88 (see also paradox) Spade, P. 47 Spinoza 204 square of opposition 131–2 starting point 105 Steinberg, S. 50 Stillingfleet, E. 111 Stoics 1, 11, 130 strict and material implication 137 Sturm, J.C. 134 subalternation 131 subjectivity 202 “sublation of the mediation” 201 Summulae de dialectica 53 Summulae logicales 53 Swineshead, R. 134 syllogism/syllogistic: (un)usefulness and (un)helpfulness 3, 45–6, 67–8, 83, 159, 164, 169, 174, 177–8

219 as addition 71, 74 as clarification of given concepts 8 as combinatory, or computational, operation 5, 68–9 as reordering schema of given data 3 as semantic, systematic whole 193, 199, 208 axiological foundation of s. 5 categorical s. 24, 75, 88, 158, 200 classification of s. 88 complex or non-complex s. 88, 91–2, 97, 99 cyrcle of s. 204 definition of s. 1, 118 demonstrative or “scientific” s. 60–1 devaluation of s. 3 disjunctive s. 158, 192, 200–1 equivalence of categorical and hypotetical s. 75 first figure s. 75, 159, 162, 164, 168–72, 176–8, 194, 196 heuristic power (lack of) 3 hypotetical, or conditional, s. 12, 24, 75, 88, 192, 158, 200 informativeness (lack of) 4, 60–1 laws, or rules, of s. 64, 195 mixed modal 2, 12, 25–6, 28, 170–1 prescrictive character 4 qualitative s. or s. of existence 192, 198, 200 rules for determining the validity of s. 89–92, 96, 99–100 s. in BARBARA 93–4, 96, 99, 133, 160, 162, 194 s. of necessity 192 s. of reflection 192, 199 second, third and fourth figures 91–2, 94, 157, 159, 164–5, 168–9, 171, 173–4, 196 series, or chains, of s. 77, 166 simple and conjunctive 88 theories of s. 132 triads of s. 9, 205–7 (see also cyrcle of s.) versus common sense 4 versus discovery 8, 61, 63 with accidental paronymous attribution 18 with fixed conclusion 84, 94

220 syllogísthai 69 synthesis 63, 76, 105, 112 Syrianus 26 system 176, 193, 204 systematicity 204 terms: 85 first and second intention terms 72–4 modalized terms 22 permutation of terms 196, 207, 210 t. signifying other terms 73 t. signifying things 73 singular terms 130 substitution of t. 97–9 term-logic or predicate logic 129 triad of terms 205 the aspect theory of predication 12 theological literature 50 Theoprastus 1, 17, 26 theory of truth 49, 70 Thomasius, J. 134 transitivity 137–8 translations 48 trivium and quadrivium 52 truth: 28, 74, 83–4, 100, 105–6, 109–10, 113, 116, 121, 147, 160, 166–7, 176–7 “as for now”-truths (ut nuc -truths) 13, 17, 26

Index accidental truth 87 hypothetic truth 195 truth-functional connetives 129, 131, 138 truth-makers 24 truth conditions: 48–9 assesment of 41 of categorical propositions 12 universals/universality 95, 111, 121, 136, 137, 148, 191–5, 198–201, 203, 206–8 universal statement 13 use of examples 100 validity 8, 46–7, 60, 84, 88, 93–4, 96–7, 113, 118, 158–9, 161, 169–72, 176, 195 Valla, Lorenzo 3, 36, 41, 45, 46 visual understanding: 52 “seeing” the conclusion in the premises 63 Winkler, K. 119 Wolff, Ch., 158–9, 162–4, 168–9, 173–5, 178 Wolff, M. 158, 171, 173 words (proper and general) 70 Wynne, J. 119 Zabarella 60

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