Grue! The New Riddle of Induction 0812692187, 0812692195

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GRUEi THE NEW RIDDLE OF INDUCTION

EDITED BY

DOUGLAS STALKER

OPEN* COURT Chicago and La Salle, Illinois

*

OPEN COURT and the above logo are registered in the U.S. Patent and Trademark Office.

© 1994 by Open Court Publishing Company First printing 1994 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher, Open Court Publishing Company, POB 599, Peru, Illinois 61354. Printed and bound in the United States of America. Library of Congress Cataloging-in-Publication Data Grue! : the new riddle of induction / [compiled by] Douglas Stalker. p. cm. Includes bibliographical references and index. ISBN 0-8126-9218-7 (cloth) .-ISBN 0-8126-9219-5 (paper) 1. Induction (Logic) I. Stalker, Douglas Frank, l 947BC91.G78 1994 161 - dc20 94-11203 CIP

Dedicated to the Memory of Henry B. Tingey

Contents

Introduction l.

Inductive Inference: A New Approach

1 19

Israel Scheffler

2. Luck, License, and Lingo

31

Joseph Ullian

3. Natural Kinds

41

W.V. Quine

4. Concerning a Fiction about How Facts Are Forecast

57

Andrzej Zab/udowski

5. Grue

79

Frank ] ackson

6.

Concepts of Projectibility and the Problems of Induction

97

John Earman

7. Induction, Conceptual Spaces, and AI

117

Peter Giirdenfors

8.

The Projectibility Constraint

135

John L. Pollock

9. Simplicity as a Pragmatic Criterion for Deciding What Hypotheses to Take Seriously

153

Gilbert Harman

10. A Grue Thought in a Bleen Shade: 'Grue' as a Disjunctive Predicate

173

David H. Sanford

11. Entrenchment

193

Ian Hacking

12. No Model, No Inference: A Bayesian Primer on the Grue Problem

225

Elliott Sober

13. Bayesian Projectibility Brian Skyrms

241

vui 14.

Contents

Learning and Projectibility Patrick Suppes

15.

263

INTRODUCTION

Selecting Variables and Getting to the Truth Clark Glymour and Peter Spirtes

273

Annotated Bibliography Index

281 459

The grue debate has been going on for almost fifty years. It started eight years before the word "grue" appeared in print in philosophy. (The word "gruebleen" appeared in print in 1939, on page 23 of James Joyce's novel Finnegan)s Wake.) In 1946 Nelson Goodman published a short paper entitled "A Query on Confirmation," and this paper introduces the grue-like predicate as.,, This predicate appears in an example about drawing marbles from a certain bowl. Goodman asks us to suppose that we have been drawing one marble per day from this bowl for ninety-nine days-indeed, the ninety-nine days up to and including Victory in Europe Day, May 8, 1945. He also asks us to suppose that each marble has been red so far. If we draw a marble on the next day, the hundredth day, we might expect that it will be red as well. After all, the first marble was red, the second was red, and so on through the ninety-ninth marble: they were all drawn from the bowl and they were all red. The evidence plainly supports our prediction about the next marble we draw: it will be red. Or so it seems. Goodman introduces us to the predicate as/) which means "is drawn by Victory in Europe Day and is red, or is drawn later and is nonred." This predicate applies to the ninety-nine marbles that we have drawn from the bowl so far. They were all drawn by Victory in Europe Day, and they were all red-so they were all S. This evidence seems to support a different prediction about the next marble we draw: it will not be red. Of course we do not expect the next marble we draw from the bowl, the one we draw after Victory in Europe Day, to be nonred. It doesn't matter that the first marble was S, the second was S, and so on through the ninety-ninth marble. This doesn't support a prediction about the next marble being nonred. But why not? Why do the marbles add up to confirmation in one case, but not the other? In 1954 Goodman published a small book entitled Fact, Fiction and Forecast. The word "grue" appears in Chapter III, Section 4, which is entitled "The New Riddle of Induction." Goodman asks us to consider emeralds that have been examined before time t, and to suppose that all of them have been green. Thus, by time t, these observations support the hypothesis that all emeralds are green, and the prediction that if we happen to examine the next emerald after

2

Introduction

time t, it will be green as well. As before, Goodman introduces a new predicate to show that things aren't as simple as they might seem. Something is grue, he tells us, if it is examined before time t and determined to be green, or it is not examined before time t and it is blue. It should be plain how this applies to the emeralds examined before time t, and all of which we have found to be green. They are all grue. Thus, by time t, we have a good deal of support for the hypothesis that all emeralds are grue, and the prediction that if we happen to examine the next emerald after time t, it will be grue as well-that is, it will be blue. Indeed, we seem to have just as much support for the green hypothesis as the grue hypothesis. Each emerald has been green, and each has been grue. Be that as it may, we know that the green emeralds (or, to be precise, the evidence statements describing the green emeralds) support the green hypothesis and that the grue emeralds (or, to be precise, the evidence statements describing the grue emeralds) don't support the grue hypothesis. Why, as before, do we have confirmation in one case but not the other? The new riddle of induction has become a well-known topic in contemporary analytic philosophy-so well-known that only a philosophical hermit wouldn't recognize the word "grue." Fact, Fiction and Forecast is in a fourth edition, and the best journals contain articles on the puzzle year in and year out. There are now something like twenty different approaches to the problem, or kinds of solutions, in the literature: the entrenchment solution the positional-qualitative solution, the simplicity solution, the natu'ral kind solution, the coherence solution, the incoherence dissolutions, the falsificationist response, the evolutionary approach, the real property approach, the counterfactual approach, the various Bayesian approaches, and so on. None of them has become the majority opinion, received answer, or textbook solution to the problem. There hasn't even been complete agreement on what the proble~ really a~ounts to. In short, the grue debate is still going on. This volume is the first collection of essays devoted to that debate, and it includes selections from the 1950s to the present. The selections are in chronological order. Seven of them have been published before, and eight are appearing for the first time. The collection ends with a 316-entry, annotated bibliography. The annotations range in length from one line to several hundred lines. They cover articles from more than forty different journals and chapters from more than eighty books. The first selection originally appeared in Science in 1958. Goodman was teaching at the University of Pennsylvania, and his

Introduction

former student, Israel Scheffler, was a lecturer at Harvard. In "Inductive Inference: A New Approach," Scheffler attempts to inform scientific readers about Goodman's (then) recent work on induction. He develops the new riddle in connection with Hume's challenge and the generalization formula, and he explains the basic ideas in Goodman's entrenchment solution. Scheffler sees Hume's challenge as a question about how to tell reasonable (rational, justified) inductive inferences from unreasonable ones, and he introduces the generalization formula as a popular answer to this question. Scheffler uses the generalization formula with a pair of opposing next-case predictions, such as "The next F will be c>> and "The next F will not be G. >> The former prediction agrees with the universal generalization "All F are G,)) and the latter prediction agrees with the universal generalization "No Fare G.)) If the evidence to date uniformly supports the generalization "All F are G)) and thereby disconfirms the contrary generalization "No F are G,)) then the reasonable prediction is "The next F will be G.)) Scheffler thinks that Goodman's new riddle of induction refutes the generalization formula, and he extends Goodman's copper example to show how it does. Consider the predictions "The next specimen of copper will conduct electricity" and "The next specimen of copper will not conduct electricity." The first prediction agrees with the generalization "All specimens of copper conduct electricity" and the second agrees with the generalization "No specimens of copper conduct electricity." If the evidence to date uniformly supports the hypothesis that copper conducts electricity and thereby disconfirms its contrary, then it is reasonable to predict that the next specimen of copper will conduct electricity, and unreasonable to predict that it will not. Or that is how it seems until we introduce a grue-like hypothesis about copper: viz., "All specimens of copper have either been examined before t and conduct electricity or have not been examined before t and do not conduct electricity." The evidence to date uniformly supports this grue-like hypothesis and thereby disconfirms its contrary as well. If the next specimen of copper will not be examined before time t> then it is reasonable to predict that the next specimen of copper will not conduct electricity because this prediction agrees with the grue-like hypothesis. The generalization formula, then, has not picked out the reasonable prediction here. Indeed, it can't even select one prediction-reasonable or otherwise-from our pair of opposing next-case predictions. Scheffler describes how Goodman's approach distinguishes the confirmable "All copper conducts electricity" from its

3

4

Introduction

nonconfirmable counterpart by looking at historical information about the predicates in each hypothesis. Their biographies differ in an important way. The predicate "conducts electricity" has been used longer and more often in formulating predictive hypotheses on the basis of positive, albeit partial, evidence. In Goodman's terminology, the predicate "conducts electricity" is better entrenched than the predicate "has either been examined before t and conducts electricity, or has not been examined before t and does not conduct electricity." Since the grue-like hypothesis conflicts with a hypothesis whose predicate is plainly better entrenched, the grue-like hypothesis is nonconfirmable or, as Goodman puts it, unprojectible. Likewise, since "All emeralds are grue" conflicts with "All emeralds are green," and the predicate "green" is plainly better entrenched than the predicate "grue," the grue hypothesis is unprojectible. As Scheffler notes, some critics believe that Goodman's entrenchment solution is inadequate because Goodman does not say enough about entrenchment itself. Joseph Ullian discusses this point in the second selection, "Luck, License, & Lingo," which he prepared for a symposium on justification and originally published in The Journal of Philosophy in 1961. Ullian presents the new riddle and the entrenchment solution in connection with Goodman's view of justification. Goodman takes justifying to be a matter of describing, defining, and codifying. On this view, we justify a particular inductive inference by showing that it agrees with a valid rule of inductive inference, and we justify a rule of inductive inference by showing that it agrees with the inductive inferences we make and accept. If Goodman's general rule accurately codifies the particular cases by taking into account the entrenchment of predicates, then it is justified on this view and solves the new riddle. However, some critics want more than accurate description. In particular, they want to know why the right predicates have become well entrenched while the spurious ones have not. Is it simply a matter of luck that the well-entrenched predicates show up in the confirmable hypotheses? Ullian believes that the real question here is about predicates in general, not just the well-entrenched or projectible ones. It is, he argues, a question about the utility of predicates or general terms. Ullian considers it remarkable that we have any use-inductive or otherwise-for our general terms. As he points out, if general terms mark off classes and there are indefinitely many classes, with each class just as good as the other from a logical point of view, then it seems extraordinary that we

Introduction

have ended up with classes which are actually .valuab'.e to us. Insofar the re is an explanation for this state of affairs, Ulhan suggests as · ad d ed to h'ts that it will be along evolutionary lines. In a postscnpt original paper, Ullian discusses the current status of Goodman's theory of projectibility. . The third selection is by Goodman's longtune colleague at Harvard, W.V. Quine. He originally wrote his essay "Natural Kinds" for a 1970 festschrift for the philosopher of science Carl Hempel. Quine describes both the new riddle and Hempel's raven paradox in terms of projectibl.e predicates. Wi~h ~empel's paradox, a white shoe ends up confirmmg the hypothesis All ravens are black" because a white shoe confirms the logically equivalent hypothesis "All nonblack things are n?nrave~1s." Wh~le "raven" and "black" are projectible predicates, Qume believes their complements are not projectible. Thus a white shoe does not confirm "All nonblack things are nonravens" any more than a green emerald confirms the hypothesis "All emeralds are grue." Quine maintains that projectible predicates are true of.things ~f ~ ki.nd, and th~t the notion of a kind is related to the not10n of s11111lanty at least 111 the sense of covariation: e.g., if we first think object a is more similar to object b than to object c and later think object a is less similar to object b than to object c, then we will likewise ch~n~e h.ow we assign these objects to kinds. In short, the more s1milanty .between objects, the more reason to count them as members of a kmd. . Quine argues that we must have an innate standard of comparative similarity in order to form any habits and expectations at all, and that this innate subjective standard makes for successful everyday inductive inferences because it is the result of Darwinian natural selection. Quine also emphasizes the development and change of standards of similarity and systems of kinds, notably from our subjective standard and intuitive kinds to scient.ifically obje~t~ve standards and theoretical kinds, such as marsupials and pos1t1vely charged particles. Moreover, he believes that wh~n a bra~ch. of. science matures, we can analyze the relevant not10ns of sumlanty and kind in special terms from that branch of science and from. logic. For example, we can analyze object a being,. from. a chemical point of view, more similar to object b than to object c 111 terms of the ratios of matching to unmatching pairs of molecules. We can then use this analysis of comparative similarity to analyze chemical kinds in terms of a paradigm and a foil. A paradigm is an example of the central norm for a kind, and a foil is an example of something that is not a member of the kind because it differs a

5

6

Introduction

little too much from the paradigm. A kind is then a set of objects such that the paradigm is more similar to the members of this set than it is similar to the foil. The fourth selection is a revised version of Andrzej Zabludowski's "Concerning a Fiction about How Facts Are Forecast." This paper was originally published in 1974 in the Journal of Philosophy, and it started an eight-year exchange between Zabludowski and proponents (notably Goodman and Ullian) of the entrenchment approach to projectibility. Zabludowski maintains that Goodman's theory has a number of absurd consequences, not the least of which is that no hypothesis is projectible. Zabludowski believes this consequence obtains because, for any supported, unviolated, and unexhausted generalization h, we can devise another generalization that is supported, unviolated, and unexhausted-and that conflicts with h. Moreover, this rival generalization will have predicates that are at least as well entrenched as the predicates in h. On Goodman's approach, this means that h is not projectible. For example, we can let h be the hypothesis "All emeralds are green" when we have examined some emeralds, found them all to be green, and still have more emeralds to examine. Zabludowski claims that the predicates "stone," " roun d , " an d "h ard" are among t h e best entrenched predicates at this time. He also claims that we know all three predicates apply to some objects at this time, and that we know "stone" applies to some green emeralds but "round" does not apply to them. Lastly, Zabludowski believes that the information we accept at this time does not prohibit the hypothesis "All stones are hard" from being true and conflicting with "All emeralds are green." Given all of this, Zabludowski introduces the following generalization as a supp~rted, unviolated, and unexhausted rival to the hypothesis in question: (x)(Sx ~ ((Rx & -Kx) v (Hx & Kx))), where