Thinking about Thinking: A Physician’s Guide to Epistemology 9781036410155, 1036410153

Table of contents :
Dedication
Table of Contents
Acknowledgements
Preface
Introduction
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Chapter 13
Chapter 14
Chapter 15
Chapter 16
Chapter 17
Chapter 18
Chapter 19
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Chapter 25
Chapter 26
Chapter 27
Chapter 28
Chapter 29
Chapter 30
Chapter 31
Chapter 32
Chapter 33
Chapter 34
Chapter 35
Chapter 36
Chapter 37
Chapter 38
Chapter 39
Chapter 40
References

Citation preview

Thinking about Thinking

Thinking about Thinking: A Physician’s Guide to Epistemology By

Daniel Albert

Thinking about Thinking: A Physician’s Guide to Epistemology By Daniel Albert This book first published 2024 Cambridge Scholars Publishing Lady Stephenson Library, Newcastle upon Tyne, NE6 2PA, UK British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Copyright © 2024 by Daniel Albert All rights for this book reserved. No part of this book 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 permission of the copyright owner. ISBN: 978-1-0364-1014-8 ISBN (Ebook): 978-1-0364-1015-5

To Ernest Nagel who steered me toward medicine and Michael Resnik and Ronald Munson who steered me back to philosophy

TABLE OF CONTENTS

Acknowledgements ................................................................................... xi Preface ...................................................................................................... xii Introduction ................................................................................................ 1 Chapter 1 .................................................................................................. 10 Common Sense Chapter 2 .................................................................................................. 16 Intuition Chapter 3 .................................................................................................. 22 Abstraction Chapter 4 .................................................................................................. 24 Natural, Artificial and Ordinary Language Chapter 5 .................................................................................................. 28 Deduction and the Evolution of Logic Chapter 6 .................................................................................................. 42 Tautologies And Definitions Chapter 7 .................................................................................................. 44 Paradox Chapter 8 .................................................................................................. 48 Induction Chapter 9 .................................................................................................. 54 Causal Inference Chapter 10 ................................................................................................ 60 Statistical Inference

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Chapter 11 ................................................................................................ 67 Probabilities and its Problems Chapter 12 ................................................................................................ 71 Observation, Experimentation, and the Scientific Method Chapter 13 ................................................................................................ 76 Study Design and Analysis Chapter 14 ................................................................................................ 80 The Practice of Medicine and the Science of Medicine Chapter 15 ................................................................................................ 84 Health Services Research – The Science Behind Clinical Medicine Chapter 16 ................................................................................................ 88 Knowledge and Belief Chapter 17 ................................................................................................ 92 Teleology and Natural Selection Chapter 18 ................................................................................................ 95 Reduction Chapter 19 ................................................................................................ 97 Reflection Chapter 20 ................................................................................................ 99 Consciousness Chapter 21 .............................................................................................. 102 Mathematics Chapter 22 .............................................................................................. 106 Aristotle versus Plato Chapter 23 .............................................................................................. 108 Computer Inference versus Human Inference Chapter 24 .............................................................................................. 110 Artificial Intelligence

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Chapter 25 .............................................................................................. 112 Decision Analysis Chapter 26 .............................................................................................. 118 Game Theory Chapter 27 .............................................................................................. 122 Health Economics Chapter 28 .............................................................................................. 125 Chaos Theory Chapter 29 .............................................................................................. 128 The Black Swan Chapter 30 .............................................................................................. 130 Abduction Chapter 31 .............................................................................................. 132 Algorithms and Checklists Chapter 32 .............................................................................................. 134 Models, Analogies and Maps Chapter 33 .............................................................................................. 136 Dual Process Theory: Heuristics, Biases and Framing Chapter 34 .............................................................................................. 139 Gedanken Chapter 35 .............................................................................................. 141 Possible Worlds and Many Worlds Chapter 36 .............................................................................................. 143 Paradigms Chapter 37 .............................................................................................. 145 Truth Chapter 38 .............................................................................................. 147 Philosophic Argument

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Chapter 39 .............................................................................................. 149 Diagnosis Chapter 40 .............................................................................................. 151 Summary References .............................................................................................. 152

ACKNOWLEDGEMENTS Any author will confess that it is very difficult to cite the many people that have contributed to a book. I am no different. Although my interest in this subject dates back to high school it was certainly strengthened by the core courses at Columbia known as Contemporary Civilization and Humanities. These are and remain the bulk of the work in the first two years of college and are generally taught by senior faculty. Anyone who went through them will acknowledge their influence on future academic endeavours. Specific teachers and students are too numerous to mention. However, I was a philosophy major and Ernest Nagel, to whom this book is also dedicated, was instrumental in encouraging me to pursue medicine. Likewise, in medical school at New York University and residency at the University of North Carolina at Chapel Hill, the intellectual rigor and constant mentoring of students focused and honed my skill at pursuing intellectual problems. While mentors at these institutions and at The University of California San Diego and Harvard Medical School provided the academic medical environment for my profession, the only true mentors for this work were Michael Resnik Philosophy Professor at University of North Carolina at Chapel Hill and Ronald Munson Professor of Philosophy at University of Missouri for whom this book is dedicated. In particular Ronald Munson read a draft of the manuscript and offered many sage comments and examples that I used to illustrate the concepts addressed. Of course, the responsibility for the accuracy is mine as is responsibility for any errors. Lastly, I would like to thank Simon Richardson for editorial assistance.

PREFACE

It is easier to explain what this book isn’t about rather than what it is. It isn’t a textbook or an essay or a lecture. It uses material from history but it isn’t a historical account. It covers several topics within economics, especially behavioral economics, psychology, logic, mathematics and, most importantly, philosophy. However, it can’t be called a formal philosophical work, since it doesn’t stake out a philosophical position, explain the claim, give the implications of that claim, then defend it from potential criticisms. It does address certain philosophical positions, but primarily to describe them and, occasionally, dismiss them. I am not a professional philosopher and this means that I may not give adequate weight to the positions I reject. I may even have misstated a philosophic claim but that is my responsibility alone. It is more of a commentary than anything else and I hope that the annotated references will give you, the reader, a clearer view of the issues I have dealt with. The point of the book is to go beyond the limits of philosophy in the study of epistemology – the theory of knowledge - drawing from other disciplines that make contributions to understanding what knowledge is, how we acquire it and how we defend it. The book draws from a range of sources and viewpoints, as my position is that all cognitive activity addresses epistemology in one way or another, and we should therefore examine the entire range of cognitive disciplines to gain a firmer idea about knowledge. This means that each segment of the book is short and easily digestible, and the style is conversational and, hopefully, engaging. The content focuses on medical issues as that is my area of expertise, but the book can be understood by anyone with a college education. I have purposely left out almost all technical discussions, especially regarding logic and mathematics, partly to avoid discouraging anyone, and partly because it is unnecessary for my goals. And what are those goals, you might ask? In this book, I hope to survey many, if not most of the disciplines that address the nature of knowledge and how we acquire it. While this makes for a diverse book (which reflects my personal interests), it also covers contributions to the study of knowledge (epistemology) that go beyond each discipline’s individual

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contributions. I draw from history, philosophy, economics, psychology, mathematics and statistics. The order of chapters follows the evolution of thought, from the most basic notions of common sense and intuition, to the more analytical concepts of logic. It then moves on to more technical areas such as mathematics, statistics, decision theory and, finally, a central concept in clinical medicine – that of diagnosis. Along the way, there are asides into related topics such as tautologies, paradoxes and truth. I hope you come away with a much more rounded view of the study of knowledge and how it transcends all the disciplines that take various stabs at understanding the process. Each chapter is sufficiently independent of the rest to be able to stand largely on its own, but it makes for a better flow if it is read from beginning to end. While there is a focus on clinical medicine, it is not a text for doctors or people working in medicine; rather, it is for anyone who is interested in how we acquire knowledge. Hopefully, there are enough anecdotes to keep you interested, but the subject matter is dense and not trivial. Although each segment is brief, the references go into more detail with sometimes exhaustive discourses. All of the references are books, as published papers would overwhelm the narrative. Think of this as a sequel to our book on clinical reasoning, published in 1988 (Reasoning in Medicine: An Introduction to Clinical Inference by Albert, Munson and Resnik), but covering different ground. It may also be considered a testimony to the undergraduate education program at Columbia, which has Contemporary Civilization as a required course. This extremely intense dive into the most important concepts in Western Civilization was crucial to my intellectual development and, as a peculiar byproduct of the COVID 19 pandemic, I was able to reread the entirety of the course material (consisting of two immense volumes). Of course, there are distinct limitations to this book. First, I have little knowledge or understanding of Eastern thought, and to the extent that it addresses these issues, this book is deficient. Also, there are areas within philosophy to which I have had little exposure, but which I have nevertheless addressed briefly. For example, the sections on reflection and abstraction are dealt with in phenomenology (the study of existence and appearance) but I have little patience for works by authors such as Heidegger and Hegel. I also ignore the entire discipline of existentialism and most of what has been termed ‘continental philosophy.’ This is not to say that existentialism, phenomenology and continental philosophy don’t

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contribute to epistemology; I just am not the right person to address them. My hope is that the book will be read by an audience that is not burdened by preconceived positions on these issues, and one that is open to a new approach for what it is worth. When I do engage in philosophical issues, they are more completely and better addressed in The Encyclopedia of Philosophy (a four-volume text) and the Stanford Encyclopedia of Philosophy (an online, updated reference work of considerable complexity). Take a look at these regardless of whether you decide to engage with them in depth. They, and the references I have listed in this text, will greatly enlarge and embellish the discussions in this work. One word of warning, though: The material is technical and difficult. However, I address the same issues from different perspectives as the book proceeds, so if you find yourself scratching your head or feeling confused, do bear with it as it is likely to become clearer in a later chapter. This is especially true for the introduction, which could be read after the subsequent chapters as it summarizes much of what follows. Alternatively, you could read it as an introduction, then read it again after the rest of the book is completed. In closing, I hope that the book is an enjoyable read. It certainly was fun writing it.

INTRODUCTION

The Thinker by Auguste Rodin As Bryan Magee points out in his introduction to The Story of Philosophy, the fundamental questions that the subject tries to answer concern the nature of existence (ontology) and the nature of knowledge (epistemology). However, underlying each of these enterprises is the question of how reasoning can answer these questions. The premise of this book is that we can address questions of what we think we know and how we think we know the answers to questions, but that questions of why may be better left to religion, as they cannot be answered through reason alone. As we will see later, the relationship between cause and effect appears to be a concept that is only used to assign blame or achieve practical results, like charging a car battery when it won’t start because the lights have been left on. Questions of a more existential nature like “why do we exist?” require what Kierkegaard called a “leap of faith” and, consequently, we won’t deal with them here. However, our “what” and “how” questions require reasoning that is rooted in philosophical analysis. This will allow us to address epistemological questions of knowledge on both an empirical and analytical level. The introduction lays out many of the issues that will be dealt with in more detail in the chapters that follow, so don’t be discouraged if you can’t initially follow the discussion: what follows will be more expansive and, hopefully, more approachable. Epistemology is an ancient but vibrant field of philosophical study. Plato, who wrote in his Meno that ‘knowledge is the basis for virtue and happiness,’

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distinguished between two domains of knowledge – the physical and the spiritual. To achieve knowledge, he thought that there were four stages – imagining, believing, thinking and perfect intelligence. This is not so far from the present paradigm of knowledge as ‘Justified True Belief’ (JTB). However, JTB ran into a roadblock known as the Gettier problem, which was published in a three page paper in Analysis in 1963 by Edmund Gettier. In this document, he noted that JTB can lead to false conclusions if the statement in question is simply linked to a known truth through an either/or conjunction. For example, either the moon is made of green cheese or 60 seconds constitutes a minute. The disjunction is true but the clause regarding the moon is false. In my view, though, this Gettier type-2 counterexample is a non-problem which arises out of an illicit use of the truth value of an ‘or’ statement. This is similar to many paradoxes (many of which we will discuss later) that arise out of twisted versions of logic, such as the liar paradox. In a different way, Goodman’s new riddle of induction also results from a time-dependent claim that can’t be verified at the present moment (we will discuss this in more detail later). That isn’t to say that illicit disjunctions aren’t a problem for human cognition. The famous Linda problem (which we talk more about later) dupes many people into believing that a bookish young radical would more likely be a feminist bank teller than just a bank teller. We will explore why this is a falsehood, and why people make this mistake. In contrast, Gettier type-1 problems are conjunctions where the observer is under the false impression that two events are true at the same time (and thus have JTB), but in the end, one or both of the clauses turns out to be erroneously true. This is a classic case of “correct for the wrong reason” - a situation which is particularly common to physicians. Let’s take, for example, a doctor who thinks their patient has an infection because the white blood cell count is elevated. On closer inspection, it transpires that the patient does indeed have an infection, but that the white blood cell count is elevated because they are on steroids. This happens all the time and doctors think very little about it because our conclusions are rarely based on a single piece of information. This is why clinical medicine is not logical; it is an empirical endeavor that is sometimes scientific, and sometimes just empirical with little or no supporting scientific basis. Even though I think the Gettier examples are contrived (a much better example is in the Book ‘Philosophical Methods’ by Williamson), the claim is correct. Ultimately, Justified True Belief is insufficient as a criterion for knowledge, which is why in a later section, I will propose ‘Verified True Belief’ (or its weaker sibling - Confirmed True Belief) as a more satisfactory criterion for knowledge.

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As is the case in all fields of philosophy, there are various schools of thought in epistemology. For example, Foundationalism contends that there are essential propositions which do not require external support (like axioms) and are the foundation of knowledge, as in Lord Russell and Alfred North Whitehead’s ‘Principia Mathematica.’ Others contend that the strength of a proposition is dependent on coherence with other supporting statements, as in Quine’s Web of Belief. Other schools include pragmatism, scientism, intuitionism and, importantly, skepticism. But just when you think philosophy never makes any progress and it is all a “footnote to Plato,” there are clearly schools of thought that have vanished like determinism (unless you are a religious conservative), which contends that the universe is one big clockwork mechanism that chugs along with no room for uncertainty. This Newtonian notion has now been replaced by uncertainty in the form of probability and uncertainty in the form of chaos (a deterministic form of uncertainty), leaving the whole question of free will in limbo. While logicians, physicists and mathematicians gravitate toward foundationalism, physicians are most comfortable with pragmatism, especially those for whom inference plays the main role in deciding on “the best” explanation (otherwise known as abduction). Abduction has long been thought to play a role in the creation of hypotheses, but it is best understood as a means of deciding between competing hypotheses. The rationale of pragmatism is the usefulness or utility of knowledge and in the medical sphere it is exemplified by the diagnostic process. This method, which was popularized by Conan Doyle (himself a physician), is exemplified by Sherlock Holmes’ approach, which eliminates all possible explanations before coming to a conclusion that is irrefutable - even if it is improbable. Even such eminent classical logicians as Bertrand Russell advocated for abduction, which he confusingly termed induction as a method of deciding between hypotheses. But Conan Doyle was not the only physician interested in logic. Galen, whose fame arises primarily from his contributions to medicine, was also an eminent logician. Indeed, abduction was first explored by C.S. Pierce (who was also an early explorer of quantification, though its roots can be traced to Senna), an 18th century American philosopher, and later by other pragmatists such as John Dewey, whose definition of truth was warranted assertability rather than an appeal to an external reality. Warranted assertability rather than objective truth is a human-centric view of knowledge and rightfully emphasizes its tentative nature as a hypothesis. It focuses on knowledge as being both defensible and explanatory; therefore, by extension knowledge plays a role in prediction. As the logical positivists

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Introduction

clearly understood, explanation is the mirror of prediction, but by making explanation the primary focus of inference, prediction can then flow organically from explanation. This is, of course, a key feature of both scientific method and diagnostic process. The logical positivists maintained that truth was a consequence of the verification of propositions by empirical data (the correspondence theory of truth, first asserted by Plato). However, this leads to never-ending trials of theories by tests that are designed to provide supportive data. Popper realized the futility of this process and introduced the notion of falsification, whereby a theory is tentatively accepted until falsifying data leads to its abandonment. This is much like Kuhn’s theory of paradigms whose edifices can eventually come tumbling down under the weight of falsifying data. Falsification does a better job of discarding hypotheses than verification does in confirming them, which is basically an extension of Hume’s critique of induction in the first place. For example, no matter how many times the sun rises in the morning, it is insufficient to conclude that this will always happen. That is to say, until falsifying data appears, we need to go forward with confirmatory data. However, explanations aren’t all equivalent; some are more compelling than others. The most cogent explanations seem to obey certain rules. These include simplicity (for example, mathematical proofs), coherence with supporting knowledge, explanatory generalizability (i.e., applying to a range of phenomena, not just one), and a lack of dependence on ad hoc elements that have only been brought to bear to bolster the explanation (Ockham’s Razor, another eminent logician). Some of the distinctions between the rules of inference and epistemic truth were pointed out by Bradley in his comparison between validity and soundness in an argument. We will expand on this confusing concept in the section on Deduction. A more contentious claim is that there is no such thing as truth outside of a paradigm. That is to say, truth is contextual. All this is very dense but it will be fleshed out in later sections. It is difficult to discuss epistemology without making reference to Kant, whose contribution was to clarify a distinction between axiomatic (or analytic) propositions, which he labeled a priori (necessary), and empirical or synthetic statements, which he labeled a posteriori (contingent). While this is an oversimplification and indeed, ideas of this nature can be traced all the way back to Aristotle, this distinction is a codification of foundationalism. If this were all he did, the contribution would have been modest, but Kant went on to characterize a class of claims that are ‘synthetic a priori.’ For example, a priori analytical statements can be exemplified by definitions such as “unmarried men are bachelors,” whereas a priori

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synthetic statements are not definitional but convey new information, such as “5+7 =12.” Of course, one can argue about both kinds of a priori claims. Unmarried men could be children, which does not fit with our conceptualization of bachelors. This is because the connotative meaning of the word itself implies the possibility of marriage. Similarly, 5+7=12 is not necessarily true in all mathematical programs; e.g., binary logic. Alternatively, a Foundationalist could claim that 5+7=12 is not synthetic at all, as it is the direct result of the axioms of arithmetic. As such, it is a priori analytical. This is in fact what Russell and Wittgenstein tried to do, but they ran into some problems that turned out to be unsolvable. Nevertheless, some philosophers and mathematicians believe that all mathematics can be reduced to logic if you add set theory. But since there is no one set that contains all subsets, even this theory has its limitations. Furthermore, some philosophers claim that a priori knowledge is innate knowledge, which seems at odds with the development of cognitive capability of infants and children, but perhaps innate knowledge is closely aligned with the wiring of our brains once we have developed cognitive skills. On the other hand, empirical knowledge is acquired through the senses, but how do we know whether an animal is a dog unless we have an understanding of what a dog is in the first place? This is the position of philosophers who believe all observation is hypothesis laden. What this means is that you cannot categorize an animal as a dog until you have a notion of what a dog is. The only situation that Kant thought was impossible was an analytical a posterior statement, but even this is debatable, since the most analytical of all statements, the law of the excluded middle (P V-P P or not P), is actually incorrect in the intuitionist conceptualization of mathematics. What does seem to be true, though, is that no a posteriori statement can be proven by argument alone as it depends on experiential data. As we will try to emphasize throughout this book, claims to truth, especially foundational truths, are difficult to support. In fact, the whole idea of analytical truths, at least according to WVO Quine (a famous logician), is suspect. What does it mean to be true? Is it the concept that bears truth, or the proposition alone? Is the statement “no unmarried man is married” the same as “no bachelor is married”? As they refer to the same thing, they are synonymous, but they have vastly different connotations (see Quine and Goodman for more extensive discussions) just as the evening star and the morning star have the same extension (Venus) but are used entirely differently (as per Gottlieb Frege – a famous logician and mathematician).

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Talking about secondary characteristics as Goodman does misses the point that the two designations have a whole family of connotations that are incompatible (see Wittgenstein). therefore, just because their extensions (meaning the objects they refer to) are the same does not in any way assure that they are synonymous. “Morning star” and “evening star” are good examples of two designations that refer to the same object (Venus) but which have vastly different connotations. Other examples of analytical statements are equally suspicious. For example, is it necessarily true that if today is Monday, tomorrow will be Tuesday? Maybe so, but not if you are in an airplane going through time zones. What about “a square has 4 sides”? Yes, but isn’t that just a convention? Besides, what process do you need to go through to verify these statements? By definition it cannot be by an appeal to empirical evidence because that is what defines a synthetic a posteriori proposition. At this point, I think most philosophers have given up on the distinction between analytical a priori claims and synthetic a posteriori statements. However, it is important to note from an historical standpoint that the distinction was critical to analytical philosophy, and its descendant is logical positivism (i.e., the Vienna Circle). The logical positivist claim was that all statements were either analytical or verifiable, meaning that they are either true by their logical structure, or true by empirical data. Thus, the basis for meaning was either analytical (by definition) or verifiable. Even Ronald Reagan was a logical positivist in this sense, as per his famous quote, “Trust but Verify” in contrast to a pragmatist view of meaning as useful. Unfortunately, he was a little out of date in this regard since logical positivism had long since been abandoned, precisely because verification was as difficult to use as a criterion of truth as induction is for very similar reasons. No amount of positive information can fully assure the presence of a truth. All swans are not white, for example. The flip side of Foundationalism is skepticism, which is sometimes attributed to Descartes (although it, like almost everything else in Philosophy, really dates back to the Greeks, especially Carneides). Descartes famously said, “I think therefore I am.” Now, he didn’t really say it, but the intent is the same as what he did say. In reality, his argument was quite a bit more sophisticated. He reasoned that he could doubt all knowledge except the fact that he could doubt. Since doubting is thinking, if he does engage in doubting, he must be engaging in thinking. In pursuing this line of thought, he was trying to get to the root of what he could know for sure, but other skeptics have gone beyond and claimed that there is no such thing as knowledge – a concept that, again, can be traced back to the Greeks. Since Descartes did arrive at a fundamental proposition, he could be considered a

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foundationalist (in keeping with his day job as an exceptional mathematician), since his skepticism terminated with his knowledge of himself. Many of these concerns are reflected in discussions of certainty, which is generally considered to be a key ingredient of correct logical propositions and sensory claims (Regarding the latter, there is no way to validate sensory claims so they can be removed from our purview, but logical propositions that preserve truth function are candidates for claims of certainty). Building on this observation, one could enumerate several types of knowledge, including a priori (or axiomatic), perceptual (what our senses tell us), memory, and inductive (the result of cumulative observation). Unfortunately, none of these types of knowledge is infallible. Because we often need to validate our conclusions to other observers, there are types of justification that support a knowledge claim. Sometimes, we resort to causal explanations, sometimes to shared experience, sometimes to a third-party source (like an encyclopedia or, more currently, Google). Again, in spite of strong validation arguments, these propositions can be fallacious. In the end, it is not necessary to appeal to tricks of logic like the Gettier problems, in order to be skeptical of all and any knowledge-based propositions. While skepticism might be the most defensible position regarding claims of knowledge, it gets us nowhere in day-to-day activities and concerns. Furthermore, skepticism itself may be the victim of a paradox similar to the Liar Paradox, which is as follows: "If there is no reason to believe any statement, why is there reason to believe this statement?” Basically, resolving all doubt raises the bar too high as a criterion for knowledge or truth. We need to move forward, and denying all knowledge is not a viable path. In the end, a true skeptic would make a terrible doctor. Let’s start with the conventional concept of knowledge as justified true belief. Clearly, this is a human-centered cognitive claim. Belief is our own mental process, but justification can come from within - such as perceptual support, or external support such as testimony. Truth is conventionally thought of as totally independent of the person possessing knowledge, since it reflects the state of the world. This is exactly why knowledge is so important—it links our beliefs to the state of the world. Whether this is correct is a matter of some debate, since there is reason to believe that, at least on some level, there is not a static “state of the world.” However, knowledge can generate explanations for the perceived state of the world and predictions about future states of the world. Both processes are critical in the care of patients, and we need to accept some risk of fallibility in order to generate explanations (causal or otherwise) and predictions, which are the primary cognitive enterprises in making diagnoses.

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For the most part, making a diagnosis (or at least a tentative diagnosis) is required in order to predict the results of testing and treatment. But as we all know, neither belief nor knowledge is an all-or-nothing phenomenon. We have degrees of belief and, consequently, incomplete knowledge. Thus, in the end, we need to weigh the degree of certainty against the possible consequences of being wrong—a position espoused by John Maynard Keynes amongst many others. This balance supports the use of subjective probability and its dependence on Bayes’ theorem – a topic about which we will have much more to say later. Furthermore, some knowledge is not based on belief, nor can it be justified. For example, I know I am hungry. There is no belief here, nor does it need to be justified to be true. There appear to be lots of types of knowledge; some are based on beliefs, some on sensations, some on testimony, some are independent of the observer, some are dependent on the observer, some are justifiable and, of course, some are not. Borrowing from medicine, where it is said that if there are a dozen different operations for a condition, then none of them is satisfactory, we can say that all of these schools of thought about knowledge have their virtues, but none are entirely satisfactory. What follows is a compilation of the types of inferential reasoning typically applied in the care of patients and other cognitive activity. The inferential process in the conduct of clinical care is one of the most demanding in all human endeavors, largely because of the complexity of the human body and the relatively limited factual input. Think of it this way: We have five senses and use only vision, touch and hearing for the most part in caring for patients. We have the mental capacity to deal with up to about 7 concepts at any one time, and yet, we are faced with an organism so complex that the number of bacteria in the gut exceeds the number of cells in our body and the number of stars in the Milky Way. It is a miracle that we can figure out anything about our patients, given their complexity and our limited cognitive resources. We do have multiple tools at our disposal, but none are particularly powerful, and we need to utilize all of them at one time or another. We will review all of these approaches in the chapters that follow. In some cases, this will require a historical approach, but for the most part, we will review types of reasoning in terms of their strengths and weaknesses, and we will also illustrate how they are conventionally utilized. Inferential reasoning is critical to clinical medicine and is epitomized by the diagnostic process. Only recently, with the attention to errors and biases, has the whole process become an important area of research. However, the process of

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reasoning has been the province of philosophers since the Greeks, and there is a huge body of thought in the field of epistemology. Unfortunately, there is little attention to this field in medical training in spite of its obvious relevance. This book explores the breadth of the issues in a survey format that will introduce the reader to some of the most important areas, along with references that permit further investigation. Each aspect is introduced but not covered in detail, and there is no claim that the extent of the discussion encompasses all of the relevant issues. However, it does provide a useful introduction. In the end, the best analogy might be that “human inference is primarily analog, whereas computers are decidedly digital.” Therefore, humans can’t compete successfully against computers in digital inference, but by using many of the techniques of inference (which we will discuss), they, at least in medicine, frequently (but not always) out-compete a computer. Before we move on, let me say this: If this discussion has been a bit overwhelming thus far, don’t be discouraged, because the following chapters will expand, unpack and clarify all the issues we have dealt with in the Introduction section. Hopefully, you will find that they do so in a way that you are more comfortable with.

CHAPTER 1 COMMON SENSE

GE Moore Common sense refers to practical judgement about everyday matters that is shared by most, if not all individuals. We are not using the term in reference to aesthetic judgement, political persuasion (e.g., Thomas Paine’s Common Sense) or theological doctrine here. Rather, we are concerned with statements made by ordinary people which, for the most part, are accepted by the community. This notion, like so many others, dates back to the Greeks where again, Aristotle and Plato formed a contrast. Aristotle referred to common sense as the aggregate impact of the five senses that are shared by all people and, to some extent, by many animals. Plato, however, had a more modern interpretation, perceiving the senses as a data source, and statements as reflecting cognitive activity. Common sense stands in contrast to rational thought, where conclusions are generated by inference from other data. This is not to say that common sense statements cannot be defended, but that they are not generated by rational thought and don’t conventionally need to be defended. For example, most people will retreat from a snarling dog with the understanding that they may get bitten. In fact, they might generalize this concept and apply the same reaction to any snarling animal. Obviously, this can be defended rationally by the observation that snarling dogs may bite, but the defense is conventionally unnecessary precisely because most people share the same

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perception and judgement. Hence, it is common knowledge. Furthermore, there is no training or instruction necessary to achieve this understanding, as although young children may not share this perception, they will acquire it though experience and observation. Thus, when Dr Johnson says, “I refute him thus by kicking a rock,” which is a commonsense opposition to Bishop Berkeley’s claim that all entities are abstractions, he is refuting idealism, which claims that only abstract ideals of cognitive entities exist. Idealism is relatively in line with Plato’s position. Likewise, when GE Moore declared “here is one hand,” he was rejecting skepticism in favor of common sense. Common sense, in effect, is an antidote to Berkeley’s idealism and Descartes’ skepticism. Common sense is, in effect, heuristic (a shortcut) but one that is widely - if not universally - shared. Of course, any heuristic is a potential source of bias, so many philosophers decried this cognitive activity in favor of rational thought. Descartes in particular claimed that the only thing he was sure of is that he existed because of his ability to doubt. Most people, including GE Moore, the whole school of British empiricists and ordinary language philosophers, and most other people, accept common sense as a valid form of reasoning. In today’s world, common sense could be viewed as type one thinking (fast) and rational thought as type two (slow) thinking (we will explain this in Chapter 33: Dual Process Theory). As a general rule, in contrast to rationalists, empiricists like Francis Bacon and, to some extent, David Hume, as well as pragmatists such as C.S. Pierce and modern philosophers such as G.E. Moore, have defended common sense. In fact, some believe that common sense observations were the starting point for most rational inquiry, even in very abstract disciplines like mathematics. Here, we will confine ourselves to defining common sense as inferences about observations that are widely or even universally held, in contrast to those that need supporting data, such as scientific claims. The snarling dog example might be contrasted with an inference that all green vegetable matter is food or that all four-legged creatures are cows, which are common erroneous inferences, made by children. It is apparent from this discussion that these generalizations are acquired through experience, both direct and through teaching. However, there are also limitations including biases and heuristics, which we will cover in Chapter 33. Some commonsense declarations are specific to clinical medicine. A good example is the question that is often posed to a physician or a nurse as to whether a patient looks sick or ill. The context to this question may be anything from a routine outpatient encounter to an emergency room situation, arising from the dilemma that patients may present with the same

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or similar complaints, but with vastly different severity of illness. Chest pain, abdominal pain, headache or any one of innumerable issues can result from situations that range from trivial to life-threatening. The question seeks to ascertain the observer’s estimate of illness severity. The answer could be justified by citing vital signs, pallor, diaphoresis, writhing, etc., but often, the aggregate assessment is all that is necessary to convey the urgency of the situation. While it is prized by physicians and other medical professionals, most would actually agree with Voltaire’s assertion that ‘common sense is not common.’ Many observers think that common sense is the starting place for all philosophical discussion. There are certain concepts we share that are taken for granted as a basis for facilitating further discussion. Examples abound but amongst them is the notion that time moves forward; it doesn’t stand still or move backward. If we can’t agree on this, then most ensuing inferences won’t get very far. That being said, linear and forward-moving time appears to be a physical reality, but it is a very controversial one that not all cultures embrace. Indeed, the ancient Egyptians had two types of time. One was cyclical, returning to the same place every period, and was probably based on the seasons or the flooding of the Nile. The other was a single transition from the land of the living to the land of the dead, and was eternal and unchanging. In neither case did time move forward, and it certainly did not move linearly. In fact, in some versions of General Relativity, time does not move forward or linearly either, as Kurt Godel found when solving Einstein’s equations (we will explore this in a later chapter). Another shared concept is that two material objects cannot occupy the same space at the same time. This is one of many aspects of quantum mechanics that makes it difficult to conceptualize, since it doesn’t seem to recognize this principle. It is said that the fundamental problem with common sense is that is far from common, which means that lots of individuals fail to recognize the obvious. Nonetheless, for rational discourse to proceed, we need to agree on a huge volume of information that constitutes our world and how we perceive it. We could not have a productive conversation if my assumption about you entailed you changing your identity as we are speaking. The Aristotelean concept of common sense was the five senses we share with other human beings, but Plato elevated it to a shared conceptual framework similar to how we think of common sense today. Descartes gave the most modern version when he spoke of common sense as sound judgement. Deviations from common sense in the sensory realm are often called hallucinations and can be induced in normal individuals

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under certain sensory stimuli, such as images of puddles on hot roads or dream states. These can be induced by certain mind-altering drugs but of course, these are exceptions and recognized as deviation from accepted cognitive input. Hallucination has a more modern connotation when artificial intelligence programs fabricate answers to questions. Interestingly, artificial intelligence hallucinations are actually confabulations since they are imaginary reasoning not imaginary visual images. In fact, in typical discourse, almost everything that is, to use a Wittgenstein phrase (actually, he said “the world is everything that is the case”) is in the realm of common sense, and what is discussed is a very tiny bit of information that represents the summit of a mountain of common sense. We simply acquire common sense as we grow up, and we achieve an ‘adult’ level of conception of the world through experience, which we gain longitudinally as we develop into an adult. When we speak of common sense, it means shared information and knowledge with which all of us are endowed, whereas beliefs represent a whole different set of information that is, by definition, not agreed upon. Sometimes, beliefs are so widespread in a given society that they are treated as though they are common knowledge, so radical restructuring of a belief system can occur with new knowledge. This is commonly referred to as a paradigm shift. The belief system of Newtonian physics was overthrown by Einstein’s revelations about time and space. What had been common sense now became an outdated belief system. So, common sense is not a static, rigidly delimited set of knowledge and cognitive processes, but is something that operates at a given time within a given society. That said, it is the basis for all our discussion as well as being at the root of all philosophical discussion, as it represents an assumption about shared information and shared reasoning. Descartes and Kant go one step further, hypothesizing that innate knowledge takes the form of a priori analytical and synthetic knowledge that all human beings have. This forms the basis for cognitive coherence, which allows people to share conceptual frameworks and, thus, to facilitate discussion. However, developmental psychology would be at odds with this, citing stages of cognitive development as a consequence of continued sensory input. Proponents of this would cite the impaired cognitive development of sensory-deprived children as support for this hypothesis. Indeed, the question of whether there is such a thing as a priori knowledge is still hotly debated. One argument in favor is that there does not appear to be any empirical data that could be generated that would disprove 1+1=2. On the other side is the claim that mathematical truths such as this one have been acquired through teaching and experience.

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So, common sense is the start of all philosophical discussion which is usually framed as a question. What is life? What is good? What is evil? And so on. To proceed, one requires a vast array of agreed-upon information and inferential processes. For example, to discuss life, we first need to agree that we are speaking of entities in our realm, not of hypothetical beings from a different imaginary world. We would also need to agree that certain processes are characteristic of living beings, such as their interactions with the world around them, which distinguish them from inanimate objects like rocks. Then, of course, we would need to agree on what interaction meant and so on. Common sense plays another role in philosophy: that of checking our inferences. If we got to the point of concluding that fire is alive since it interacts with its surroundings by creating heat, we would need to rethink our criteria for being alive, as fire would be a common-sense example of something that isn’t alive. Positions that philosophers have held in the past that fail the commonsense criterion (which epidemiologists call ‘face validity’) include that time doesn’t exist, the world is made of water, or that all existence is fire, water and earth. The rise of pragmatism and ordinary language philosophy has elevated the role of common sense as a shared cognitive framework. In fact, C.S. Pierce called pragmatism ‘Critical Common-Sensuism’ and G.E. Moore wrote an essay entitled ‘A Defense of Common Sense,’ which exemplified his approach to philosophy. Moore would argue that if a philosophical claim did not stand the commonsense test, then it should be discarded. The question of where common sense comes from is hotly debated. Clearly, experience plays a role – the repeated example of dogs' results in the general assumption that all dogs have four legs, but that all 4-legged creatures are not dogs. Experience cannot be the whole story, though, since one’s cognitive capacity needs to be able to accept, integrate and process this information. To what extent the structure of the brain defines these processes is a current subject of investigation. In defense of the limitations of our conceptualizations based on our senses and/or cognitive capacities, is the obvious differences in world view of non-human animals who depend on smell, such as dogs. On the one hand, this argument is supported by structuralists like Chomsky, who think we are limited by our senses and our capacity to process sensory data. On the other hand, others are impressed with our neural plasticity, which can adapt to varying circumstances in order to expand and contract our inferential processes. They cite cases in which normal neurological function is absent and unusual abilities surface, such as perfect pitch, photographic memory, or mathematical savants. Common

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sense is not only used to refute obvious fallacies but it also used to acquire and generate evidential information to use in arguments about inferences. Three-legged dogs and black swans are often cited as examples that are used to point out fallacies in our generalizations. Common sense is crucial to our day-to-day activities. Imagine how hard it would be to care for a patient if we could not agree on the fundamentals. Breathing, or at least respiration, is necessary to sustain life. A certain level of perfusion, usually signified by a blood pressure, is required to oxygenate tissues and so on. We need a vast amount of basic anatomy, physiology and biochemistry as a background for everything we do.

CHAPTER 2 INTUITION

Kant While common sense is an inference (albeit a simple, shared and widely accepted one), intuition, as it is conventionally thought of, is in a sense the opposite, since it is knowledge that is achieved (not acquired) privately. Of course, it could be shared after the fact, but it is necessarily not held by any other individual. For example, the sensation of pain may be considered intuition, since it doesn’t require inference and yet, it is knowledge. As such, rationalists have trouble with the notion of intuition, since they consider all knowledge as being a product of rational thought. Yet, there appears to be a whole body of knowledge that isn’t dependent on at least explicit rational thought. Colors, sensations, visual data, and auditory phenomena are examples of intuitions, although some observers would also include hunches which are in effect predictions and, as such, are inferences rather than intuitions. Is an intuition then different from an inference, and do we then have two bodies of information – one acquired by inference, the other acquired by intuition? Linguistic philosophers would argue that the distinction is invalid since one cannot have an intuition unless it can be formulated in language. This seems implausible since prelinguistic children and animals appear to have intuitions, whether they can formulate them in words or not. Likewise, the claim that intuitions are justified true beliefs that cannot be supported rationally (as claimed by Ryle and Wittgenstein) is

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vague to the point of being useless. The example of knowing that something is a dog by looking at it and not being able to defend the inference, is completely dependent on the observer’s intelligence and knowledge base. This seems to be quite a different matter to claiming something is white, loud or foul smelling. While both types of claims may be difficult to defend, in the first case, the ability to tell whether something is a dog is dependent on the observer’s knowledge or intelligence; whereas the other inferences have little or nothing to do with intelligence or knowledge, but just depend on personal sensory input. If this is the case, then what about the claim that a patient looks sick or ill? Is this an intuition? By this analysis, it is not. The claim that a patient looks sick is potentially defendable with a number of observations about said patient, whereas the claim that I am in pain or that an object is red, is not conventionally defensible. However, the former is readily appreciated by other observers and, if correct, could be a matter of common sense. There are schools of philosophy that grant the notion of intuition but still claim that it is an unconscious inference, such as phenomenalism. Perhaps this is true in the sense of pattern recognition as a kind of inference, even if it is a shortcut that has presumably been generated by repeated episodes of the association. However, this is hard to reconcile with the claim of pain, which doesn’t appear to be the consequence of repeated episodes of conditioning an association. In fact, it doesn’t appear to be an inference at all - just an expression of the state of the observer, rather like the claim of being hot or cold. These products of sensory input are undoubtably different from saying a patient looks sick or an animal is a dog. We can conclude from this discussion that claims that are potentially defendable are not intuitions, at least as they are conventionally understood. So, what is the point of this discussion? First, while most knowledge and claims of knowledge are the products of inference, at least a small number of valid claims are private, not defendable, and yet extremely useful. We need to know whether we are hot, cold, hungry or sleepy, because this is what keeps us alive. Furthermore, they are critical in a clinical encounter, since patients themselves are the only source of this information, and its validity strongly influences the management of their illness. Much of what we get in a patient’s history is data of this kind. Where does it hurt? How long have you had the pain? Is it localized or more diffuse? And so on. By our definition, these are intuitions (but not hunches) and lead us to make inferences about the illness at hand. The sense of self is clearly an intuition, regardless of the mental gymnastics Descartes went through to derive this notion. If you remember, he said ‘I can doubt everything except my ability

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to doubt, and therefore, that is the one thing I can be sure of.’ Certainly, when we ask a patient their name, they don’t go through the same process. The knowledge of who, where, and when we are is a series of intuitions in the sense that it is knowledge that cannot be defended by a rational inference, no matter what Descartes said. Why, then, is a child unable to express these notions? For the same reason an animal cannot. They simply don’t know the language that they would need in order to express them. Only after instruction can a child associate the word ‘pain’ with the sensation that previously generated a non-linguistic cry, just as a dog in pain will bark. Unfortunately, we appear not to be able to teach a dog language, but children learn these linguistic expressions over time. In this sense, the intuition is always there, but the language to express it comes later. This version of intuition is similar to Kant and Russell’s idea that intuition is an immediate appreciation of an object or, in Russell’s notion, appreciation of objects and concepts. The problem of not being able to express the intuition until language is acquired does limit the ability to communicate this knowledge, but it doesn’t exclude it. Dogs and children that limp are communicating discomfort as clearly as they would if they spoke. In conclusion, intuitions are not hunches and are different from common sense. Rather, they are a form of knowledge which may be correct or fallacious and can generally be communicated to others more or less accurately, depending on the intuition and the verbal skill of the observer. They are a body of knowledge that is not arrived at through inference, and can be useful in medical contexts, particularly as data for diagnostic and therapeutic management. Cognitive psychologists have studied intuition from expert observers in particular. Studies involving chess experts and experts in other fields such as firefighting have suggested that the primary mechanism of intuition in these individuals comes from pattern recognition from stored memories of similar situations. The easiest of these to understand is the chess expert that recognizes intuitively the similarity of the current problem to many similar situations they have encountered previously. From this, they then form a basis for a plan of action. In the framework of Kahneman (Chapter 33), this is a System 1 thought process; i.e., an associative inference. Sometimes, this is supplemented by a System 2 approach that tests the conclusions of a System 1 inference against the available data, either confirming or refuting it.

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Some philosophers have equated intuitions to opinions, while others have stated they are beliefs. In neither case is it convincing that intuitions can be reduced to these processes. Opinion is commonly used for circumstances in which there are alternatives and one must choose from one of two or more options, generally based on a weighing of evidence (even if the evidence is incomplete or biased). Intuitions, however, are quite different. They spell out a prediction based on associative thinking (System 1). For example, if pain is the intuition then the prediction is that you sensed discomfort whereas a belief could be based on a report that you read. The prediction may be in the future or the past. Intuitions are not simply beliefs, since one can have a belief about anything but to have an intuition implies a prediction about what generated that intuition. For example, you can have a belief about aliens but if you have an intuition about them, it implies some form of alien activity. Likewise, the concept of an intuition as being a disposition to believe gets us to the point of willingness to have an intuition, but it doesn’t get us to actually having an intuition. Of course, intuitions may be taken as evidence, but that is a separate consideration. Philosophers have attempted to study intuition in an empirical fashion by presenting scenarios to subjects in order to get responses and, thus, test theories about intuitions. There are concerns about these survey methods, though, including framing, statistical reliability, reproducibility, and so on. Intuition is a markedly different concept in the philosophy of mathematics. Developed by the Dutch mathematician LEJ Brouwer, it is based on the notion that mathematics is a mental construct and belongs in the realm of mathematical constructivism. Brouwer takes as a starting point that only inferences that can be proven are true. Thus, the starting point is no assumptions, no axioms. This isn’t entirely true, since proof theory requires assumptions, but axiomatic approaches to mathematics and logic like Peano, Frege, Russell and early Wittgenstein are discarded along with treasured and hallowed principles of reasoning, such as the law of the excluded middle (PV-P), which is not only not accepted but actually false in intuitionism. In the sense of starting from a more restrictive cognitive apparatus (fewer assumptions), intuitionism is more rigorous than classical mathematics. Intuitionism makes no claims that mathematics reflects objective reality; just that it is an internally consistent framework that reflects the cognitive activity of the human mind. Thus, truth in intuitionism equals provability, whereas falseness equals refutability. Intuitionism would support the notion of mathematics as cognitive modeling rather than a description of the physical world. Intuitionism in mathematics is one of a group of conceptual frameworks called constructivism. While intuitionist approaches are interesting, the field is in direct conflict with classical mathematics and logic,

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which is the predominant paradigm at the present. In the end, it is amazing how far one can get with an approach that eschews many assumptions of mathematics and logic. However, it is not quite how most people interpret the word ‘intuition’, but it is somewhat similar to the idea that concepts can arise without evidence. In a sense, it is a more structural approach to cognition that emphasizes the role of brain structure over experiential acquisition of knowledge. Intuitionism sits in contrast to classical logic, which determines whether a statement is true or false. In intuitionism, a statement is provable or refutable. There is no existential truth or falsehood, which stands in contrast to the Platonic interpretation of mathematics implying the existence of mathematical objects. It also stands in contrast to mathematics as a language devoid of meaning, while agreeing that when expressed as a language, it is useful to communicate between mathematicians and with the public. Intuitionist interpretation does address the peculiar mental processes that result in mathematical solutions, but it leaves unexplained why so much of the world we live in is precisely expressed in mathematical terms. Its major conflict with classical mathematics (besides conceptualizing truth as provability and falsehood as refutability) is in its rejection of the law of the excluded middle. (P V -P), which is an axiom in classical logic, but is rejected in intuitionist mathematics as unproveable. Let us summarize. If common sense is the basis for much of what we do, then what is intuition? There are numerous interpretations of intuition. Some commonplace notions are suspicions, private knowledge or cognitive processes that are pre-evidential (a hunch). It seems peculiar that one can have knowledge without conscious inference, but that appears to be what intuition is. The immediate apprehension of a visual, auditory or olfactory sensation seems to fall into this category, but the familiarity of the item may lead to a shortcut not unlike those we typically use on our computers. Rationalists like Descartes rejected the notion that you can have noninferential knowledge, so they either deny intuition exists or recast it as condensed inference. It is not that you can’t question intuitions, but that the process is clearly inferential and a secondary event. Some behavioralists claim that formulating intuitions in a language is a prerequisite, but this is obviously incorrect, since we can intuit smells which, even in retrospect, we cannot describe in words. Both Kant and Russell agreed with the nonlinguistic explanation, as did the phenomenalists. The same sort of discussion is relevant to the intuitive understanding of concepts.

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Going forward, we will use common sense as a starting point, a test of our conclusions and a mechanism for acquiring information used to address questions that arise in our discussions. The use of common sense was also paramount in the natural language school of philosophy, which we will encounter later. We will also use intuition as non-inferential sources of information, which may play a role in both common sense and rational thought.

CHAPTER 3 ABSTRACTION

John Locke Abstraction in a cognitive context is the extraction of a particular property of sensory input, reflecting a particular aspect that is subsequently available to be used in an inference. It is very tightly associated with induction, since an inductive inference is the generalization of an observation. For example, by observing a ball bounce, one could then generalize that spherical objects tend to behave this way. Of course, while this is true for balls, balloons and ball bearings, it is not true for spherical drops of liquid, or even the spherical drop of cake batter that landed on my kitchen floor this morning. The point is not the accuracy of the generalization; it is the role of abstraction in the process. Children and animals perform the same process as is evidenced by a child calling all four-legged creatures dogs until the claim is corrected. Likewise, animals, especially dogs and cats, will associate certain sounds with the arrival of members of the family. Generalization is an almost automatic process that facilitates inferences about the world around us. In order to generalize, we need to abstract the property of the input to be generalized upon. Abstraction is also closely linked to language, since language permits naming. Naming is important in generalizations but not absolutely necessary. However, the flip side of that is that language does require abstraction, or else we would have nothing to talk about. Likewise, abstraction is necessary to develop new concepts. In essence, a concept is a

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generalization about an observation; thus, concept development is a form of inductive inference. The mental process that results in abstraction is still somewhat mysterious and different observers of the same sensory input will abstract differently. For example, a light in the night sky could be a star, a planet, a satellite, or an airplane. How we interpret the sensory input results in different abstractions. Abstraction is used in slightly different contexts in different disciplines, but in some instances, it is confused with induction. Induction is a two-step process – first comes abstraction, then generalization. As above, seeing a spherical object bounce results in the abstraction that spherical objects have the capacity to bounce, but induction would entail the application of this concept to other spherical objects – either correctly or incorrectly.

CHAPTER 4 NATURAL, ARTIFICIAL AND ORDINARY LANGUAGE

JL Austin Natural language takes the form of verbal expressions that humans developed to facilitate communication and to express ideas. It differs from constructed languages in grammar and syntax, semantics (meaning), and the lexicon of elements (words). Natural languages are complex and the rules that govern them lie within the province of linguistics. While some observers have linked the structure of natural language to the cognitive capabilities of the human brain, more recently, the cognitive capacity of the human brain has been considered to exceed language, and we know that many thought processes are not in fact performed by converting sensory input to language. However, language is the primary means to express and communicate thought; thus, it merits intense investigation. Some study has been conducted by analyzing natural language but more recently, the necessity of duplicating natural language by computers has in a sense reverse-engineered the problem. Philosophically, the emblematic scenario was described by John Searle in the Chinese Room Argument, in which a machine using a set of rules could decrypt a statement in Chinese and then express it in English. The question is this: Would the observer outside of the room think that the function was

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carried out by a human or a machine? This is an elaboration of the famous Turing test, which ponders the notion that if a human observer could not distinguish between a human response and a machine response, then the machine was, in effect, thinking in order to produce it. Although it satisfies the Turing test, the Chinese room machine doesn’t understand anything. However, to the observer outside the room the participant looks knowledgeable. More recently, with ChatGPT 4, the ability to analyze and respond to natural language queries has represented a quantum leap forward in Natural Language Processing (NLP) using artificial intelligence and machine learning, which easily satisfies the Turing Test. The original computer decision algorithms were primitive and quickly replaced by statistical approaches, and these in turn have been more recently superseded by neural networks. The consequence is that when inquiries are handled by automated devices, such as calling for advice or to schedule an appointment, the responses will duplicate and, in some circumstances, exceed what a human in the same situation could achieve. The potential for AI in medicine is extensive; for example, an electronic medical record that can scour input for meaningful answers to queries. A more everyday case is the speech-totext-process in common dictation (note taking). Dragon (proprietary), for example, does a remarkable job of recognizing words from a huge vocabulary and coping with different accents, types of elocution, tones and volume. The reverse, text-to-speech, can also be found in programs that are designed for the visually impaired. Language translation programs that allow on-the-fly translation of spoken text are used in Google Translate (proprietary) and similar programs. All in all, we are on the cusp of an iteration of machine intelligence that will mimic and, in many cases, exceed human intelligence. Considering the complexity and variable ambiguity of natural language, the field has made spectacular advances. Thus, we have Turing to thank for the definition of artificial intelligence, but also for solving the Enigma machine, which was instrumental in the allied victory in World War ll over the Nazis. Finally, of course, he designed the machine that acted as the forerunner of the computer. Not a bad resume for an Olympic-level runner. Natural language is sometimes referred to as ordinary language but in philosophy, ordinary language refers to a school of thought that originated at Cambridge University in the early 20th century. Ordinary language philosophy arose as a reaction to the failure of analytical philosophy to give a logical foundation to both mathematics and philosophy. Russell’s program of rooting all of mathematics in set theory (Principia

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Mathematica) came to the same unhappy end that he himself engineered for Frege’s program of rooting arithmetic in logic. Ultimately, it falls foul of Russell’s paradox, which shows that certain sets can only be members of themselves if they are also not members of themselves (see The Barber example). Russell’s answer was a theory of types, which did not solve the problem, but kicked it down the road. Likewise, Wittgenstein’s early work ‘Tractatus Logico-Philosophicus,’ which he thought solved all of philosophy’s problems through the picture theory of meaning (and caused him to retire from philosophy and become an unsuccessful school teacher) was a failure as well. After all, we use other senses beyond the visual to establish meaning. Sounds, smells and tactile sensations all have meaning and are used in cognitive inference. Eventually, convinced that the Tractatus was incorrect, Wittgenstein returned to Cambridge and championed the notion that all philosophical problems arise from misunderstandings of ordinary or natural language. In a certain sense, this has some traction since natural language has so much ambiguity that problems do arise from misinterpretations, but equally, some problems arise regardless of the ambiguities of natural language. Examples abound and include ‘what is knowledge?’, ‘what do numbers represent?’, ‘what is truth?’, and a whole host of others. Analytical philosophy came crashing down in the early 1900s, falling victim to the paradoxes of self-reference. This project of Frege, Russell, and early Wittgenstein to root all of philosophy, logic, mathematics and, by, extension all of science in a formal language, ended well before the contribution of Gödel's incompleteness theorem, which functioned as the coup de grace. That said, Russell never abandoned the quest and, in some sense, the analytical tradition lived on in the logical positivist movement which it segued. We will have more to say about the logical positivist approach in later sections. As mentioned above, Wittgenstein was a proponent of the analytical approach and, satisfied that he had answered all of the pertinent questions of philosophy with his Tractatus, retired from philosophy to teach elementary school and later, become a gardener. Eventually, awoken from his cognitive slumber by the reigning monarchs of British philosophy, he returned to establish the school of ordinary language philosophy which had as its premise the notion that all significant philosophical problems were rooted in the ambiguity of ordinary language and could be solved by paying close attention to how words are used in common parlance. In this sense, the ordinary language school was a paradigm shift from the analytical approach. This group, which was originally centered at Cambridge University, included Wittgenstein, Norman Malcolm, Fredrich Waismann and others, all of whom explored what Wittgenstein termed ‘the language game.’ The

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center later moved to Oxford University where Gilbert Ryle, J.L. Austin, Paul Grice, Geoffrey Warnock and P.F. Strawson were major contributors. The basic idea is that philosophical problems arise from attempts to interpret commonplace concepts like truth as specific entities, rather than accepting that there is a range of usage that defines a family of related concepts. In this way, ordinary language philosophy is a type of linguistic philosophy and is clearly in opposition to analytical philosophy. The crux of the issue is whether by defining the range of usage of a term like ‘truth,’ we then obliterate the philosophical problems associated with the concept. That is for you to decide. There is an interesting parallel between the evolution of philosophical thought and the development of NLP (Natural Language Philosophy) which is a major goal of artificial intelligence. Early on, language recognition and generating programs were strictly rule-based, but this cumbersome methodology was limited and inflexible. Every advance needed additional rules that had to be programed into the software. Later, more general rulebased approaches that evolved from algorithmic language analysis (think Chomsky) were more general in concept, but still relatively inflexible. Modern approaches use observed linguistic patterns as a guide through neural net software. This technology adapts to ongoing usage, which facilitates machine learning and is teachable. In this sense, natural language preserves meaning, reflecting Wittgenstein’s notion of family resemblance. Thus, a formal analytical approach has given way to an ordinary, languageflexible approach, and this now powers revolutionary AI programs like Chat GPT. In a more general sense, though, philosophy frequently presages developments in other fields; especially mathematics, physics and computer development. It is no accident that early pioneers in computer science were philosophers like Alan Turing and John Von Neumann.

CHAPTER 5 DEDUCTION AND THE EVOLUTION OF LOGIC

Aristotle Contemplating the Bust of Homer When people think about analytical reasoning, they are generally referring to deductive reasoning. Deductive logic dates back thousands of years to the Greeks (primarily Aristotle) and their focus on axioms or postulates (assumptions) and rules of inference. This form of reasoning is conventionally known as formal logic and is divided into two categories. Propositional logic is the prototypical syllogism, which may be viewed as an “if, then” statement: P or Q -P Therefore Q (Where P and Q are statements and -P is the negation of P).

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Unfortunately, people’s eyes tend to glaze over when encountering symbolism, either in logic or in mathematics. Part of the reason is that it requires a great deal of mental energy to work through a symbolized argument or proof (arguments and proofs are one and the same). I will try to minimize the necessity of this, while still being true to the discipline. Another problem is the variation in symbolism and, when possible, I will use an English word instead of a symbol. For example, I will use the word “and” instead of “.” and “or” instead of “V”. Another problem with notation is that it comes with special terms. For example, “or” is called a disjunction and “and” is called a conjunction, whereas the arrow in an “if, then” statement is called implication. However, when quantifiers are introduced, it is designated predicate (firstorder) logic as follows: All men are mortal. Socrates is a man. Therefore, Socrates is mortal. This syllogism is attributed to Aristotle, whose logic ruled the field throughout the Middle Ages, and is an example of a valid argument or valid inference. A valid argument has a certain form defined by its truth function – made popular by Ludwig Wittgenstein. Valid arguments can lead to true conclusions if the premises are true, but not if they are false. Furthermore, a true conclusion can be generated by an argument that is not valid. Validity is a matter of the form of the argument, not its content. A sound argument is a valid argument with true premises and, therefore, true conclusions. Some syllogisms are true regardless of their content. For example: P or Q -P Therefore Q But some syllogisms are dependent on content, such as the Socrates one shown above. These syllogisms are content dependent. Thus, the truth of many if-then statements is dependent on their content as well as their form. Special cases where content is irrelevant include tautologies, such are P or -P (law of the excluded middle), or the opposite, which is called the law of

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non-contradictions (i.e., - (P and -P)). We will deal with tautologies in more depth in a later section. Modus Ponens If P then Q P Therefore Q Modus Tollens If P then Q Not Q Therefore Not P Disjunctive Syllogism Either P or Q Not Q Therefore P Or Either P or Q Not P Therefore Q The truth value of a statement is the semantic definition of truth, and the obedience to the rules of logic is the syntactical definition of truth. In propositional logic, the semantic and syntactical definitions of truth are equivalent. The truth value of propositional statements can also be determined by an algorithmic process (or a computer program) using truth tables. This is known as decidability. Propositional logic is decidable; however, the predicate calculus is undecidable. This result of Alonzo Church (the logician) and AM Turing (the logician, mathematician and computer scientist of Enigma fame) was shown in 1936. Thus, when you introduce quantifiers there is no algorithmic (or computer programable) solution to the truth value of statements. The propositional logic is also complete, which means every well-formed formula in propositional logic is either true or false. In contrast, the predicate logic is semantically complete but not syntactically complete. If you don’t understand this, don’t worry. It isn’t necessary for this argument except to show that once one introduces quantifiers, the ability to establish the truth of a statement is compromised. Even more difficult to understand is the

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proposition that Saul Kripke proved, which states that modal propositional logic (the logic of possibility and necessity) is complete and decidable (when he was in High School!!) We will have more to say about this later. Contingent propositions are dependent on content like the Socrates syllogism. A word of caution, though. Some syllogisms appear to be valid, but in reality, are fallacies. For example, if P implies Q and Q is true to conclude P is an affirmation of the consequent and is a fallacy. By contrast, if P implies Q and Q is false, then P must be false (modus tollens). Note that even though affirming the consequent is a fallacy, P could still be true, thereby reinforcing the distinction between a valid argument and the truth of the content. An argument is valid if and only if its premises imply its conclusions in the form of a syllogism. An argument is sound if it is valid and the premises are correct therefore the conclusion is true. The paradoxes of material implication emphasize the difference between a content-dependent true statement and a valid inference If Q is true, then P implies Q is a valid inference, but just because I like coffee, it makes no sense to say, “it is raining outside (when it is sunny); therefore, I like coffee.” In short, even though this is a valid inference, it makes no sense. In fact, in an implication as long as the consequent is true it doesn’t matter if the antecedent is true or false – it is still a valid inference. Thus some valid arguments appear to be nonsensical. Deductions in propositional and predicate logic can result from a set of rules (axioms similar to mathematics, especially Euclidian geometry) or from the natural procedures arising from the rules of inference alone. In either case, the intent is to generate valid conclusions from a set of premises, keeping in mind that a valid inference is only truth-preserving if the premise is true; i.e., a sound argument. Two forms of Invalid Arguments; i.e., fallacies: Denying the Antecedent P implies Q Not P Therefore Not Q Affirming the Consequent P implies Q Q Therefore P

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Let’s try an argument that outlines a current issue: There are fewer people available for the workforce. When there are fewer workers available, competition to hire them increases. When competition for workers increases, salaries go up. When salaries go up, companies need to increase prices to maintain profits. When prices go up, there is inflation. This is a valid argument. However, if you reversed the fourth statement as follows: When prices increase, salaries go up. Then, this is (unfortunately) not true. How do we get these rules in the first place? One option is to establish some baseline assumptions concerning the rules. This is known as axiomatization. There is an ongoing argument about whether axiomatization is either necessary or even useful. Russell and Whitehead thought it was; Wittgenstein did not. Variants of syllogisms are found in Indian and Arabic philosophy but not in Chinese, which was more focused on personal enlightenment and codes of behavior. The Arabic philosophers were the first to tightly fuse logic with medicine, starting with Avicenna. There was a relative paucity of progress in logic in the Middle Ages largely because of the dependence on Aristotle, but there were exceptions, such as William of Ockham (Ockham’s Razor). Many advances from Aristotelian logic were made after the Middle Ages. Key contributions include Leibnitz’s observation that syllogisms resemble arithmetic statements and thus could be expressed in abstract terms. This might have been influenced by Ramon Llull, whose complex epistemology was symbolic, correlative and based in part on the alphabet. For example, the classic syllogism “All men are mortal. Socrates is a man; therefore Socrates is mortal” could be expressed as “All As are Bs. S is an A; therefore, S is a B.” Leibnitz also introduced the equivalence notation and an assumptionless argument form called Reductio ad Absurdum. In this argument, the assumption of the truth of an hypothesis that you want to reject

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leads to a contradiction. Reductio arguments remain important techniques in modern mathematics and in logic. Unfortunately, the results of reductio arguments can lead to proofs of almost any hypothesis, so the results of arguments using reductio need to be scrutinized carefully. In intuitionist mathematics, reductio arguments can disprove a hypothesis, but this doesn’t permit one to assume the opposite; i.e., reductio arguments can disprove a hypothesis but not prove one in intuitionist mathematics. Other contributions include De Morgan’s Formal Logic and Boole’s Mathematical Analysis of Logic, which we still use today in the form of Venn diagrams. Thereafter, there was a turn away from logic in any form with the British empiricist movement, which was overtly anti-logical and, by extension, anti-mathematical. Starting with Hamilton in Scotland, there was a resurgence of interest in mathematical logic, spurred on by his introduction of quantification in the form of “all” and “some,” which began to look like modern predicate logic. All these advances were on the assumption that statements were either true or false - in the vernacular, the law of the excluded middle, or bivalence. However, some statements are neither true nor false, such as predictions of future events. The classic example is “there will be a sea battle tomorrow.” While Aristotle mentioned this statement, he did not develop a clear answer. In the Middle Ages, this logic acquired a philosophical context about God’s control over events in the future. It was picked up many centuries later and developed into a field called multivalued logic that, as yet, has not captured a domain-specific use. Another offshoot originally identified by Aristotle deals with the logic of necessity, possibility, and related concepts - now called “modal logic.” Modal logic naturally extends into the arithmetical equivalent, which is the probability calculus that leads to subjective probability, including Bayes’ Theorem and its role in induction, which we will tackle later. For example, if something is possible, it is either true now, in the future, or in an alternative conceptual framework. In other words, it is either true now or in some possible world (analogous to the many worlds conception of quantum mechanics). Most of the subsequent advances were in mathematical logic, especially by the influential logician George Boole, who wrote a small pamphlet entitled “Mathematical Analysis of Logic.” He was the first to recognize that variables such as x and y stand for classes and can be analyzed algebraically. John Venn’s Venn Diagram persists today as a beautiful and economical

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visualization of Boolean logic. Although several mathematicians contributed to the budding field of mathematical logic such as Peano, Cantor, Dedekind and Hilbert, the start of the modern era of logic began with Frege, who developed the axiomatic theory of arithmetic as well as quantifiers such as “all,” “some,” or many. Lewis Carroll, an accomplished mathematician and logician (Rev Charles Dodson) made fun of Aristotelian logic in Alice in Wonderland, when Alice says, “I see nobody on the road” and the King replies “I only wish I had such eyes… to be able to see Nobody! And at such a distance too!” Frege believed that the propositions of arithmetic were analytical a priori, in contrast with Kant, who believed them to be synthetic a priori. Kant’s version of this distinction, which he expounded on in the Critique of Pure Reason, was an extension of the analysis of both Hume and Leibnitz. Simplified analytic statements are definitions or tautologies, such as “bachelors are unmarried men.” Fundamentally, the subject and predicate are the same information, since one can be substituted for the other. Meanwhile, synthetic statements contribute new knowledge like” rocks are minerals.” But what about arithmetic statements? Is 1+1 = 2 analytic or synthetic? You decide, since there is no agreement. While this is an oversimplification, it conveys the meat of the issue. I think it is fair to say, following Quine and others, that there is no hard and fast distinction between analytical and synthetic statements. John Stuart Mill (a British philosopher) believed arithmetic consisted of inductive generalizations, somewhat anticipating the intuitionist view of mathematics as an abstraction of a conceptual notion or a mental construction. Frege was analytic. His work was based on Peano’s five axioms or postulates: 1) 2) 3) 4) 5)

0 is a number The successor of any number is a number No two numbers have the same successor 0 is not the successor of any number Any class which contains 0 and which contains the successor of n whenever it contains n includes the class of numbers

When supplemented by arithmetical operations such as addition, multiplication, subtraction and division, this will generate the arithmetic of natural numbers. Frege’s other major contribution was to clarify the ambiguity in propositions depending on their context. Thus, feeling hot or cold could be a bodily sensation, an emotional state or even an observation about sensory input. Frege’s logic is called propositional calculus since it dealt with

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propositions joined by connectives such as “and” and “or” and “not.” From these, the propositional calculus emerges. Later Frege used the propositional calculus with Georg Cantor’s set theory to establish the logical foundation of arithmetic. Unfortunately for Frege, Russell pointed out a paradox that arises in Frege’s foundations of arithmetic related to sets that are members of themselves, which he later tried to solve with his theory of types. The publication of Principles of Mathematics by Bertrand Russell in 1903 represented the culmination of the logical (analytic) approach to mathematics. The view was that all mathematics deals with a small number of fundamental logical concepts and all of its propositions can be derived from a small number of logical principles. This utilized Frege’s quantifiers but clarified their meaning and created the Predicate Calculus, which was distinctly different from the non-quantified Propositional Calculus. For example, “all cows have four legs” translated to “there is nothing that is a cow and does not have four legs.” The completed formal project was published in 1910-1913 as a three-volume work entitled Principia Mathematica by Russell and Whitehead. It covers some of the same ground as Frege’s work Grundgesetze der Arthrithmetik, but uses Peano’s symbolism primarily, and Cantor’s work on set theory. A major goal of this project was to address certain paradoxes such as entities that are a member of a set that contains itself. This resolution, called The Theory of Types, did not seem to solve these self-referential problems (think of the liar paradox – all Cretans are liars, as spoken by Epimenides the Cretan (i.e., he was from the island of Crete). Another approach to the liar paradox was to declare that sentences which referred to other sentences were properly considered to be statements in a meta language (Tarski), which essentially bumped the problem upstream rather than downstream, as Russell’s solution did. The attempt by both Russel and Tarski are to isolate sentences about sentences into a separate category to as to remove the paradox. However, neither approach was successful and the problem remained. Another approach based on the axiomatic method was taken by the formalists, led by Hilbert, who sought to establish an axiomatic basis for mathematics without any notion of the relevance of the symbols to the real world. Whether this approach is applicable to natural languages like English is an open question. However, the need to use alternative conceptual frameworks like neural nets, machine language and other techniques of artificial intelligence suggests that a rigid axiomatic approach, particularly in light of Godel’s Incompletenes Theorem, is unlikely to mirror a complex natural language that is full of ambiguity and context-dependent meaning. We will describe Godel’s contribution in

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more detail in a later chapter. Another opposing system to formalism was developed by LEJ Brouwer, which rejects the axiom P V -P (the law of the excluded middle) as unproveable and, as a consequence, implies that reductio ad absurdum arguments are not valid. Godel subsequently proved that both intuitionist logic and classical propositional logic are both consistent. The logical approach was extended to additional fields beyond mathematics (like quantum mechanics) by a prominent member of the Vienna Circle of logical positivists, Rudolf Carnap. Carnap was a student of Frege’s who subsequently embraced different forms of logic in addition to classical logic, such as fuzzy logic, which permits partial truths and partial falsehoods; and modal logic, which permits emotive terms like “probably true” or “probably false.” These are members of modern logic in distinction to the classical logic of Russell and every logician before him. Logic is still an active field with branches that include mathematical logic, symbolic logic and philosophical logic. Each comes with its own goals, but they are all dependent on proof theory, which in turn is dependent on the definitions of connectives such as “and” and “or.” Much of symbolic logic lives on in the design of the function of digital computers. At the root of the computer language is machine language which is a series of on/off switches that form the basis for advanced computer languages, starting with “Basic,” which was invented by John Kemeny (a mathematician) at Dartmouth. Computer program operations are the same as symbolic logic – both use &, V, and -. If more than one value is needed, modern logic such as fuzzy logic is applied. Imagine search algorithms that require exact spelling (classical logic) versus those that will tolerate errors, like Google. Fuzzy logic tends to be much better at pattern recognition like spelling or images. Neural nets are examples of fuzzy logic machines. Unfortunately, even these expanded forms of logic are not sufficiently flexible to accommodate all of the experiential world. For example, quantum mechanics doesn’t appear to obey the rules of either classical or non-classical logic. Thus, logicians have resorted to what amounts to empirical logic, which is analogous to observational decision making, as we will encounter later. By inference then, perhaps all logic is empirical. However, our ability to understand these observational structures must imply that we are cognitively equipped to understand them; i.e., they are not so alien to us that we won’t be able to understand them. At the present, we are on the threshold of quantum computers that will be able to capture these empirical forms of logic.

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Deductive logic is generally encountered in middle school in the form of Euclidean Geometry. The Euclidian axiomatic method was largely ignored for centuries in favor of Aristotle’s methods, but had a gradual resurgence starting with Galileo, followed by Descartes and Leibnitz, and culminating in the work of Russell and Whitehead. The structure of deductive logic is relatively simple, although the derivations and proofs may be long and intricate. There are a small number of axioms that are assumed to be true and, from these many theorems, can be proven with the confidence that a well-constructed proof will result in a valid conclusion. Axiomatized Euclidean Geometry and, later, axiomatized arithmetic were major achievements in the history of mathematics. They were considered to be paradigms for all valid inferential systems because they were consistent and complete. Attempts were made to axiomatize other branches of science such as physics and chemistry with little success. But proof theory is amazingly efficient. From a few axioms, an enormous number of theorems can be proven. For example, Leibnitz’s four axioms are: a=a -(p&-p) PV-P (a=b & b=c) = (a=c) By the way, if you think of Leibnitz as an obscure philosopher, keep in mind that he invented calculus (as did Newton - and they fought over who should get credit, which is generally given to Newton, but the symbolism we use today is from Leibnitz), as well as one of the first mechanical calculators that could multiply. In mathematics the axiomatic proof procedure appeared to be successful and led to a major contribution (as I previously mentioned) by Lord Russell and Alfred North Whitehead, entitled Principia Mathematica. In logic it, led to the Tractatus Logico-Philosophicus by Ludwig Wittgenstein, which starts with the phrase “The world is all that is the case.” The meaning here is that the world represents all possible truths. Therefore, we can substitute values for the variables in the equations, and that will represent the world. It ends with “of what we cannot speak we must remain silent,” meaning that if you cannot express a thought, then it doesn’t exist (Chomsky is a direct descendent of this point of view). Wittgenstein made several important contributions, including the formalization of truth tables that can be used to establish the truth of falsehood of propositions. This played a role in the development of the proof theory that underlies logic and mathematics. He also developed a theory of language based on its ability to represent pictures.

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He thought logic, mathematics, and natural languages all had this feature in common. Later, though, he abandoned this with counter examples such as abstractionist painting or even realistic paintings such as pop art and paintings of surrealists such as Magritte, which question the interpretation of the image. In fact, one of the enduring attractions of art is its ability to engender different interpretations in different observers. But others in the British ordinary language school thought much philosophical confusion was a result of differing interpretations of language, and words in particular. Another formalist who contributed immensely to proof theory was David Hilbert, a brilliant mathematician who legacy includes a portion of Quantum Mechanics called Hilbert Spaces, which was named by John Von Neuman when he mathematically formalized the field. We will have much more to say about Von Neumann in our discussion of Decision Analysis. Hilbert’s approach to mathematical consistency was dependent on proof theory, and the proof he offered was in the form of a reductio ad absurdum argument. Several problems arose from the axiomatic approach to logic and mathematics. First, it was noted that under certain circumstances, aspects of this program resulted in infinite regressions due to the circularity of the definitions or other forms of self-reference. A charming example of this was a (possibly apocryphal) story about a public lecture that Lord Russell was giving to a garden club on the origin of the universe. One of the ladies in the audience told him he had it all wrong, because the universe was resting on the back of a giant turtle. Lord Russell cleverly responded, “but if that is the case, what is holding the turtle up?” to which the woman responded that it was “turtles all the way down.” A related problem revolves around the self-reference issue that generated many paradoxes such as “This sentence is false.” The topic of paradoxes and tautologies will be covered in much more detail in a later chapter. A form of self-reference underlies Godel’s famous incompleteness theorem, where metamathematical statements are buried within an arithmetic system, leading to inconsistencies as somewhat predicted by Lowenheim and Skolem. Kurt Godel’s brilliant mathematical exercise showed that no axiomatized system could be both complete and consistent, which was kind of analogous to Heisenberg’s Uncertainty principle. In both cases, there are limits on the certainty of some assertions. In Godel’s work, one can generate valid inferences from axioms but they will not necessarily include all valid statements in a system such as arithmetic. Conversely, if you assemble all the valid inferences in arithmetic, they lead to inconsistencies in the axioms. In Heisenberg’s Uncertainty Principle, one cannot definitively know the position and momentum of subatomic particles. In both, there are limits to

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our knowledge. In the end, axiomatized systems are best considered demonstrations of logical inference with clear-cut limitations, rather than being a complete and accurate description of the world. While the axiomatized formal system program as envisioned by Frege, Hilbert and Russell, was derailed by Godel, it continued to be utilized by the philosophic school of logical positivists in their analysis of the scientific method. In brief, they thought that the scientific method proceeded from laws or law-like statements to conclusions about the world, which were either validated by instances that conformed to the inferences, or negated them. Thus, a law was “proven” by consistency of the findings in support of its foundational laws. A simplistic example would be a law that stated, “all rocks are minerals” which is true, and conversely “not all minerals are rocks” is also true). This law would be established by observations such as iron, gold, silver, etc., but also water, hydrogen and helium as true negatives. These instances support the law and thus “verify” it. This program was very popular early in the 19th century, through the works of the members of the Vienna Circle such as Hempel, Nagel, Neurath, Schlick, and Carnap who felt that philosophy rested on science and logic (as well as mathematics). The hypothetical deductive interpretation of scientific progress which emphasized verification was one of the signatures of the Vienna Circle. However, it came to a crashing halt, not because of Godel, whose work took decades to penetrate the field (primarily because it is so mathematically challenging), but because of another philosopher, Karl Popper, whose falsification theory was instantly recognized as a formidable opponent to logical positivism. Popper’s falsification theory states that hypotheses are only tentatively embraced, and constantly subject to tests of validity that potentially invalidate it (Think of Einstein’s Theory of General Relativity tested innumerable times, most recently by the observation that a rapidly spinning massive star can drag space-time along with it). Popper did accurately distinguish real scientific theory from pseudo theories like astrology, in that real theories are able to be falsified, whereas pseudoscience cannot. But what does that make psychoanalysis – science or pseudo-science? However, as Kuhn pointed out, a single instance that contradicts a paradigm doesn’t lead to its abandonment. It requires a substantive number of false predictions as well as a competing paradigm to overthrow the prevailing theory. Quine’s response is that a theory sits in a “web of belief” and while individual contrary results can damage the web, it may be quite resilient - at least until an alternative arrives, demonstrating a greater ability to explain and predict observable phenomena. Thus, the web is anchored at its periphery in experiences, but not every aspect of it is

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bound to an empirical observation (this is somewhat analogous to clinical medicine, where therapy is anchored by randomized clinical trials but a host of other observations support the web). Because the truth of a scientific explanation cannot be ascertained in isolation in Quine’s view, the conclusion is that scientific theories differed in their social and political implications, which were the determining aspects of their acceptance. However, this would mean that the concept of HIV being a punishment from God would have the same merit as it has a viral etiology depending on the prevailing social milieu. This may hold for a few people, but not for the weight and bulk of the scientific community or the population at large. In summary, the context of a scientific explanation is important for more objective reasons than societal beliefs. Interestingly, about the same time as Popper was elaborating his theory, Sir Ronald Fischer was putting forward a very similar idea about statistical hypothesis testing, where the assumption of truth is tentative, and tests for inconsistent results may lead to rejection of the “null” hypothesis. We will have more to say about this in a later chapter. Later, Hempel and his colleagues in the Vienna Circle realized that verification is a slippery slope. Certainly, a black raven verifies the law that all ravens are black, but so does a white dove, since “not-black, not-ravens” are logically equivalent to black ravens. This seems wrong (and it certainly is). In addition, it does not distinguish between association and causation. “When it is cold, the furnace turns on” is a causal inference but the reverse, “the furnace is on; therefore, it is cold” is just an association. In fact, both verification and falsification play roles in scientific inquiry. Certainly, positive results lead to the increased robustness of a theory and negative results weaken it, but these are incremental issues that are subject to alternative explanations, hedging, and modifications of the theory. Just remember what the great sage Yogi Berra said: “In theory, there is no difference between theory and practice; however, in practice, there is.” For example, many different tests of General Relativity have taken place over the intervening century and, occasionally, potentially negative results occur; for example, observations suggesting that some entities travel faster than the speed of light. However, there has rarely been any serious question about General Relativity, except in terms of its incompatibility with Quantum Mechanics. But apart from its obvious role in the philosophy of science and in Euclidean Geometry, why should we care about this difficult and somewhat esoteric field? It turns out that these rules of logic underlie most of what we use to draw conclusions from observations. Once we have a hypothesis as an explanation for an observation, we seek to validate it

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through a deductive argument. We wonder why the dog got out of the house, why the car won’t start, why the bread is stale, or about any of the zillions of questions that arise during the course of everyday life. In every case, we reason in an if-then fashion, or an either-or fashion to generate a conclusion. Here, we are using deductive logic (either correctly or, in some cases, committing a fallacy), but all of this kind of reasoning is based on the rules of logic. For a more thorough practical discussion that is medically based, see Chapter 5 (Deductive Inference) in our book “Reasoning in Medicine.” In summary, deductive reasoning has limited but powerful means to validate statements, but the statements must be considered tentative, and subject to further data and potential modification or rejection. Deductive reasoning’s major role is in formulating consequences of laws and theories that are explanatory, predictive and testable. Another equally challenging issue is this: Where do the premises in a deductive argument come from? Saying that they are assumptions simply begs the question, and most observers starting with Sextus Empiricus thought that they arose from inductive inference. As we have indicated, deductive logic is only one of many types of logical systems. Later, we will discuss inductive logic, but we will touch on fuzzy logic, modal logic, many valued logic, Boolean algebra, mathematical logic, and abductive reasoning. Each of these is a system in and of itself, and each has a unique contribution to the study of inference.

CHAPTER 6 TAUTOLOGIES AXIOMS AND DEFINITIONS

Gottlieb Frege Tautologies are statements that are true by virtue of their structure. The most cited is the law of the excluded middle (PV-P) or its equivalent – (P and-P), sometimes called the law of contradiction. The whole point is you can substitute anything you like for P and the sentence remains true. Something is or it isn’t; there is no middle ground. The validity of the law of the excluded middle is central to first order logic and without it, the axiomatic first order calculus is incomplete. As we mentioned earlier, intuitionist logic exists without the law of the excluded middle, but it is much less robust than first order calculus and not able to prove many of the theorems in traditional logic. Definitions are also an essential feature of logic because they are necessary to describe the role of operators in logic. For example, “conjunction” is defined as “the sum of propositions,” whereas negation is the opposite of a proposition. Definitions in an axiomatic system can be thought of as the rules of inference. The most commonly recognized axiomatic systems are the axioms of Aristotelean logic as follows:

Tautologies Axioms and Definitions

1) 2) 3) 4) 5) 6) 7)

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If all bs are ys and all as are bs, then all as are ys If no bs are ys and all as are bs, then no as are ys If some as are bs, then some bs are as If no as are bs then no bs are as If all as are bs, then some bs are as No as are bs only if it is not the case that some as are bs Some as are not bs if and only if not all as are bs

Axiomatic systems are judged on the basis of many criteria, including consistency, completeness (i.e., all valid inferences can be proven), decidability (i.e., an algorithmic or computer program can prove all of the valid theorems), and independence. The other well-recognized axiomatic system is the Axioms of Euclid, which are somewhat similar: 1) 2) 3) 4) 5)

Things that are equal to the same thing are equal to each other If equals are added to equals, then the wholes are equal If equals are subtracted from equals, the remainders are equal Things that are consistent with each other are equal to each other The whole is greater than the part

These are augmented with postulates that are well known from Euclidean Geometry: 1) 2) 3) 4) 5)

A straight line can be drawn between any two points A finite straight line is part of a continuous straight line A circle is a line equidistant from the center of itself All right angles are equal to each other Straight lines that are parallel don’t meet

Aristotelean logic uses the previously mentioned axioms in contrast to intuitionist logic and modal logic, in which these axioms are discarded. Euclidean geometry is opposed by non-Euclidian geometries that do have applicability in the natural world, especially in General Relativity. In summary, axiomatic systems like Aristotelean logic, Euclidean Geometry and Decision Analysis (to be discussed later) are marvelous examples of the scope and power of the human intellect, but they cannot be accepted as descriptions of the world without caveats.

CHAPTER 7 PARADOX

Willard Van Orman Quine A paradox is, in some ways, the opposite of a tautology in that it is a contradiction that is unable to be resolved through simply reasoning. Why do we care? Because if the problem cannot be resolved, it shows that there must be something wrong with the framework in which we are operating. If the framework is logic or mathematics, this is a serious problem. It may mean we have to discard the framework. After all, when Russell sent Frege his paradox (remember the sets that include those sets that do not include themselves?), Frege responded that the arithmetic wasn’t sound. That is to say, the entire concept of reducing arithmetic to logic was thrown into question just by this paradox. And what about the liar paradox? We mentioned previously that the liar paradox is just that – a statement that is not easily refuted, since whatever truth value you assign to the components, the result is a contradiction. Epimenedes, who was from the island of Crete, stated that all Cretans are liars. Of course, if he is lying the statement is false and he is therefore telling the truth. But if he is telling the truth, he is lying, and vice versa. This is an example of a logical paradox which is not easily resolved, except by forbidding all self-referential sentences. However, self-referential statements

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are used frequently in common conversation and are not always troublesome. For example, “he thought of himself as intelligent.” Another of these types is Cervantes’ Hanging Paradox of Sancho Panza. In this example, Panza is made governor of an island, where a visitor must always declare their plans for their visit, or be hanged. He encounters a visitor who says his plans are to be hanged. Again, this is a paradox of self-reference. Similarly, the barber paradox of the barber who shaves all those and those only that do not shave themselves. Like the Liar paradox, either way you think about these results is a contradiction. Both the barber paradox and the liar paradox concern a set of results that are self-referential and not solvable, to everyone’s satisfaction at least. Some paradoxes are simply rhetorical and not really paradoxical, like Shakespeare’s “there is method in his madness” or Shaw’s “The Golden Rule is that there is no golden rule.” Some are solvable, like Zeno’s paradox, which described Achilles running towards a goal, but first having to get halfway, then halfway again, so that he never actually gets to the finish. A variant of this is Zeno’s Achilles and the tortoise, where Achilles starts behind the tortoise but can never catch up because he needs to continually halve the distance between them. This is a problem in calculus, whereby one needs to take a trajectory to the limit to reach the destination. Others are simply vague, like the Heap and Ship of Theseus. The heap paradox starts with a single grain of sand, which is clearly not a heap. Of course, adding one more grain will not make it a heap either. Therefore, sequentially, there is no number of grains that will constitute a heap. This is called the sorites (meaning “heap” in Greek) paradox, and is attributed to Eubulides of Miletus in approximately 400BC. The Ship of Theseus is similar. When Theseus returns from his trip to Minos, where he slayed the Minotaur, his crew replaced the rotten timbers on his ship plank by plank. At what point in this process is the ship a new ship? The Sorites and Ship of Theseus seem to be straightforward problems in ambiguity, but think of yourself instead. You have changed, and continue to change throughout your life, but are you the same person? Are you like Parmenides stepping into the river (you can never step into the same river twice)? Maybe you aren’t the same person, and if so, when and how often did you become someone else? Some paradoxes are property attribution problems. For example, Socrates is always Socrates. Old Socrates is old, but young Socrates is not old, so old Socrates cannot be old either. Naming objects can get us into trouble. For example, Frege’s Morning Star Paradox, which states that the morning star is not the same as the evening

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star, but since they both refer to the planet Venus, they must be the same. Question begging is also a type of paradox. “When did you stop beating your wife?” has no correct answer if you assume that you don’t actually beat your wife in the first place. Logic can also be problematic, as is seen in Hempel’s paradox of Ravens, which states: All ravens are black. All non-black objects are non-ravens, which means that a black raven confirms the statement that all ravens are black - but so does a white shoe. How about this one: You are not in Rome. You are not a bishop. But the conjunction “you are not in Rome or you are a bishop” is true, since you are not in Rome. Therefore, you are a bishop? This works for any arbitrary conjunction and is similar to a Gettier type 2 problem. In Goodman’s “a new riddle of induction,” he defines “grue” as something green before an arbitrary time, and blue after that time. He goes on to define “bleen” as the opposite. The point is that no amount of empirical data can decide between these claims. For example, is an emerald green or grue? The answer might be something along the lines of an inappropriate definition, since while physical properties do change with time, time, as a condition of the definition, seems inappropriate. So, the statement “a sea battle will happen tomorrow” simply does not possess a truth value, since the future is not decidable in the present. Time dependency also seems to play a role in counterfactual conditionals, since it postulates something that hasn’t happened. Part of the problem is that the antecedent in the counterfactual didn’t happen, and thus is false. That paves the way for any consequent to be true. For example, “if that pat of butter were heated to 150 degrees, it would have melted” is factually correct, if the pat of butter wasn’t heated then from a logical standpoint, so is “if that pat of butter were heated to 150 degrees, it would not have melted.” The problem is that any false antecedent permits any consequent to be true, even if it is contradictory. This particular problem of counterfactual conditionals is the subject for a great deal of

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philosophical debate. Quine divides paradoxes into three categories. Antinomies are paradoxes like the liar paradox, which are inherently contradictory. Veridical paradoxes are exemplified by the barber paradox, which contains a statement that appears to be true but leads to an absurd consequence. Falsidical paradoxes are simple mistakes likes Zeno’s paradox. Other paradoxes that have received a great deal of philosophical attention can be found in decision analysis. The paradox hinges on the infinitesimal chance that one person’s vote will be crucial in an election; therefore, by extension, all voting is inconsequential. This is an obvious falsehood. In my view the voting paradox is analogous to the Zeno paradox of the tortoise, since both of them inappropriately extrapolate to the limit. Arrow’s impossibility theorem, for which Kenneth Arrow was awarded the Nobel Prize (amongst many other contributions) in Economics, is a different sort. It shows that no ranked voting system can be free of contradictions (i.e., no consistent community-wide ranking system will be satisfactory) if there are three or more alternatives. More elaborate preference systems that rate the alternatives rather than rank ordering them can overcome this and provide a coherent voting rule, in contrast with simple preference ordering. (Interestingly, this was first proposed by Rev. Charles Dodson (AKA Lewis Carroll) who in real life was a mathematician and wrote a nearly incomprehensible textbook on logic that in a certain sense presages Wittgenstein’s truth tables.) However, rank ordering candidates is not a practice that is in general use. No wonder people are skeptical of elections in the United States. After all, there are clear instances in which the candidate receiving the majority of the total votes (Hilary Clinton) was not elected (Donald Trump was made President despite losing the popular vote). In my view, the easiest way to think about paradoxes is to divide them into the following categories: Logical (Liar, Barber, Raven), mathematical (Russell, Arrow, Zeno) and language (Ship of Theseus, Heap, Evening Star-Morning Star, counterfactuals and Goodman's new riddle of induction). In summary, paradoxes come in many shapes and forms. Some of them are resolvable either with newer mathematical techniques or restrictions on the use of language, but some of them are windows into valid problems either in mathematics, logic or language; or in the limits we need to apply to models of reasoning like decision theory.

CHAPTER 8 INDUCTION

Nelson Goodman Induction is the opposite of deduction and in terms of reasoning, proceeds from individual instances to generalizations. To put this another way, induction is reasoning that extrapolates from particulars to general law-like statements. The classic example is that repeated sightings of white swans infers that all swans are white. This conclusion appeared to be correct for centuries until black swans were found in Australia. Likewise, the observation that the sun rises every day is not conclusive proof that it will do so tomorrow. Induction was first recognized as a form of inference by the Greeks, especially Aristotle and particularly Carneades, who introduced degrees of probability. Aristotle took a particularly prominent position for this form of reasoning in his exposition on logic. It was thought to be an accurate approach to establishing laws that govern our world, until David Hume demolished the validity of the approach in his publication, A Treatise on Human Nature. Since then, it has become known as the “problem of induction” or Hume’s fork, since it questions the ability of empirical data to establish laws. This is a major problem, as all empirical science is focused on establishing laws based on observations (Levi, 1967) or, as C. S. Pierce said, “Induction is ampliative since it infers something about individuals not yet encountered.” There are many types of induction: enumerative, where there is an inference about a class of individuals; proportional, where it is a

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characteristic of the class that is inferred; and propositional, where it is an inference from one sample of a population to another (typical statistical inferences in epidemiology, and even deductive arguments about inference from one population to another, etc.). All statistical inference is based on induction, as we will explore in a later section. As a general rule, inductive inference plays a much greater role in day-to-day thinking than deductive reasoning, which is largely reserved for mathematics, logic and parts of physics. This is an unfortunate truth, as pointed out by Francis Bacon, who lamented that deductive arguments are thought to be valid, and if there are truthful premises, the arguments are sound. On the contrary, inductive arguments, which are the bread and butter of the scientific method, are always burdened by the “problem of induction.” While in medicine, many inductive inferences are causal in nature, the problem of induction is independent of whether the inference is causal or not. For example, Nelson Goodman’s famous New Riddle of Induction envisions a law that all emeralds are “grue” (as I explained above, this represents green before time t and blue thereafter). Observing a green emerald supports two conflicting laws that all emeralds are grue and all emeralds are green. This is reminiscent of the uncertainty of a truth value of a statement about the future. Consider the statement, “There will be a sea battle tomorrow.” But of course, this statement’s truth value cannot be ascertained until tomorrow. The true values of time-dependent propositions are inherently problematic. However valid an inductive inference appears to be, it is limited by the gulf between actual reality and the sensory appreciation of it, let alone the next step, which is the generalization of a prediction. Touch, vision, hearing, taste and smell are our connections to the real world, but they give us a human-distorted picture, and that data is the only data we have available for empirical generalizations. Obviously, dogs, with their superior olfactory apparatus and cats, with their superior night vision, will have a vastly different notion of what the world is made of and, consequently, different conclusions from their inferences based on their sensory input. The primacy of sensory input led to the rise of phenomenology – the study of the conscious mind. Knowing things then becomes an act of the conscious mind rather than an inference about the world we live in. Sensory input results in mental events, but it is a leap to conclude that they say anything about the world we live in. But if we can’t conclude anything about the world in which we live, it does not help us to move the world forward or assist in our communication with others.

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Analytical philosophy agreed that sensory input is our source of data about the world, but further dissected it in terms of its relationship to the world in its capacity to identify objects (reference), its ability to convey meaning about the objects (sense), and its link to language - specifically, in our ability to use language to communicate about these objects. This is Frege’s interpretation; he separated reference and sense as two features of our use of words. An opposing view is that meaning is strictly the product of how a term is used. However, use implies that there is a purpose, which is to refer to an object and convey its sense. Think of the word “ball.” This can refer to an object or a type of dance party. The use implies a purpose, and to “have a ball” could mean either. According to Kripke, proper names do not have a separate reference and sense (intention). They simply refer to an object, which he calls “direct reference.” The meaning you ascribe to it is the issue and depends on what information you bring to the conversation. In our example, if you are in a game, then “ball” means the object you are playing with. But if you are preparing for a party, the “ball” refers to the event, and so on. If the object in question is a single entity, the term given by Kripke is a “rigid designator.” This means that however you use the term, it is always referring to the same object, so a proper name is a rigid designator, while a generic object like a ball is a direct reference but not a rigid designator. This distinction overcomes a problem with the traditional theory of meaning, which makes the description the same as the object being described. This is clearly not correct. Descriptions are not the same as the object being described for several reasons, not least of which is that objects can be described in many different ways. In this view, analytical statements are necessarily true and a priori, like PV-P, but most of the necessarily true statements are a posteriori, like “water boils at 100 degrees Celsius” (true only at sea level). Some observers distinguish between various forms of induction. Specifically, they separate out the process of generalization, which we can say very little about except that it is commonplace for observers to attempt to categorize observations by virtue of their characteristics and lump them together – a process called intuitive induction. John Stuart Mill thought that this form of induction was simply empirical generalization. He went on to say that all deduction is based on induction; thus, induction cannot be criticized because it isn’t deduction. He said that even mathematics is a form of empirical generalization, rather than a natural law. Is 1+1=2 an empirical generalization or a law of nature? Mill thinks the former; most people (and most mathematicians, logicians, and philosophers) think the latter. Furthermore, there are aspects of mathematics that are not only not empirical generalizations, but are in fact contrary to everyday experience.

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Think of features of general relativity or quantum mechanics. As Einstein noted, the universe is not only stranger than we think it is; it is stranger than we can think. In addition, empirical generalizations are not pure statistical phenomena as they require organizing and selecting certain features of the observations to categorize and organize the data. Thus, induction is said to be “theory laden.” Empirical induction differs from perfect or complete induction, where every member of the class can be enumerated and judged to be in possession of the characteristic or not. Lastly, inferential induction is the process of inferring a characteristic of a class without specifically knowing each member of that class. This is the traditional view of induction and the one that Hume correctly pointed out was a leap of faith. Some observers, especially in the sciences, believe that the inferential process is always deductive, even when the appearance is that of an inductive inference. For example, my ten-year-old son claimed that my experiment of adding agents to increase cyclic AMP and measure the doubling time of sea urchin embryos was not science because, in his words, there were no equations (he subsequently became a physicist). If I had recast the data in a formula, he would presumably have been satisfied, even if it included a probability statement such as “the double time of sea urchin embryos is 90 seconds plus or minus 10 seconds with no addition of an agent to increase cyclic AMP, and 60 seconds plus or minus 10 seconds when the agent is added.” What he was really asking for was a deductive inference (whether it includes a probability statement or not), as this matched his concept of “real science.” Reformulating an inductive inference as a deductive one by using probability statements is more akin to what we do in medicine and science, but it does not eliminate the challenge of inferring from particulars to generate a lawlike statement, although it is the approach that J.M. Keynes proposed. Carnap extended this program and, later, Kemeny and Hintikka contributed. Even Popper’s repudiation of verification, which in a sense is a form of induction (i.e., verifying a law with instances that support it is in fact an inductive inference, since it is saying the instance supports the law), doesn’t really address the issue. In order to falsify the lawlike statement, you have to have first generated the law-like statement. Induction is just another form of inference with its own merits and deficiencies. Although these are different from the merits and deficiencies of deduction. In summary limitations plague both forms of reasoning. Any attempt to reformulate an inductive inference in terms of a deduction requires positing

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a lawlike statement from which a conclusion can be reached. This is a form of circularity, since the instances are used to infer the lawlike statement, thus negating the entire enterprise. A much more pragmatic approach is advocated by Pierce and Reichenbach, who suggest that in the absence of any other approach, inductive inferences are the most compelling way to move forward. This is an approach to which most physicians can relate, since we are often desperate for any possible explanation that will help formulate a management plan. Most physicians will agree with C.S. Peirce’s statement that all scientific assertions are tentative and dependent on available data. While this approach (entitled “vindication” by Herbert Feigl) is practical, it also opens the door to innumerable hypotheses that are marginally supported by the data and, therefore, destined to mislead the person making the inference. Even putting limits on the kind of inferences as suggested by Wesley Salmon does little to ensure the success of this approach. Pierce’s approach is in fact much more sophisticated and clearly foretold the practice of taking random samples of populations and applying statistical testing to ensure that the inferences applied to a population as a whole are sound - as we typically do today. His insight concerning abduction arose directly from his views on induction and forms a solid counterpart to deductive reasoning, since it does eventually arrive at a conclusion supported by the data. In the end, statistical inference and Pierce’s method of abduction seem to be a far better solution to the problem of induction than Hume’s blanket skepticism. The most obvious use of inductive inference is statistical inference that we will encounter later but sometimes, the inductive nature is somewhat opaque. Statistical inference (Chapter 10) can be formulated as a deductive argument as we saw above in the sea urchin example. Another common form of inductive inference is the use of analogies and models (Chapter 32), as we will discuss subsequently. Another approach to induction is through observations on how humans develop the ability to generalize. Some of this appears to require a certain developmental maturation process that children go through, as described by Piaget and Chomsky. Piaget from a developmental standpoint, and Chomsky from a cognitive approach, focused on commonalities amongst languages in their structure and syntax. The idea is that the cognitive processes we possess are dependent on linguistic commonalities that reflect how our brain is structured. To some extent, linguistic structure informs computer software design, although there are many languages that do not obey the same syntactical structure as typical western languages. Whether

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linguistic ability is innate or acquired is a matter of some debate. Of course, it could be the reverse - that we acquire linguistic ability empirically, and the plasticity of our brains then adapts to it. At present, most artificial intelligence programs rely on less formal structures and more empirical, data-driven approaches like neural nets, which learn by altering their configuration as they acquire new information. By inference, people seem to think more like a neural net than like a formal logic machine. However, when sufficiently instructed, motivated and accepting, humans are good at logic and mathematics, and view it as a superior form of reasoning over brute empirical approaches. Neural nets in people appear to be quite different from the same sort of neural nets in a computer, even if they spew out the same conclusion. People, then, at least according to John Searle, have a sense of the meaning of their conclusions, whereas a computer does not.

CHAPTER 9 CAUSAL INFERENCE

David Hume Attributing causality to events is essential to human endeavor. We need to fix things, diagnose illnesses, solve mysteries, apprehend criminals, and a host of other activities that depend on attributing causality to events or individuals. Since events arise out of a matrix of conditions, it is not easy to single one thing out as “the cause”. Yet, as occurred to me this morning, a poor water flow from my shower, which I attributed to the new water heater, was actually found to be due to a sticky master valve in the shower. This example emphasizes the practical nature of causal analysis, whereas broader questions such as “why does water boil?” have answers that can be attributed to the source of heat, the atmospheric pressure, the purity of the water, etc. How we use the notion of causality depends on the purpose at hand. Usually, it is a factor that is missing, defective, or involved in such a way that it is preventable or at least remediable. Since many different causes of an event can be attributed depending on the situation, conflicts frequently arise. The traditional way to view this is that the set of conditions is sufficient for the occurrence of the event. That is the “whole cause.” This approach is not very useful, though, since a complete recitation of all the conditions sufficient for the event could be endless, and is not how we typically think of a cause. As in the example above, we focus on a feature that is crucial in some way to the process and differs depending on the focus.

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Think of a gas explosion in a house. The cause could be the spark from the furnace, the leak in the stove, the person who left the gas on, the failure of the monitoring system, or a whole host of other contributing factors. This is in part why causal analysis is so judgmental. By and large, causal factors are at least necessary and, in rare circumstances, are both necessary and sufficient. In some instances, the “cause” is identified and the circumstances (i.e., standing conditions) are spelled out, but this is an elaborate forensic analysis for events that result in crimes, insurance issues, or the like. Frequently, causal factors are categorized as being necessary or sufficient and, occasionally, as both necessary and sufficient. In the house explosion, a number of factors (actually, too many to name) are necessary, but none are sufficient in themselves; therefore, no one single factor is both necessary and sufficient. When we speak of a “cause,” we are referring to different types of factors. Sometimes, it is the triggering factor, like the spark in an explosion. Alternatively, it might be an unusual factor that is singled out for a particular purpose, like a gas leak. Sometimes, it is a volitional action that could be singled out for responsibility, like the absence of a modern heating system. Causal reasoning is not a type of inference in itself and can be viewed in either a deductive or inductive framework – or, more commonly, both. As a general rule, an observation generates a hypothesis, which is then either validated or refuted with information obtained in an investigation. This is an example of induction followed by deduction. The whole concept of causality is very controversial in itself. Even Bertrand Russell remarked, “the word cause is so inextricably bound up with misleading associations as to make its complete extrusion from the philosophic vocabulary desirable.” Since causality as a truth-preserving form of reasoning ended with David Hume, we need a more modest role of causal reasoning that mirrors its role in cognitive activity. Clearly, we utilize causal inference on almost a minute-to-minute basis during our lives, so dismissing it entirely as fallacious is ludicrous – a bit like accepting Zeno’s arrow paradox of never getting from point a to point b. It is simply not helpful. We need causal reasoning, and we need to deal with it as a form of reasoning, while rejecting the notion that causality is universal, uniform, or truth preserving. By that, I mean that what is a cause for one person, may not be a cause for another observer, and a cause in one situation may not translate to the same cause in a different but similar situation. However, science requires that experimental results be reproducible, so isn’t that an endorsement of uniformity? Furthermore, doesn’t science endorse the notion that all phenomena have events that precede them and are essential for their development, which is a

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requirement for universality? I think we can be comfortable that science does endorse causality and utilizes it to make progress. Of course, it is an acceptance that should be taken with a proverbial grain of salt, since the conclusions of causal inferences are themselves tentative. For Hume, even if causal relationships are inherently suspect, he was satisfied that if the event labelled “cause” immediately preceded the event, it was called “consequence,” and whenever the event called “cause” occurred, the event called “consequence” followed. For Koch, this was not nearly sufficient, as he required additional stipulations, including the concept that removing the cause eliminated the effect, and transferring the cause to a different situation resulted in the same effect. Koch’s assertions define causality in medical circumstances, even though there are causal relationships that don’t entirely obey them. This is especially true for environmental agents, where Koch’s positions cannot be rigorously tested. For example, the theory “benzene causes cancer” cannot be tested without experimentally subjecting human volunteers to benzene exposure. Koch’s notions would preserve causality for typical infectious diseases, but reject it for the proposition that” just because day precedes night, it doesn’t mean that day causes night.” On the other hand, Hume’s conception of cause would permit this. In any case, causal relationships, if uniform, imply that there are laws that describe these relationships - typically referred to as laws of nature. Of course, this conception falls apart in a rigid sense for the same reason that induction falls apart, but it is a useful expedient. In this sense, a law of nature is implied in the requirement for reproducibility in experimental science and, by extension, in medical science - even if we cannot experimentally reproduce a disease in other human subjects as we can in animal models. Reproducibility is a modest requirement, as is temporal sequence; however, insisting on a necessary relationship between cause and effect is much more stringent. This has been quite problematic for most philosophers, who rightly assert that there are no logical or empirical laws that permit this sort of assertion. If a necessary relationship between cause and effect is rejected, what about a sufficient relationship? Here, the waters are a little muddier. It is true that if one could reproduce the situation in its entirety, the “causal” conditions would be sufficient to generate the effect. But this is hypothetical, since at least one aspect cannot be reproduced – the fact that time has elapsed and this could potentially alter the relationship. Bearing this in mind, even this less stringent condition is difficult to adhere to. A strong formulation of this is the counterfactual approach that states “X causes Y if, and only if, without X, Y would not exist.” This approach has the same

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limitations that we mentioned above. In addition, many counterfactuals do not imply causality. For example, “a figure is a triangle if, and only if, it has three sides” does not describe a causal relationship - just a descriptive or definitional relationship. The practical nature of medicine requires a set of guidelines to infer a causal relationship. There are three basic formulations. One is Koch’s assertions, which have several formulations but require the isolation of a causal factor, its uniform relationship to the observed effect, the ability to reproduce the relationship experimentally and, if possible, that the causal factor is eliminated and the absence of the effect can be observed. This is primarily oriented toward infectious agents. Koch originally applied it to tuberculosis which, at that time, was not clearly an infectious disease, although it can be applied with modern molecular biologic techniques to genetic disorders and even some non-genetic non-infectious diseases. A second set of guidelines comes from John Stuart Mill, a polymath who was a leader in the Utilitarian theory of ethics and a member of parliament. His analysis of causality is called Mill’s Method, and consists of the following: Mill’s Methods 1) Direct method of agreement, where if two instances of the same phenomenon have only one thing in common, then that is the cause. 2) Method of Difference, where if an instance of a phenomenon only differs by one factor from another instance, then that one difference is the cause. 3) The indirect method of difference (also called the joint method of agreement and difference), where if two or more instances of a phenomenon have only one circumstance in common, and two or more instances have nothing in common except the absence of that factor, then the factor is the cause. 4) The method of residue means that if you subtract any part of a phenomenon, the result will be the product of only the remaining elements of the phenomenon. 5) The method of concomitant variations states that when one component of a phenomenon varies in the same manner as the effect, then the component is a causal factor.

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The other set of guidelines is Austin Bradford Hill’s criteria of causation from an epidemiologic standpoint. They are strength of association, consistency, specificity, temporality, dose response, plausibility, coherence with known biology, experimental evidence, analogy to other causal relationships, and if possible, reversibility. The famous story of John Snow turning off the water pump from the Lambeth Company in London, thereby eliminating the epidemic of Cholera, reflects these guidelines. As guidelines, though, they are neither necessary nor sufficient, but when satisfied, they represent a strong argument in favor of a causal relationship. Many environmental agents are causally associated with disease using these guidelines, including smoking cigarettes and lung cancer, asbestos and mesothelioma, vitamin B12 and pernicious anemia, vitamin B6 and pellagra, vitamin C and scurvy, and innumerable others. Since none of these is a deterministic relationship, it rests on probability and, in that sense, could be considered a contributory cause. These sets of criteria are guidelines and are neither required nor sufficient enough to establish a causal relationship, but adherence to any one of them is a good reason to believe that the relationship is causal. This is much more rigid than a simple if - then statement that does not require a temporal sequence. “If Michael were outside playing then he could not have been in school” is a perfectly good if - then statement, but it doesn’t imply causality or a temporal sequence. It is just a statement of fact. Hume’s view of causality was that repetitive association leads to causal inferences. “The sun always rises in the morning” leads to the causal association between morning and sun rise. However, modern psychology disputes this interpretation (see Chapter 33). Hume’s conception is a system-2 function, whereas in most situations, the assertion that there is a causal relationship arises out of single observations and is an automatic system-1 inference. Even very young children and animals make causal inferences with single observations. This psychologically prepares us for operating in the world, and appears to be a default inference which may lead to erroneous conclusions that are corrected by a system-2, in a retrospective analysis of the situation in question. For example, the low tire pressure warning light in my car came on after servicing, but it wasn’t the service technician’s fault; it was the low temperature in the garage that reduced the tire pressure. Causal inference and blame for events are a natural reaction and often erroneous. The value, however, is to identify problems that could be avoided or corrected.

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In spite of the limitations of causality, or perhaps because of those limitations, causality is what underlies most, if not all, religions. It is the source of explanation for the events we cannot understand. In this paradigm, God is the prime mover. He/She looks out for us and provides a path for us to succeed in our aspirations. Whether things go well or not, it is comforting to know there is a reason for this. Reliance on good or bad luck is less satisfying than someone or something actually being in charge - whether or not this causal explanation makes sense. Austin Bradford Hill Criteria for a Causal Relationship 1) Strength of association, 2) Consistency, 3) Specificity, 4) Temporality, 5) Dose response, 6) Plausibility, 7) Coherence with known biology, 8) Experimental evidence, 9) Analogy to other causal relationships, 10) Reversibility.

Koch’s Postulates 1) The organism must be found in diseased individuals and not in healthy ones. 2) The organism must be isolated from the diseased individuals and cultured. 3) The cultured organism causes disease when introduced into a healthy individual. 4) The organism must be isolated from the experimentally diseased individuals.

CHAPTER 10 STATISTICAL INFERENCE

The statistics we use in today’s world arose from two different legacies. In the 1700s, gambling was a frequent pastime and led to statistical approaches to predict the odds of winning bets on cards, rolls of a die, etc. Then, a separate chain of reasoning occurred much later when theoreticians were trying to analyze the results of experiments with plants – a direct descendent of Mendel’s experiments with the color of pea plants during hybridization experiments. In both of these cases, the results were a formal or logical approach to statistical analysis in contrast with those derived by the Reverend Thomas Bayes (an amateur mathematician), which gave rise to the field of subjective probabilities. Ironically, subjective probabilities correspond to one’s willingness to bet on outcomes, but they are not completely constrained by the number of combinations that underlie dice games of chance. To give a concrete example, the chance of rolling a pair of ones on the throw of two dice is 1/6 X 1/6, or 1/36. However, your willingness to bet on this occurrence could be quite different, depending on what is at stake and how much of a gambler you are. In general, if the stakes are very high (either monetarily or in terms of well-being), people tend to be very conservative, and vice versa for low stakes. However, if you use a subjective probability estimate in a game of dice, you may find yourself in the uncomfortable position of making an ill-advised bet, which would result in a losing position. In situations where the outcomes are countable (i.e., there aren’t too many to be counted), subjective and formal or logical approaches to probability estimates should converge; however, in situations that don’t lend themselves to definable and limited outcomes, subjective and formal approaches can diverge. Weather is an excellent example. Probability

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estimates in weather forecasts are a combination of subjective (since counting the number of possible scenarios is impossible) and formal, based on very complex mathematical models. That is why a 40% chance of rain means there is a 4 in 10 chance of rain, not that it will rain 40% of the day. Furthermore, since there is no opportunity to rerun any given day (in spite of the movie Groundhog Day), 40% does not mean we will have 4 rainy days in ten identical days. I will have more to say about this later. The primary purpose of statistical inference is to derive properties of populations from samples taken from that population – a form of inductive inference. Determining whether the samples are from the same or different populations then leads to hypothesis testing, as long as the samples are accessed in an unbiased fashion. For example, a sample of men aged between 40-60 from New England was assessed for height, then compared with a sample from the Midwest. Provided the measurements were accurate and the samples were unbiased, we could compare them and determine if there were a height difference. This notion of accuracy and precision is found in many disciplines under different names. For example, precision in data analysis is known as “noise” in cognitive psychology, or “reliability” in clinical epidemiology, but it is the same concept of variability on test and retest, or observer to observer. “Bias” is systematic error, which is sometimes called “accuracy.” These are deviations that are inherent in the measurement, such as a gun sight that is always off by a certain degree. But if you think that bias and noise (meaning lack of precision and accuracy) are complex issues within statistical inference, you are much mistaken. As is amply documented in the book “Noise,” the judicial system is so biased and unreliable that one could argue that the whole system needs to be discarded in favor of simple algorithms. In fact, the authors Kahneman, Sibony and Sunstein effectively make this point, then discard it later because it is too restrictive and prevents expert judgement. However, noise is not limited to the Judicial System. Indeed, the Medical System, places an enormous superstructure of commodification on top of the bias and noise attached to diagnosis, making everything a profit-driven decision, which then distorts the already fragile accuracy of medical care (see Martin Shapiro’s The Present Illness: American HealthCare and its Afflictions). Noise in judgements is a ubiquitous problem and affects most human activity. Attempts to reduce bias and intra- and inter-observer variability include algorithms, guidelines, training, using multiple independent observers and criteria, and a host of other techniques. Nevertheless, no solution can ever be entirely successful. That is just the nature of human judgement.

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The overall approach to statistical hypothesis testing is somewhat peculiar in that the common determination rests on whether the measurements of groups are sufficiently different to be able to support a claim. Let’s say that two populations are less than one in 20 (or one in 100 or one in a thousand, etc) the same, which indirectly supports the hypothesis that data samples were drawn from different populations. The process of “rejecting the null hypothesis” (i.e., rejecting the claim that the two groups derive from the same population) would be the most common form of statistical hypothesis testing, and comes from Sir R.A. Fischer in the 1930s. If that rejection occurs incorrectly, it is a type-one error. Of course, the hypothesis can also be the other way around, with the null hypothesis being that the two populations are different. Rejecting this would imply that they are from the same population. This is very useful in establishing that a certain form of medical treatment is as good as the standard approach, but perhaps cheaper or less troublesome in any number of ways. If this assumption is made incorrectly, then the error is called a Type 2 error, and the standards for rejecting it are conventionally a little laxer. Various concepts of probability – classical, empirical, subjective and axiomatic are beyond the scope of this discussion but for the most part, clinical medicine uses empirical (frequentist) and, occasionally, subjective (Bayesian) approaches. For a more detailed discussion, see Philosophy of Medicine: An Introduction by Thompson and Upshur, Chapter 5, Probability and Randomness. Virtually every conclusion in clinical medicine is inductive in the form of a statistical inference. Even when speaking in conventional or “natural” language, we are using synonyms for probabilistic estimates. For example, the use of “common” implies a probability estimate, as does “rare,” “exceedingly rare,” “not uncommon,” and so on. Unfortunately, the precise meaning of these utterances exists largely in the mind of the individual using them, and can quite often be misunderstood by the listener. In defense of these statements, though, the actual estimate is frequently unknown with precision, and some leeway in the interpretation of these statements may be warranted. Even seemingly firm estimates like metrics for height and weight can have a degree of uncertainty associated with them, such as different scales generating different weights. So, what exactly are we saying when we give a probability estimate? Here, the water gets muddy. Let’s talk about genetic conditions using a classical Mendelian approach. If a pea has a dominant heterozygous characteristic, say green color (GY), and this is crossed with a recessive trait like yellow (YY), the offspring yields will be GY, YG, YY, YY. In this case, 2 of 4 plants will be green and two will be yellow. Therefore, the ratio of green to yellow plants is 1/2 or 0.5,

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or 50%. This number is fixed by the logical framework of Mendelian genetics, which can be axiomatized. This is a very uncommon form of probability statement, as it can be formulated as a deductive argument. This form of probability is almost never used in clinical practice, in part because it requires an exhaustive and mutually exclusive series of outcomes. This is a requirement that is rarely met in clinical practice, except in certain monogenic, autosomal, dominant or recessive conditions; and even here, there is variable penetrance, so the numbers won’t be exactly like the above pea example. An exception is the inheritance of the risk factor for a disease called ankylosing spondylitis. Here, the risk factor is an autosomal codominant gene called HLA B-27. Since most Caucasian people with AS are heterozygous for the gene, and most people without the disease are negative for this gene, the predicted proportions of offspring with this risk factor are the same as that which we observed above for the green and yellow peas. However, possessing the risk factor does not mean they have or will get the disease since only about one in 10 individuals with the gene get the disease. Another example is sickle cell disease. but here, the disease is only present as a homozygous recessive trait in individuals, so the results would be the same as above if a patient with sickle cell had children with a carrier. The statistical or frequentist interpretation is a strict recitation of experimental data. One hundred patients were given a medication and 50 of them developed a rash. This means the probability of a rash in a patient given this drug is 50%, or one in two. When physicians engage in evidenced-based medicine, they calculate various parameters based on clinical trial and observational cohort studies. These calculations include test sensitivity, specificity, predictive value (positive and negative), likelihood ratios, number needed to treat and, conversely, number needed to harm. We will review how to do these calculations in Chapter 13. These data can be used to evaluate a test or a treatment in a clinical situation. What this approach lacks is the ability to formulate a probability estimate for a single event, which is the most common use of probability statements in a clinical encounter. Patients aren’t particularly interested in detailed analytical descriptions of trial data; they want to know what is likely to happen to them if they chose a certain course of action. Frequentist, empirical, formal and logical approaches to probability estimates do not permit application to a single individual; they only apply to populations. However, the subjective approach to probability estimates does apply to individual cases. Thus, when you claim that there is a 50% chance of a certain occurrence, the vast majority of time, you are using a subjective probability estimate - unless you are gambling with dice or engaging in some other game of chance. Whenever a physician says there is a 50%

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chance of cure or toxicity or a particular diagnosis, it is a subjective probability estimate based on Bayes’ Theorem. That is why it is so important to understand conditional probabilities, as we will explain below. Let’s imagine an experiment where you roll two balls down an inclined ramp and ask which one will reach the bottom of the ramp first. In this case, you apply the Newtonian law of universal gravitation to address the question, and conclude that they should reach the bottom at the same time. Thus, the probability estimate is based on a natural tendency (propensity) to reach the bottom at the same time, which in turn is based on the application of Newtonian physics. Propensity, in this sense, is the action dictated by the laws of physics. Unfortunately, in medicine, we rarely have laws to generate these propensity statements, so this interpretation of probability does not fit with ordinary usage in clinical medicine. Instead, we need a more flexible approach to probability theory that will permit all of the above uses and, in addition, capture the typical use of probability statements in clinical encounters. Probability statements used in discussions with patients about future events is more akin to betting at the race track than any of the above concepts. Fortunately, there is a use of probability that does capture this sense, called subjective probability theory. This theory arose out of games of chance, but became more rigorously employed after it became apparent that in order to make subjective probabilities work, they had to obey certain rules. These rules state that probabilities for outcomes of an event cannot exceed 100%; nor, for that matter, can they be less than 100% if all the possible outcomes are specified. Lastly, the odds need to be what is termed coherent. In other words, betting on events cannot be structured so that the result is favorable to one individual (this, for unknown reasons, is called a “Dutch Book”). For example, let’s look at a scenario in a two-horse race, where one gambler takes the bet that if horse A wins, he gets $100, but if it loses to horse B, he pays $50 (and conversely, his opponent pays $100 if horse A wins, but gets $50 if horse B wins). Assuming there is an even chance for each horse, this is a Dutch Book, because the net gain for gambler one is $50, but the net gain for the second gambler is -$50. All bookies structure their bets to generate a Dutch Book, thus guaranteeing their income. The same is true for gambling casinos and card games in Las Vegas. That’s why, in the long run, the house always wins. Assuming the physician is not betting with the patient, but is instead trying to impart information about odds of events occurring in the future, this use of probability is subjective and is the same use of probability that we see in

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sporting events, weather, political contests and so on. In fact, it is flexible enough to encompass all of these uses of probability we have mentioned above. In addition, it permits the use of probability in decision-making, as we will see in a later section on Decision Analysis (Chapter 26). To prepare for the use of subjective probability in Decision Analysis, we need to introduce the Inverse Probability Law and its extension, Bayes’ Theorem. This formula was derived by Thomas Bayes a Reverend, philosopher and mathematician, then published after his death by another clergyman, mathematician Richard Price. It was first read at the Royal Society as a paper entitled “An Essay towards solving a Problem in the Doctrine of Chances” (1763) and published in the Philosophical Transactions. The formula is as follows: P(A/B) = P(B/A) P (A)/ P(B) The inverse probability law is a codification of what is referred to as conditional probability. In fact, Bayes’ Theorem is a straightforward derivation of the definition of conditional probability. To explain this, I will give two examples. The first is on a coin flip, where the chance of a head or a tail appearing is 50%. This is true no matter what the preceding results were. If you flip a coin 10 times and it always lands heads up, presuming the coin is fair and the flip is fair, the chance of heads on the 11th try is the same - 50% - as it was on the other ten tries. Conditional probability plays no role in coin flips. However, the same is not true in other situations. For example, in our green/yellow pea experiment, the odds of a yellow pea plant in the mating of a green and yellow plant will differ, depending on whether the green plant is homozygous or heterozygous. Thus, the result of the mating is conditional upon that fact. In the heterozygous scenario, the progeny will half green, half yellow; however, in the homozygous mating, the result would be all green heterozygotes. Another common example is the odds of a face card in a shuffled deck, which depends on whether the deck is full, or whether cards have already been played and are therefore unavailable. In clinical medicine, the probability of an illness in a random individual is represented by the frequency of the illness in the general population. However, if anything is known about that individual, such as gender, age, etc., the probability of the illness is conditional on that information. For example, the probability that an adult has rheumatoid arthritis in the general population is about 1 in 200, but since the disease is about 4-fold more

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common in females than males, if you know the gender of the patient, the odds will increase in a female and down in a male. Bayes’ Theorem states that the probability of a disease in a symptomatic patient (P(A/B)) is follows: P(A/B) = P(B/A)P(A)/ P(B/A)P(A)P(B/-A) The probability of the disease in the general population (P(A)) multiplied by probability of the symptom in a diseased patient (P(B/A)), divided by the numerator multiplied by the probability of the absence of the disease in the general population multiplied by the probability of the symptom’s presence in non-diseased people (P(B/-A)). Why is this so important? First, we are always trying to estimate the chance of a patient having a disease. It is otherwise difficult to formulate a management plan. Second, most of the time we are seeking to acquire additional information about a patient that clarifies our thoughts about what is wrong. In terms of Bayes’ Theorem, each additional piece of information alters the probability of the diagnosis. In typical encounters, the history and physical exam provide hundreds of pieces of data, all of which can contribute to the probability of the diagnosis in question. This is the essence of the role of subjective probability in the management of patients. Because of the central importance of this approach, there are many different formulations of these concepts, including test characteristics such as sensitivity, specificity, predictive value (both positive and negative), and likelihood ratios. All of these are utilized in an attempt to increase certainty about a diagnosis and reduce uncertainty. This will be shown in more detail in Chapter 13. It is also important to point out that this process is identical in non-medical situations, when one is trying to make an assertion about a situation based on available data. For example, a plumbing problem, an electrical problem, an automobile issue, etc.

CHAPTER 11 PROBABILITIES AND ITS PROBLEMS

Thomas Bayes The different concepts of probability sometimes come into conflict with each other. There is little surprise that empirical verification of theoretical probability estimates differs from the predicted results. In the classic Mendelian experiments with peas, the color and shape differed from the predictions based on autosomal dominance and recessiveness, but they were close enough to validate the principles. However, there are famous examples in which probabilities differ vastly from statistical predictions according to the approach to which one subscribes. One example is the probability of heads or tails with a fair coin after a run of heads. From a frequentist view, it is 50/50. However, if one were to take a Bayesian approach, it would be quite different. The base rate is 50% but the observed run of 3 heads in a row is .50x.50x.50 = .125 or 12.5 %. A subsequent head would make the conjoint frequency .0625 or 6.25%. If you know the base rate of .5 or 50% and you know the long run frequency is 50%, wouldn’t it then make sense to bet on a tails result? Another way of thinking about this is the famous (or infamous) regression to the mean. The performance of an action that is statistically unlikely is usually followed by one that is closer to what is expected, or “regression to the mean.” Thus, brilliant performances are more often followed by more disappointing results, and vice versa. Following this concept, if the expected frequency of a series of coin flips is 50/50, then three heads in a row might indeed be more likely to be followed by a tail. These alternative ways of

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conceptualizing probability are in stark contrast to the frequentist approach. But are they incorrect? There are whole fields of cognitive psychology devoted to why people don’t obey statistical predictions based on a frequentist approach. The answer is that the subjective probability approach cannot be proven or disproven, since these alternative ways of thinking about the odds of an event occurring are based on subjective probability estimates, which are a quantification of beliefs. You cannot disprove a weather prediction of 60% chance of rain either by a rainy day or a sunny day, since that data is not relevant for the prediction. The only way to disprove it is by showing that the person’s belief structure is faulty. For example, they might believe that it can be both sunny and rainy, or that neither will occur. Another famous example is that of Tversky and Kahneman (who won a Nobel Prize for this and related work), who posed the now-classic Linda problem. Linda is described as bookish, and as someone who is involved in radical political movements, and the following question is then asked: Is it more likely that Linda is a bank teller, or that Linda is a feminist bank teller? The answer from a frequentist standpoint is clearly the first, since the conjoint probability has to be less than each single attribute. There is another field of cognitive psychology dedicated to why people chose the conjoint as being more likely that the individual case (bank teller alone vs bank teller and feminist). Much of the work focusses on the notion of plausibility as a cognitive default, when statistical evidence seems intuitively wrong. Another way to view this is from a Bayesian standpoint. If Linda was indeed a bank teller, which seems very unlikely given her political viewpoint, then wouldn’t it be in some way normalized to recognize her political persuasion in the form of feminism? Statistically, if the likelihood of Linda being a bank teller is 20% and the likelihood of being a feminist is 80%, then the Bayesian result is a posterior probability of 0.4 or 40%. Thus, being a feminist bank teller is indeed more likely than being simply a bank teller. This is the basis for people believing that streaks of good luck run out, and vice versa. “This good weather won’t last forever” and many other predictions generate a conflict between the Bayesian and frequentist versions. Another similar problem is pointed out in the book “Noise,” where the order of attributes (that are presumably independent – but this is not explicitly stated) affects the probability of a prediction. For example, predicting whether someone will succeed in a job is affected by describing the applicant as industrious, meticulous, irritable and a perfectionist, versus describing the applicant as irritable, a perfectionist, industrious and

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meticulous. Assuming all these attributes are independent (which of course is untrue), the first series of descriptors gets a higher score than the second set. From a frequentist standpoint again, assuming independence, it should not make a difference. However, from a Bayesian standpoint it does, since the first description gives the baseline probability and this is then adjusted up or down depending on the subsequent descriptors. But which is the correct interpretation? That is strictly a matter of opinion. The frequentist says the order shouldn’t matter but the Bayesian says it does. Why should it matter, though, because the descriptor that is most weighted would be the first one in many, if not the majority of circumstances? In fact, for the most part, when people make predictions, they are making them based on subjective probabilities. I can’t emphasize this enough. There is a significant body of work based on the apparent failure of people to estimate probabilities correctly from a frequentist viewpoint. I am not saying Tversky and Kahneman didn’t deserve the Nobel prize but I am saying people’s estimates of probability when they differ from the frequentist approach aren’t necessarily in error. Many times if not most of the time, they are reasoning correctly from a subjective probability standpoint, rather than being cognitively deficient. Of course, there are numerous examples where the Bayesian approach doesn’t hold, but the Bayesian interpretation of data is especially commonplace in situations where there is attribution or causality at play. That isn’t to say people aren’t mistaken. Take, for example, the Taxicab problem. A witness claims the color of the taxi involved in an accident is blue. The taxi fleet’s colors are 85% green and 15% blue. He is 80% accurate, and the chance of the taxi actually being blue works out as 41%, which is much lower than many people think, and much higher than others claim. The problem here is that this is a difficult mathematical problem, and it has nothing to do with a conflict between different conceptions of probability. However, the Monty Hall problem does actually represent a conflict between frequentist and Bayesian approaches. Here, a contestant is told that there is a car behind one of the three doors. He has to choose one, and he picks door one. Monty Hall, the MC (Master of Ceremonies) opens door one to reveal a goat. The question, is “should the contestant switch from his original second choice of door three to door two?” The answer is very very counterintuitive. As he had a one-in-three chance of winning with his initial choice, he will improve his chances to one in two if he switches to door two. The frequentist answer is that it doesn’t matter; there is still a 1 in 3 chance. However, the Bayesian answer is that given door one had a goat, his chances if he switches will be 1 in 2 that he will win the car. Interestingly, this has been explored numerous times and the Bayesian approach appears to be

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correct. He will indeed increase his chances of winning the car if he switches doors. But does that mean that the Bayesian approach is always correct? The answer to that is unknown. Here is another one. The two-envelope problem. For this, you are given two identical envelopes, each containing money, but one has twice as much money as the other. You chose one envelope. Should you now switch? The frequentist answer is that it doesn’t matter, but the Bayesian answer is you should always switch. I’ll leave that one to you to solve. The main message here is that different conceptual frameworks for probability give different results and sometimes, there appears to be a direct conflict between what individuals suggest is the correct answer, and what a frequentist approach suggests. People are not either stupid or misinformed; they are simply thinking about the problem in a different way. However, because the frequentist approach leads to different results from a subjective probability method, many statisticians reject the whole subjective probability approach. This makes little sense, since entire fields are dependent on projections like weather forecast, market trends, economic forecasting, etc. I hope your brain is not overloaded by this, because it is certainly quite confusing and, to some extent, unsettling.

CHAPTER 12 OBSERVATION, EXPERIMENTATION, AND THE SCIENTIFIC METHOD

Francis Bacon If one discounts the notion of a priori knowledge, then the central role of observation in developing testable hypotheses is key for both science and medicine. In a fundamental sense, medicine as a practical discipline is essentially identical to science in its approach and method. Biological science is performed on substrates that are exposed to interventions, and the results are analyzed. Frequently, this is a model system in mice and other laboratory animal testing, but also in tissue culture, where mice are replaced by cells in a culture and, sometimes, with components of living organisms such as nucleic acids, proteins, carbohydrates or lipids. One makes observations about these experimental entities then tests the hypotheses by one or another manipulation. Does exposure to lead cause anemia in mice? Does cyclic AMP increase the mutation rate in HeLa cells? Does an alkylating agent produce DNA strand breaks? And so on. There is an endless number of questions and an unlimited array of approaches to test the hypotheses. Sometimes, the hypotheses are within a given framework - that is, a theory results in a prediction that a certain event should occur, and by

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performing the experiment, you are testing the hypothesis and indirectly testing the theory. On other times, you are creating a scenario and simply observing the outcome in order to generate hypotheses, which you will then test in the subsequent experiments. These observations are rarely at random, leading some observers to suggest that most observations are theory laden, meaning you can’t really interpret an observation unless you have a hypothesis which the theory addresses. However, the whole observation process sometimes generates a surprise that, in one sense, couldn’t be a surprise unless it was unexpected, so it must have been contrary to a theory or a hypothesis. This brings up the question of whether truly novel observations without an underlying theory ever occur. This is hotly debated, but Watson and Crick’s (with Rosalind Franklin) observation of the structure of DNA generated a hypothesis about a genetic code that appears to be so novel that there was no theory laden observation. While there was a hot debate about the nature of the genetic material (some thought it was protein and others thought it was nucleic acid), what was unique about the Watson Crick explanation was the triple helix (alpha helix was proposed by Pauling) and the three-nucleotide sequence that specified an amino acid. Thus, both the structure of genetic material and the code that specified the structure of proteins was illuminated in one short manuscript. Other seminal discoveries have also occurred in this category. The discovery of penicillin was an unintentional mistake (Alexander Fleming), generating a line of inquiry that led to the discovery. Transposons (Barbara McClintock) are also in this category, as was the discovery of radiation by Marie Curie after a chance juxtaposition of a photographic plate and radium. We can argue this point, but there are clear instances where the observations are not theory laden. However, the fundamental pattern of science is to test hypotheses based on observations, the results of which then either strengthen or weaken that hypothesis. This was the claim of the logical positivists when they proposed the hypothetical deductive (or deductive nomological) model of scientific inquiry. Hypotheses are lawlike statements which can be tested. A strong theory will both explain the results of these experiments, and predict the results of future experiments. This is the verification principle in the hypothetical deductive theory of scientific method, and is the way science is conducted much of the time. The more verification, the stronger the theory. Notwithstanding Popper’s objection that the real role of science is to try to falsify a theory, the basic logical structure is the same. But what about medicine? As it is practiced, the source of data is in the medical history, physical examination and laboratory tests. These data are used to both generate and test diagnostic hypotheses. Let’s take a hypothetical case. A 50-year-old man comes to see you with chest pain. You

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ask him to tell you more about it, and he tells you that every time he gets on the treadmill, he gets a pressure-like sensation that occurs after a few minutes of exercise. It then goes away when he stops. Based on your appreciation of the characteristics of angina, you formulate a hypothesis that he is suffering from coronary artery disease. You pursue this with a stress test and when it is positive, you send him to a cardiologist for a coronary angiogram that demonstrates a stenotic lesion at the origin of the left anterior descending artery - the so-called “widow maker.” He then gets either stented or revascularized and is cured, at least for a while. How different is this from a scientific inquiry? Not very - except there is usually a more expeditious timeframe in clinical care. And is it any different from other fields in which diagnosing the problem leads to a series of tests, hopefully culminating in a diagnosis and a treatment plan? Similar patterns of inquiry occur with automobile mechanics, electricians, plumbers, and in a host of other fields. In fact, cardiologists and urologists do sometimes refer to themselves as plumbers. In rheumatology, it is rarely so simple, except for gout, which tends to be its most straightforward disease. Let’s go back to our 50-year-old gentleman, but this time, instead of giving you the treadmill story, he tells you it occurs after eating a meal. Perhaps you will think it is reflux or esophageal spasm, especially if tests for elevated muscle enzyme levels and an electrocardiogram are negative. You would likely pursue this line of investigation even if he had risk factors for cardiovascular disease like obesity, hypertension and stress. You give him some Tums and send him home with an antiacid/reflux program. He then seems to get better. At least, that would appear to be the correct inference, but in this case (and this is a true story), I was wrong and the patient came back later that evening with a classic myocardial infarction. The moral of the story is that not all hypotheses turn out to be correct, even when the evidence seems compelling. This why the practice of medicine, like science, is not like mathematics or logic. Things can go wrong even under the best of situations. We call it “going sideways” which, although it is stolen from criminals, is an accurate description of a hypothesis that appears to be valid but turns out to be incorrect and, in its place, a statistically less likely hypothesis is born out by future events. Of course, the aim of these investigations is to come to a conclusion about the truth of a hypothesis. In science, it appears to be a causal relationship which, as we have seen, is a schematized version of the relationship between events that can be manipulated experimentally. Heating water causes a phase shift as it turns from a liquid to a gas. The cause is the heat applied, but there are numerous other conditions that are assumed in this framework such as atmospheric pressure, altitude, presence of oxygen in sufficient

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amounts to support the source of heat (if it is a flame), etc. Likewise, in medicine, the cause of a person’s problem could be an infection for which we identify a specific organism as the cause, but this comes against a background of the host’s defenses (or lack thereof), exposures, other comorbidities, etc. The major contributors to the development of scientific method are Roger Bacon and Sir Francis Bacon (Novum Organum) from an inductive viewpoint. Who while unrelated and living in different centuries both emphasized experimental methodology. Others who contributed from a rationalist perspective and based on his primary vocation as a mathematician, Rene Descartes published a text entitled “Method of Rightly Conducting the Reason and seeking the Truth in the Sciences.” These principles were sharpened by one of the most outstanding scientists that ever lived, Isaac Newton, who published the methodology in Mathematical Principles of Natural Philosophy. It was Newton’s fully developed method which explicitly described the use of experimental manipulation and the role of prediction, thus relegating history and the social sciences to non-scientific disciplines, except in the occasional situation that there is an experiment. While this need not be a purposeful manipulation, for example an experiment of nature (so to speak), like migration or a plague - as long as the event can be tied to an outcome that proves a hypothesis and permits a prediction. What is less clear is where the hypotheses come from in the first place. This topic has already been discussed in the section on induction, but to summarize, there is no consensus on the process of hypothesis formulation. While there is a great deal of heterogeneity in how science is actually conducted, the most economical presentation of the methodology is the formulation by the logical positivists, who developed the hypotheticodeductive method that we previously touched upon. The hypotheticodeductive or deductive nomologic model is often invoked, but frequently, it is a rational reconstruction of events, not one that describes how the scientific investigation proceeded. The practice of medicine is in many ways similar to scientific inquiry, with the development of diagnostic hypotheses which we seek to either verify or prove wrong by accumulating data. This is then used to predict response to treatment, prognostic predictions and related conclusions. It is sometimes possible to proceed without a diagnostic hypothesis, such as in an emergency, when one is concerned with the ABCs (Airway, Breathing, Circulation), but most of the time, the centrality of a diagnostic hypothesis is directly analogous to a hypothesis in experimental science. However, while medicine can be scientific, its motivation is practical and not simply

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the acquisition of new knowledge. Patients don’t wait for the slowly grinding pace of scientific inquiry to progress; we need diagnosis and management plans in a timely manner. While the basic human biology is the foundation of medicine, it also sits in a larger context of social, societal, and pragmatic concerns. Thus, medicine cannot be “reduced” to biology just as engineering cannot be reduced to physics. For more detail, see “Why Medicine Cannot be a Science” by Ronald Munson (Journal of Medicine and Philosophy 6: 1981 pp 183-208. Later, we will discuss shortcuts and roadblocks to this process in the section dealing with heuristics and biases (Chapter 33).

CHAPTER 13 STUDY DESIGN AND ANALYSIS

Austin Bradford Hill Statistical inference is at the root of almost all of the data we acquire in the science of medicine. In order to test hypotheses, we need comparator groups – the experimental group that has had an exposure either through natural events, or through an intervention. If the exposure is natural, it is an observational study and if it is through an intervention, it is an experimental study. In either case, we compare exposed versus non exposed groups. The simplest comparisons are for dichotomous events. Cancer, no cancer, heart attack, no heart attack, and so on. More complex comparisons involve continuous variables like height, weight, temperature, etc. Statistical tests are available for these types of comparisons and other more complex ones, including life table analysis, quality adjusted life years, cost-benefit analysis, cost effectiveness analysis, etc. Methodology exists for qualitative analysis but in all cases, there is a comparison if there is a hypothesis to be tested. The rest of the studies that do not test hypotheses are descriptive and often, but not always, serve to define a situation that can be utilized at a later date to test a hypothesis. While the science of medicine is defined by hypothesis testing, so is clinical medicine. For example, let’s say we encounter a patient with abdominal pain and hypothesize that he has appendicitis. We acquire data to test that hypothesis by doing a complete blood count and finding that he has an

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elevated white blood cell count. This is a common finding in appendicitis, but it is very nonspecific.; any inflammatory condition can elevate the white blood cell count, like a kidney or bladder infection, diverticulitis, pancreatitis, etc. We are partially reassured by the elevated white blood cell count, but a more specific test would be needed to be reasonably confident. This would necessarily include a urine analysis result that is not consistent with a kidney or bladder infection, and normal liver and pancreas testing, but even then, we would want more specific positive information about the appendix. This is typically achieved by a CT scan or an ultrasound that can look at the appendix directly and tell whether it is inflamed. Each of the abovementioned tests has certain test characteristics with regard to the diagnosis in question. These are generally referred to as sensitivity and specificity. Sensitivity is the positivity in the presence of the disease, whereas specificity is negativity in the absence of disease. In addition, the test characteristic of the predictive value rounds out the statistical parameters of the test with regards to the diagnosis in question, as shown below: T+ TD+ TP FN Sensitivity is TP/TP + FN D- FP TN Specificity is TN/TN + FP PPV (Positivity Predictive Value) is TP/TP + FP PPN (Predictive Value Negative) is TN/TN + FN TP= true positive FP= false positive TN= true negative FN= false negative By using these statistical parameters, one can close in on a diagnosis by sequentially applying the tests, striving for a high enough probability of disease that it becomes evident. However, it is important to note that in most circumstances increasing sensitivity decreases specificity requiring a multistage approach of sensitive testing followed by specific testing. Of course, it is a lot more complicated than that. The tests may not be independent and treating them as such will increase the final probability more than it should. Also, all tests have limitations beyond their accuracy with regards to a given diagnosis, since they may have some unreliability or even bias. What we mean by “reliability” is test-to test-variability, and what we mean by “bias” is systematic distortion of results. Finally, the point in the diagnostic evaluation at which we start to treat is very variable and

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subject to judgement. For example, if the diagnosis requires surgery, we might demand a higher probability of disease than if it was a matter of giving antibiotics. For these decisions, we often turn to decision analysis, which we will discuss later. Incidentally, statistical analysis of observational and experimental studies can often be analyzed in a similar manner. S+ SH+ TP FN H- FP

TN

H+= hypothesis is true H-= hypothesis is false S+= study results are positive S-= study results are negative FP in this context is a type 1 (or alpha) error, which we minimize by reducing the probability to less than .05 or .01 FN in this context is a type 2 (or beta) error, which we minimize by reducing the probability to less than .2. Here again, efforts to reduce type 1 errors often result in increased type 2 errors and vice versa. For more complex analyses where we are constructing scales, criteria of validity must be fulfilled, including face validity (does the scale appear to be representative of the entity in question?), content validity (does the scale embody all of the features of the entity in question?), criterion validity (does the scale match a known variable associated with the entity?) These scales are abundant in rheumatology to measure disease activity in many, if not most rheumatic diseases, but they are also prevalent in other disciplines as both diagnostic and therapeutic criteria. To give examples, the Jones Criteria for Acute Rheumatic Fever, Wells Criteria for Pulmonary Embolism, SF 36 for quality of life, and so on. In theory, no matter what the objective of the study is (whether it be a diagnostic evaluation, a disability assessment or a quality-of-life estimate), the task at hand could be performed algorithmically. That is, a set of rules could be established to make the inferences without a judgmental process. However, one would need to know all of the test characteristics and how they interact with each other. For example, in the appendicitis situation, elevated white blood cell count is linked to elevation in blood (serum) proteins involved in inflammation, like the c reactive protein. The two assays - white blood cell count and c reactive protein - are not independent, and their interdependence

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depends on the patient and his or her disease. These characteristics are rarely (if ever) known, so the use of these tests in conjunction with each other leads to a judgement about how much each one contributes to the overall diagnostic accuracy. Thus, the process has some uncertainty even if each test is well characterized. How well algorithms perform in this environment depends on the diagnosis in question and the tests being considered. At present, algorithms are useful for some very simple problems like urinary tract infections, but not for more complex problems. In this sense, clinical medicine is different from predicting whether job applicants will be successful, certain political candidates will win, or the appropriateness of judicial decision. All these are examples of where simple algorithms are more accurate than expert opinion. However, clinical medicine has a great deal of objective information available to doctors, and their expert opinion performs better than algorithms. This is fortunate for patients, since expert opinion regarding elections is notoriously unreliable. The caveat is that recent experiments with large language models such as Chat-GPT indicate that they can - and do - perform as well as physicians. Sometimes, they do so even better.

CHAPTER 14 THE PRACTICE OF MEDICINE AND THE SCIENCE OF MEDICINE

John Snow As described above, the practice of medicine uses the same inferential processes, as well as modes of inquiry as the science of medicine. The same can be said for all the practical trades such as automobile or bicycle repair, electricians, plumbing, and so on. All of them are primarily hypothesis driven. You have an idea of what is wrong and then try to prove or disprove it. As previously mentioned, cardiologists and urologists occasionally refer to themselves as plumbers. Of course, what differentiates these trades from scientific inquiry is that they work within a framework of known facts, whereas scientific inquiry seeks new knowledge. In fact, scientists often refer to mundane observations as “not contributing new knowledge.” That by itself isn’t enough to say that something isn’t science because it validates the existing paradigm, because confirming existing knowledge is an essential part of the scientific enterprise. However, science hinges on observations that are either experimentally generated, or novel observations on natural phenomena in the hope that the results will shed new light on the process. When the observations reaffirm the existing paradigm, they are still science, but it is less interesting and less informative than an observation

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that changes the view of the process in question. The practice of medicine in this sense is not science, but much more like a trade. That isn’t to say that inventiveness isn’t part of the practice of medicine, since more knowledgeable and creative clinicians can often find syntheses that others have overlooked – a process that is sometimes referred to as the art of medicine. However, the practice of medicine may show results that are difficult to understand with the present knowledge about a condition, but it still isn’t science in the sense of purposely seeking new knowledge. The exception to this is when, in the course of clinical care, observations are made or interventions are executed that generate new knowledge about a pathological condition. Case reports are typical examples of this, where the case in question illustrates something novel about the clinical problem. The paradigm for this is the aphorism “bench to bedside to bench.” “Bench to bedside” implies the translation of scientific discoveries to the care of patients. Meanwhile, “bench to bedside to bench” indicates that the process can go in the opposite direction; in other words, observations made at the bedside can inform the science underlying the illness in question. Thus, the practice of medicine contains features that are similar to scientific inquiry, but it differs in other ways. Chief among these differences is the absence of a purposeful seeking of new knowledge, and the need to care for patients under variable degrees of urgency, which is unlike scientific inquiry (aside from the need to fund the studies through grants). New knowledge can be generated through the practice of medicine, such as new manifestations of existing diseases or new consequences of a pharmacological agent, but this is not achieved purposefully. In addition, it is clouded by the liberal use of scientific disciplines such as biology, genetics, pharmacology, pathology and biochemistry, all of which form the basis for preclinical medical education. These disciplines have a knowledge base that forms the foundation of the practice of medicine. For example, drugs given for a condition depend on the pharmacokinetics of the medicine, the biochemical function of the compound and the host biochemical environment that makes the drug effective. The same can be said for any other intervention, whether diagnostic or therapeutic. Medical schools typically employ legions of scientists within their faculty in order to advance knowledge in these areas, and on occasion, clinicians also engage in the pursuit of new knowledge, either in the laboratory or as clinical investigators. Of all of these disciplines, the one that is unique to the practice of medicine is clinical epidemiology. Clinical epidemiology is as old as the practice of medicine itself, and is based on observations of the natural history of diseases and their response

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to therapy. Dating back 3000 years in Western tradition, Hippocrates made critical observations of this type. He recognized many disorders, attributed names that are still used, such as “diagnosis,” “prognosis,” “mania,” “therapy” and a host of others, and also contributed a few therapies such as colchicine for gout, valerian root for anxiety and insomnia, St John’s wort for depression, and others. These observations require inferential reasoning and empirical validation and, thus, are clinical science. This is not to discount the enormous contributions of Asian (particularly Chinese) and Islamic Medicine, which also reflect rigorous observation and experimentation. More formal applications of this type of reasoning evolved through subsequent centuries, often as a consequence of the results of herbal medicine for a large array of conditions. A more recent example is the use of foxglove extract (digitalis) to treat heart failure, as introduced by William Withering in the 1700s. Another seminal event in medical science occurred in 1854, when John Snow discovered the cause of a cholera outbreak in London based on the geographic distributions of cases, which correlated to the distribution of water from one of two major suppliers to the city. The one in question drew its water supply from the Thames downstream, where it was contaminated with human waste, which distributed the cholera bacillus to the population it supplied. The iconic act of shutting off the water pump from the Lambeth Water Company, thereby eliminating the source of the epidemic, is said to be the birth of modern epidemiology. Interestingly, this technique of identifying a possible pathogen by the geographical distribution of cases is still used, and was critical to the discovery of the cause of Lyme disease. In 1975, a small (5 patients) outbreak of juvenile rheumatoid arthritis in the town of Lyme, Connecticut was recognized by the mother of one of the children. Thinking this rare disease shouldn’t have happened in this many children, she sought guidance from physicians at Yale (Alan Steere and Stephen Malawista – both rheumatologists), who used the same technique as John Snow, placing pins in a map of the area and identifying that cases were clustered adjacent to a forest preserve. The investigators reasoned that it must be a transmissible agent related to the wildlife in the preserve. Eventually, the spirochete was identified by Willi Burgdorf and named Borrelia Burgdorferi, transmitted by the black legged tick Ixodes scapularis, whose common hosts are deer and mice - both of which are abundant in the forest preserve. Thus, again, a major disease was discovered by the use of the techniques of clinical epidemiology. More recently, the same techniques were used to identify the pathogen of

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our current pandemic, conventionally referred to as COVID. The pathogenic agent is a corona virus of the same family as about 30% of common colds, but this virus, SARS CoV-2, was identified on 2/11/2020. The origin of the virus is still hotly debated, but it appears to have come from a bat virus that infected an intermediate host, then transmitted to humans through sale of said intermediate host at a “wet market.” The specific intermediate host is also debated and could be a civet cat or a pangolin, both of which are sold as food at the Wuhan market, but some investigators think that it was created in a viral laboratory and accidently released. Either way, the techniques of epidemiology are key in the investigation of many infectious diseases. They are also used for non-infectious disease to track down possible exposures that result in diseases. Benzene as a cause of acute myelogenous leukemia, cigarette smoking as a cause of lung cancer, eating polar bear liver as a cause of vitamin A toxicity, and innumerable other examples of non-infectious agents that cause disease have been tracked down by epidemiologic techniques. We will explore this in more detail in the next chapter.

CHAPTER 15 HEALTH SERVICES RESEARCH – THE SCIENCE BEHIND CLINICAL MEDICINE

James Lind Clinical medicine, including the practice of medicine, utilizes all the relevant sciences to support the analysis of patient problems. This is obvious with regards to biology, but chemistry (especially biochemistry), molecular biology, genetics and a host of other disciplines are also utilized. The way medicine is practiced is vastly different in different settings. In fact, the Dartmouth Atlas details practice variation across the country. It was initiated by the observation that tonsillectomy rates differed several folds in very close geographical communities, probably due to training variation and the availability of ear, nose and throat (ENT) doctors for children. This has been extended to many areas, one of which is end-of-life care, which is very expensive in New York and less so in rural communities. The impact of

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malpractice suits is likely a contributor to this. Variation in the US is nothing compared with the variation between countries, particularly between developed/developing and so-called third world countries, which lack the resources necessary to conduct modern evaluation and treatment. But in all geographical locations, no matter the resource availability, the reliance on basic scientific disciplines is paramount. However, the practice of medicine has its own scientific discipline, known as Health Services Research, which encompasses epidemiology (especially clinical epidemiology), health delivery science, medical decision-making (which in turn encompasses decision analysis), game theory, cost-benefit and cost-effectiveness analysis, and related procedures. Each one of these areas is a discipline in itself, each with its own specialist textbooks to which you can refer. However, as a brief introduction, we will outline some of the major features of clinical epidemiology that impact the mainstream of our discussion. We will leave decision analysis, economic considerations and game theory for subsequent chapters. Epidemiologic approaches fall into two categories - observational studies and interventional studies. Observational studies come in three forms, depending on the timeframe at issue – retrospective, prospective and cross sectional. Typical association studies are cross sectional. If you want to know if obesity is correlated with gout, for example, you might study obese patients and control patients with a normal BMI, and look for the prevalence of gout. If you want the incidence of gout, you need to do this study prospectively. Ideally, this is by following a gout-free population of obese patients and a control group with normal BMI without gout, then calculating the occurrence of newly diagnosed gout in both populations. A retrospective approach to this same issue is to study gout patients and non-gout patients, then calculate the relative rate of obesity in each population. All of these approaches are viable, but they give somewhat different perspectives on the problem. In addition, each approach has its own statistical methods. In one case, you are using relative risk; in another, hazard ratio, and in another, odds ratio. There are deep mathematical reasons for these differences, but they are beyond the scope of this discussion. Standard statistics texts go into detail about these and many other related issues. Interventional studies primarily take the form of clinical trials. The first of these was conducted by a Scottish surgeon, James Lind, in the Royal Navy. He was curious about the high frequency of scurvy in sailors, which was a mostly fatal disease at the time. He divided 12 sailors suffering from scurvy into 6 groups of two. Group one was given cider, group two a small dose of

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dilute sulfuric acid, group three got vinegar, group four got seawater, group five got two oranges and one lemon, and the last group were given barley. Only group five, the citrus fruit group, recovered, although the cider group did a little better than the others. While randomization, blinding, and a host of other innovations lay ahead, this was a remarkable advancement in medical science. Trial design is a field in itself, and its complexity is mirrored by the complexity of the planned statistical analysis. Fundamentally, trials compare an intervention with a control group for a primary outcome, with a range of secondary outcomes typically enumerated. The outcome can be assessed at a point in time (so-called “landmark analysis”) or against some form of longitudinal outcome, such as a life table or survival analysis. Trial design depends to a large extent on the question at hand, but also takes into account practical aspects such as the number of participants available, the budget for the trial, the number of centers involved, and projections on the relative effectiveness of the intervention that, in turn, informs sample size calculations. Many trials go astray because of one or another of these considerations. In fact, it is a rare trial that gives clear unequivocal results. In rheumatology, the infamous rituximab trials for systemic lupus (Explorer and Lunar) were both failures when, in fact, the drug is highly effective. The conventional wisdom is that the control group received a standard of care that was so effective that the margin for improvement was minimal. The recent trial of anafrolimab for lupus was negative initially (Tulip 1) and only when the outcome measurement was changed in Tulip 2 did the drug achieve statistical significance over the placebo. Clinical trials are divided into stages. Preliminary investigation (stage or phase 1) of a drug for a disease is an open labelled, non-controlled foray into the safety and efficacy of a compound in a small number of healthy volunteers. A stage or phase-two study involves assessing the kinetics of the drug to determine its half-life and any safety signals in patients. Stage or phase 2 b is a controlled trial for preliminary efficacy, and stage or phase three is a registry trial to determine the safety and efficacy of the drug for the disease in question. This trial is large, randomized, controlled and double-blind (both the investigator and the patients are unaware of the allocation of the drug). It is often done in collaboration with the Federal Drug Administration (FDA), which will analyze the data from previous trials and determine what parameters they will accept for the licensure (approval) of the drug for that disease. These trials often cost millions of dollars which, in conjunction with the cost of the research, generates high prices for new drugs. Often, there is a stage or phase four, which is called a

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post marketing survey, the goal of which is to determine rare side effects of an already approved drug. There is much, much more to say about this process, but it is beyond the scope of our discussion. As a general rule, clinical trials are rather crude measures of the effectiveness of interventions. The vast majority of useful drugs have not been shown to be more effective than placebos in clinical trials for the particular situation for which they are commonly used, simply because they have not been evaluated in a clinical trial for that indication. A drug is licensed based on clinical trials for a particular condition, but not for all the conditions for which it is used. That is part of the reason that a drug is licensed for an indication by the FDA, but once licensed, it can then be used at a physician’s discretion for other indications regardless of evidence (as long as it can be paid for, which means insurance company approval in most circumstances). It costs an enormous amount of money to support the trials necessary for FDA approval. Recent examples include diabetes drugs, which have been repurposed for obesity. In fact, the whole notion of repurposing available drugs was a field in itself for treatment of SARS CoV2 (Covid). Since drug approvals coincide with patent protection, the lifetime of a drug as a brand name is limited, and many successful drugs are then recreated as biosimilars (highly similar copies of the original drug) once the patent runs out. However, to get biosimilar designation, the new drug must be shown to be identical to the parent (patented) drug. Real clinical science is conducted when a drug that has already been approved for one indication is tested for a new disorder. So, both the original studies and any derivative studies are designated as clinical science, using methodology from clinical trial design and analysis.

CHAPTER 16 KNOWLEDGE AND BELIEF

Rene Descartes Epistemology is the study of knowledge, but what is knowledge? The conventional answer is “justified true belief ...” Let’s dissect that. Justification is the act of providing evidence for a claim. Is this relevant to the concept of knowledge? Wouldn’t it be better framed as verified true belief, since justification is strictly in the eyes of the beholder? What counts as justification for one observer, may count as totally irrelevant to another. The argument for something being justified lies in the notion that knowledge is a personal attribute. My knowledge is not your knowledge, unless it is shared knowledge. But is that what we want to achieve? In a sense, knowledge is personal, but in another sense, it is independent of the observer. It should exist on its own, or else why would we bother with references like Google or encyclopedias? The knowledge with which we are most concerned is knowledge that can be shared and agreed upon by multiple observers - not the inner private thoughts of an individual. In this broader sense, verification (or at least confirmation), as Ronald Reagan pointed out, is a critical portion of the claim to knowledge. This is fine, but then, what about verified true belief? This indicates that a person who has a claim that can be externally validated is entitled to then state that he or she has knowledge.

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What, then, does this formulation do to the Gettier problem, which we touched on in the introduction? If you recall, Gettier pointed out that a justified true belief is not enough, as your justification might be erroneous and lead to a false conclusion. You saw someone open your mailbox and a US mail truck on your street. You conclude that the mail was delivered. You are wrong, as the person opening your mailbox was putting a flyer in, not the mail. You were justified in your belief, but it was erroneous. So, how about our formulation of verified true belief? You saw someone open your mailbox and you saw a mail truck on your street. However, while you might have been justified in believing the mail was delivered, you would be wrong. In contrast, you would not have been wrong if you had verified the delivery or lack thereof by examining the mailbox and finding a flyer, but no mail. In fact, the mail truck whizzed by to the houses on the other side of the street before returning to your side to deliver your mail. Of course, this simply kicks the can down the road, as you now have to decide what does and does not constitute verification. In a sense, it is like the logical positivist approach to scientific inquiry, since what you are claiming as knowledge is the same as claiming that a scientific hypothesis is true. This is the problem that led Popper to claim that all hypotheses are tentative, and only valid until they are shown to be false by contradictory evidence. The ability to verify or confirm a hypothesis is an essential part of scientific inquiry and separates science from competing world views, such as astrology, which was very widely accepted in the prescientific era (even Newton believed in astrology). Even today, claims in psychoanalysis are difficult to reconcile without a process to verify them, and for this reason and others, they have gone out of favor. Unfortunately, that doesn’t get us very far since we need a hypothesis to begin with. Where hypotheses come from is still a mystery. They are clearly generalizations that derive from an inductive inference, but how they arise in the first place is unclear. Nevertheless, when we have a hypothesis, flimsy evidence is better than no evidence, and hypotheses sit on a spectrum from pure guesses to highly substantiated claims. There doesn’t appear to be a rigorous way to quantify them, so we are stuck with some knowledge that is very speculative and some knowledge that is convincing. If the standard for knowledge is truth in some absolute sense, then all of what we call knowledge is speculative. However, this is at odds with how we use the term, since we commonly distinguish between knowledge and guessing. The testing of a hypothesis by whatever means separates knowledge from speculation, even if there is some latitude on what constitutes verification, or its weaker version, confirmation. Of course, the whole verification

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business can be taken to extremes as Descartes did when he claimed that the only thing, he knew for sure was his ability to doubt; therefore, he must exist. This gateway to solipsism (the concept that only one’s mind is certain to exist) is a dead end and not commensurate with how we function in the world. Are there instances where one knows something to be true, but doesn’t believe it? The death of a loved one may be an example, but on deeper reflection, that is a shabby form of knowledge when someone, purely on the strength of their belief, will seek additional information about the veracity of the “knowledge” by consulting detectives or palm readers to verify the truth of their dearly departed. I think one can say with confidence that if someone truly knows something, they believe it as well. Any deviation from this is more of a playful interpretation of what knowledge entails. This is the use of knowledge as it applies to a claim, not knowledge of how to do something. The latter is a totally different use of the word, although both are a product of learning. Without stating the obvious, the difference between belief and knowledge is illustrated by a real occurrence. For example, my daughter arranged to go to Morocco for an immersion course in Arabic while she was in High School. A single young woman traveling alone in Morocco is dubious, to say the least. I addressed the situation by purchasing a fake wedding ring for her, which was very effective as a deterrent to amorous males. They believed she was married and their belief was justified by the ring and her traveling alone. The fact that she was 16 or 17 was irrelevant in their minds, since many girls are married as soon as they reach their teenage years in Morocco. Anyway, it was very effective and she was not hassled at all. But what about knowledge that can’t be verified, such as perceptions? This form of personal knowledge is a different entity from the knowledge required for human interaction and progress of society. It is not only unverifiable, but undeniable, and simply has to be taken at face value. That is why physicians have so much trouble when they encounter patients who claim to be in excruciating pain, yet go about their daily activities without restriction. This morning, for example, a parent messaged me about her teenage daughter, who claimed to be in 10 out of 10 pain all weekend despite having fully participated in three lacrosse games. Telling her that she couldn’t have been in that much pain if she could play such a demanding sport would do nothing to resolve the issue. This is a type of knowledge that doesn’t lead to testable or verifiable conclusions. Private and public knowledge are very different forms of knowledge, and should be treated

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differently. Claims for the verification of private knowledge are uniformly unsuccessful and should not be sought as a general rule. Another form of knowledge is that which requires no verification. Tautologies, definitions, mathematical truths, and logical truths fall into this category. Whether there is an observer claiming this knowledge or not is irrelevant, since the statements stand on their own without need for any verification or justification. Whether this form of knowledge achieves truth is dependent on the structure from which it has arisen. In mathematics, it might be derivations from axioms, or just from the rules of inference. Logical knowledge has the same characteristics, and definitions and tautologies achieve this through the concepts themselves. In summary, the definition of knowledge is “verifiable beliefs” for the most common use of the term. The exceptions to this are private knowledge, which is unknowable, and definitional knowledge, which is true independent of an observer. None of these versions of knowledge guarantees that it is truth or even certain, but the closest is the third sense (true by definition), where the knowledge is as close to certainty or truth as possible. Then again, even this is subject to dispute. For example, the law of the excluded middle is true by definition in classical logic, but is not accepted in intuitionist schemes. Private knowledge is also not always the case. Have you heard someone say “I thought it was (name, color, sensation, voice)” but then admit that they were mistaken? If truth is defined as impervious to doubt, then there is no truth whether private, public, or definitional. Philosophers have a lot more to say about this topic, including distinctions of knowing, but they do not have a bearing on the fundamental problem of “what is knowledge?” A most troubling aspect is the issue of faith, where beliefs have no evidence and yet believers claim knowledge. Belief in God and other articles of faith are best considered private knowledge, and unassailable by evidential arguments. These are also good examples of the difference between belief and what we call public knowledge, since they are unverifiable.

CHAPTER 17 TELEOLOGY AND NATURAL SELECTION

Charles Darwin Teleology is the now largely defunct notion that the function of any entity is a consequence of it purpose. For example, “the sun is there because it is needed to grow plants” or some such nonsense. Asking what the purpose of something is gets at its function, but the purpose is not causally related to the function. The purpose of the heart is to pump, and thus circulate, blood. No argument there. However, implying that the heart exists for that purpose implies a willful action that generated a heart so that it could provide that function. As a heuristic, biologists sometimes look for explanations of a particular structure in its function, but they do not attribute this to purposeful action. This is one of the few things Aristotle got wrong, although one can argue that natural selection is a kind of teleology. However, if function is the primary actor in this scenario, it implies a primary mover, hence a rationale for God. Teleology was used as a justification for the Deity by many observers, including St Augustine, whose argument for the existence of God is predicated on the need for a prime mover. Even when we look to more modern examples, such as the Newtonian concept of the universe as a Swiss watch, there is an implication that there must have been a watchmaker around to have made it, or at least someone to wind it up. This is the basis for the most celebrated defense of teleology - that of William Paley, who described a hypothetical scenario in which he discovers a watch while walking on a beach. Knowing that its purpose is to tell time,

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he dissects the complex mechanism and concludes the watch must have had a designer to construct it for the purpose of telling time. He thus argues that the universe is much more complex than a watch; therefore, the designer must have been much greater - hence the existence of God. But how good is this argument? Well, for one thing, the analogy between a watch and the universe is quite a stretch. Furthermore, we have alternative explanations including stochastic models of the universe and evolutionary models for the development of life. Chief amongst these is natural selection, with the selection being dictated by “survival of the fittest.” There is overwhelming evidence that natural selection as enunciated by Darwin is a major influence on the observation that, for the most part, (appendixes are an exception) the structure of a biological organism is tailored to its function. In other words, form follows function, as opposed to form following purpose. Of course, nothing is so simple and there is complexity in the genetic selection process, including some rather Lamarckian aspects, such as the influence of the female on her offspring through epigenetic mechanisms. Sometimes, survival of the fittest leads to some “unintended” consequences. Take for example the genetic disease, familial Mediterranean fever. This is caused by a mutation in a gene that codes for a component of the immune system; specifically, the MEFV gene that codes for a protein called pyrin, as identified in a triumph of molecular biology. Recent data suggests that the mutation confers a selective advantage to individuals possessing this mutation, when they are exposed to a disease that used to be rampant in the Mediterranean basin: bubonic plague (AKA The Black Death). So, these individuals that possess the mutation will survive bubonic plague, but at the expense of recurrent episodes of fever that eventually lead to a fatal condition called amyloidosis. Survival of the fittest doesn’t imply that people don’t act in a purposeful manner. Of course, most of our actions are purpose driven, whether work or play related. This extends to our pets, who remind us in no uncertain terms when they are hungry and, furthermore, to the actions of many other sentient beings. However, it is one thing to attribute a dog begging as an attempt to get fed, and quite another to look at paramecium under the microscope and infer that their motion is dependent on purposeful activity. The difference is the ability to perceive and feel things, but more than that, it is the ability to translate those perceptions into meaningful actions. A person or a pet would satisfy these criteria, but a paramecium or a bacteria would not. The distinction is blurry, but while a sea anemone and an octopus might both withdraw from a noxious stimulus, we would typically attribute the octopus’s actions to purposeful behavior, and the anemone’s as mere reflex.

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Alternatively, attributing all of our actions to purposeful behavior is a mistake. Motor tics, muscle spasms, reflexes and the like are not purposeful. A mistake that is occasionally made in the ICU is to attribute all facial expressions to voluntary behavior. Grimacing, withdrawal and other involuntary movement, for example, are not necessarily purposeful or consciously directed. A modern form of teleology is the anthropic principle. The anthropic principle states that the parameters of the universe must be such that life is possible. A stronger version of the anthropic principle claims that the most likely theories should be those that are the most favorable to the advent of life. While many physicists are believers it seems only viable in a very general sense that life forms do require some structure of the environment they arise from. However, alternative life forms exist even on our planet such as organisms on the sea floor that require no oxygen and others that are sulfur based rather than carbon based. Isn’t it more reasonable to think that life forms adapt to the environment they face. The constraints are on the organisms not on the environment they reside in. In other words tailoring a theory of the universe to fit existing life forms imposes is a form of teleology rather than life forms adapting to the structure of the universe which fits better with survival of the fittest.

CHAPTER 18 REDUCTION

Bertrand Russell While all biological processes are based on chemical reactions and all chemical reactions are based on physical properties, it is incorrect to assume that we can “reduce” them to these basic principles. There are two problems with reduction. First is that there is uncertainty surrounding how basic processes explain more complex phenomena. How quantum mechanics results in atomic physics is not completely understood, and the same goes for atomic physics and chemical reactions. The second issue is what has been termed “emergent properties.” The idea is that complex systems give rise to phenomena that are not explained by the basic processes. A good example of this is consciousness. While wakefulness can be explained as neural activity that is well described, consciousness cannot, and represents an emergent process that cannot be reduced to neurobiology, at least at present. Emergent processes are not limited to biological entities and can be exhibited at every level of complexity in both natural and artificial systems. For example, the new chatbot Chat-GPT exhibits emergent properties that are somewhat surprising and disconcerting. Chat-GPT seems to understand empathy and civility without obvious prompting. In any case, reductionism like teleology is an interesting but debunked approach, in spite of the efforts of some of the most brilliant thinkers, such as Bertrand Russell, who tried

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to reduce mathematics to logic. In fact, there are many fields within mathematics that have little or nothing to do with each other, such as calculus, topology, number theory, etc., so reduction isn’t even an option. Lastly, many disciplines have additional motivations, constraints, purposes and other features that make reduction impossible. A good example is the inability to reduce medicine to biology, as we mentioned in Chapter 12.

CHAPTER 19 REFLECTION

Fredrich Nietzsche Reflection is a cognitive process that requires introspection, memory and inference in an awake and conscious individual. We typically reflect on past events, either for enjoyment of the pleasure they give us, or for problemsolving purposes. This process is frequently referred to as self-reflection, as it emphasizes the internal nature of the events. However, unlike some internal cognitive processes, these thoughts can be recounted to an external observer and, by doing so, individuals may even clarify their thought processes. In medicine, telling the case history of a patient to a colleague or student is a typical use of self-reflection that can sharpen, clarify and illuminate the problem or problems. Much of the inferential work of problem-solving in medicine and other cognitively demanding disciplines is achieved through self-reflection. Self-reflection can generate new ideas about an event, a situation or a problem. This phenomenon of generating new insights by self-reflection is akin, if not identical, to the concept of emergence, where a new concept is generated from existing information. Emergence, as we mentioned previously, is a phenomenon of complex systems, whether biological or chemical, physical or computational, in which novel concepts arise in an unpredictable way. Reflection is entirely different from abstraction, which involves generating a concept from an observation. Rather, it is wholly dependent on memory for the substantive basis of the actual act of reflection. However, both abstraction and reflection are crucial cognitive processes in order to generate hypotheses. Much of Nietzsche’s work involves reflection and the act of reflecting is, in his view,

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necessary to understand ourselves, others and history. His famous phrase “that which does not kill us makes us stronger” is a plea to reflect on the most poignant events in our lives, in order to learn and grow from them.

CHAPTER 20 CONSCIOUSNESS

GW Leibniz Consciousness is not just wakefulness, since one can be awake without conscious activity. In fact, it is not at all clear what it is, as evidenced by a famous wager between a philosopher and a cognitive neuroscientist being settled in favor of the philosopher, who had bet that in 20 years, the riddle of consciousness would not be solved by a biological explanation. He was right. Whereas, philosophy of mind has a long and fruitful history, what these concepts are on a biological level, is still unclear. Certainly, wakefulness is a requirement of conscious cognitive activity, but cognitive activity also occurs during sleep, although it may be of variable value to the dreamer. Many dreams are incoherent and sometimes incomprehensible, but they are occasionally productive. Several nights ago, I fell asleep with a computer problem that threatened this entire project. Microsoft Office wouldn’t work and I could not figure out why. As you might expect, I was very disturbed by this, since I only had a very old version of this manuscript on a thumb drive. I woke up at 3AM and knew that I had to uninstall Microsoft Office, then reinstall it. In fact, I was actually unable to do that, since I was locked out of the software, but I took it to a computer shop and they did just that by overriding the hard stop. I was then able to purchase the software suite and reinstall it. The message here is that cognitive activity in sleep can be purposeful, though in my own experience, this is rare.

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By and large, we limit reflection of a purposeful sort to conscious activity, although daydreaming is sort of an in-between state of non-purposeful but, in some sense, productive reflection. Perhaps it is similar to the concept of life flashing before you in your dying state, which has some neurobiological correlations. Meditation may also reside in this in-between state of wakeful, but not clearly conscious activity. When they refer to cognitive activity, most people are thinking of wakeful, conscious, purposeful cognitive activity; however, these other states such as dreaming, meditation, daydreaming, the dying experience, and perhaps others should widen our appreciation of the many states of mind of which we are capable. For centuries, philosophy of mind was caught up in the question of the mind-body problem. Some thought that they were two different things; thus, the notion of dualism emerged, while others thought that mind arose out of brain activity. Most people believe the latter and give evidence for this in terms of physical representations of mental activity. There are fMRI (functional magnetic resonance imaging) correlations of thought processes, as portions of the brain are devoted to certain tasks, such as the occipital lobe for visual processing, the amygdala for emotional states, etc. While we are a long way off from being able to “read people’s minds,” we are much further along in this endeavor than we were even 10 years ago. There are even some ongoing attempts to insert thought processes into recipients using electrical and magnetic stimulation. Seizures are an interesting example of the brain’s effect on the mind. Patients with seizures often have premonitory sensations, called aura, which are clearly mental processes with neurophysiological origins. They can be auditory, visual or olfactory, and are just as real to the patient as if the sensation had occurred through environmental stimuli. This also answers the question of where sensations reside. Clearly, the answer is in the brain, so when doctors say, “it’s all in your mind,” they are undoubtedly correct. Unfortunately, that dismissive message totally misses the point that all sensation, whether originating in the environment or internally, is a function of brain activity. Another question in the philosophy of mind is whether other animals or machines can think. Anyone who owns a dog can testify to them being quite capable of complex thought, whether it is problem-solving, their ability to read your emotional state of mind, or their amazing ability to predict seizures when trained as a service animal for diabetic patients. As for machines, the famous Turing test was quashed by John Searle, who constructed a gedanken experiment called the Chinese Room, where a machine would translate from English to Chinese or vice versa and appear to be thinking. Thus, the Turing test is not sufficient to ensure that a machine

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can “think;” however, the line is significantly blurred by Chat-GPT 4, which responds in a very thoughtful and human-like manner, even to the point of displaying self-doubt, formulating charming and engaging responses, and being self-deprecating. The use of this rapidly evolving technology is so explosive that it is threatening to some knowledgeable observers. For example, a robot armed with sensory apparatus that could feed visual auditory, olfactory and touch data with the ability to self-program and selfpreserve could be a formidable comparator to human behavior if equipped with a large language program like Chat-GTP 4. In fact, Chat-GPT 4 itself certainly passes the Turing test, but it goes beyond “appearing” to behave like a human to being a creative cognitive entity that can synthesize data in novel ways that emulate human intelligence.

CHAPTER 21 MATHEMATICS

Pythagoras Probably the most troublesome area of epistemology is the analysis of mathematics. Certainly, mathematics may be considered a language, since symbols used in mathematical statements stand for concepts that could be described in a different language. Typically, mathematical statements are explained in English to familiarize the reader with the concepts being expressed. However, there is much more to mathematics that sets it apart from other languages. Most importantly is its ability to solve problems. In mathematics, this involves using operators and variables, as is commonly taught in elementary algebra. In fact, most individuals are familiar with at least four different types of math. Perhaps that’s why the British expression is “maths,” which highlights the notion that mathematics is not one entity, but numerous different conceptual schemes. Algebra, arithmetic, trigonometry and geometry are separate disciplines commonly taught in elementary and high school. What links them is the many features they have in common, including: 1) 2) 3) 4) 5)

They are formal languages They use symbols to stand for concept and entities They have operators like addition, subtraction, multiplication, etc. They are used to solve problems They start with assumptions, often called axioms, which are considered self-evident and indisputable. All results derive from, and are dependent on these axioms

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To reiterate, different mathematics have different symbolism, different variables and operators and, most importantly, different assumptions (i.e., axioms). All mathematical truths derive from the use of these tools, and from the axioms that are assumed to be true. These axioms are considered to be intuitively true or, using Kant’s nomenclature, a priori true. Herein lies the crux of the matter. If the axioms are indeed a priori true, then everything that logically follows from them is also true a priori. To put it another way, they are true in all logically possible worlds. Any world that obeys the assumptions of arithmetic will comply with the valid statements in arithmetic. For example, 1+1 will always = 2, or a triangle will always have vertices whose angles add up to 180 degrees. This sounds reasonable and impossible to argue with, leading some logicians, mathematicians and philosophers to a vision of mathematics that is Platonic. Think of Platonism as stereotyping or profiling; i.e., as an abstract conceptualization. These are abstract entities that capture the majority of what we consider to be essential for a concept, but the reality often differs from the idealized version. For this reason, stereotyping and profiling have a bad reputation, although they are commonly used heuristics. What is meant by Platonism in mathematics is that the rules are the same as those that govern the universe, and that in this sense, numbers are real entities. By extension, mathematicians discover mathematical truths; they do not create them. Opposing this is intuitionism, which claims that mathematical statements are mental events and not real in a Platonic manner. In fact, intuitionists do not accept any of the axioms of arithmetic or even logic, so the law of the excluded middle (PV-P) goes out the window. A variant of intuitionism is constructivism, which agrees with the mental aspect but accepts the truth of statements that conform to the precepts of the mathematical construct. So, in this case, the axioms of arithmetic. Overall, I think the Platonic approach is mistaken in many ways, even if the majority of mathematicians hold it to be correct. First, axioms are not a priori true; they are assumptions from which we derive conclusions that are true in relation to the assumptions made, but are not true in all possible worlds. Think of non-Euclidian geometry, which is used to describe space time in a manner that is much more accurate than Euclidean geometry. Even the assumptions of arithmetic are subject to considerable controversy. Second, what does it mean to be real in a Platonic fashion? Plato’s analogy of the cave asserted that shadows were assumed to be real until the cave dwellers were released and realized that they were representations of material objects. How does that correlate with a Platonic vision of numbers? Presumably, numbers are the shadows that stand for concrete objects, and

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not real themselves. Rather, they are symbols that represent real objects when one is using arithmetic to count objects. Another version of the Platonic vision is that all material objects are instantiations of a perfect version of the entity in question. Thus horses, which all look different, are all defective versions of the perfect horse. In this version, numbers would be the perfect representation of countable objects, but there is no further claim that the numbers are the real entity and the objects being counted are illusional. The claim is just that to manipulate the concept of a number, one needs to abstract it away from the objects being counted. In either Platonic conceptualization, numbers themselves are not “real” entities, but symbols to be manipulated under the rules of the type of math with which you happen to be working at the time. The universe is not filled with numbers; it is described by them, more or less accurately. Third, in her book, “Are Maths Real? by Eugenia Chen (a mathematician), she suggests that numbers are as real as Santa Claus. Regardless of the analogy, Santa Claus is a myth; the only thing real about him is the imagination of the children who believe in him. So, if mathematics is like Santa Claus it detracts from the objective nature of numbers that characterizes the Platonic vision. Fourth, even the logic underpinning arithmetic is fraught with paradoxes that derailed Russell and Whitehead’s attempts to ground it in logic. For example, the set of all sets that don’t contain themselves is similar to the liar paradox of Epimenitides the Cretan (remember him from earlier?) Fifth, Gödel's incompleteness proof showed that no set of axioms could account for all the true statements in arithmetic, or else they would generate contradictions. Peculiarly, in spite of his incompleteness theorem, Gödel himself espoused a Platonic version of mathematics. How can a system that is either inconsistent or incomplete be commensurate with numbers as objects? While I don’t have an answer for this, perhaps mathematicians distinguish different types of objects as empirical (i.e., physical objects) and conceptual (i.e., abstract objects). It is difficult for me to defend this, but it may be how they are thinking. Interestingly, an equally famous logician to Gödel, WVO Quine, espoused a physicalism view, so we can certainly say that not all logicians and mathematicians are Platonists. What can we conclude from all of this? First, there are no statements that are a priori true. Second, like logic, mathematics is a collection of different theoretical programs that uses different assumptions to generate sets of conclusions. These results are true in the context of the assumptions of the

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program, and may or may not have direct applicability to the world we live in. The antiquated notion that mathematics is somehow true, independent of empirical verification, probably dates from an era in which the known world was described by elementary mathematics and logic, in the context of Euclidean geometry and Newtonian physics. The real world is anything but that neat clockwork world and, on a fundamental level, is a probabilistic (based on the concept of probability) environment in which 1+1 does not always equal 2, where parallel lines do meet at infinity, and where the vertices of triangles don’t add up to 180 degrees. In physics, theory is useful to explain and predict, but it is experiments that dictate what is real.

CHAPTER 22 ARISTOTLE VERSUS PLATO

Aristotle and Plato We have touched on this before, but two major categories of inference are exemplified by contrasting Aristotelean versus Platonic approaches. Simply put, the Aristotelean approach is empirical and data driven. The accumulation of data reveals patterns that generate law-like statements that can be used to explain and predict the results of further inquiry. This is inductive inference. Opposing this is the Platonic approach of generating concepts that describe categories of entities (think of sets or classes), which can be manipulated to address questions. Think of this as deductive reasoning. The approaches seem different, but in reality, they are one and the same. For example, one cannot randomly collect data about objects without a hidden or subliminal hypothesis. Any material entity has innumerable properties and, in a hypothesis generation, an observer needs to accept some and reject others in order to generate the data necessary to form generalizations. This is the so-called hypothesis-laden acquisition of information. From the Platonic side, concepts do not appear out of nowhere; they are the result of observations that may be unacknowledged or even unconscious. In both cases, the initiation of hypothesis generation can then remain in an abstract realm until one wants, or is forced, into making an empirical observation. Mammals are living organisms that have many

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characteristics that set them apart from other living things, such as respiration, warm-blooded thermal regulation, the ability to procreate, etc., but at one point or another, we need to address whether a given organism actually fits into this category. Jellyfish do not, mice do. Some scientists fit more neatly into one category or the other. For example, Linneas’ work was largely empirical and thus Aristotelean. Newton’s work, however, was more Platonic. Nevertheless, in the end, hypothesis generation needs data and the ability to generate abstract concepts about said data. Some mathematicians are largely Platonic, but if one digs deeper, you might find that the assumptions behind their work is empirical. Physicians, by contrast, tend to resonate between the two extremes, acquiring data that leads to numerous hypotheses, which are then pursued with additional data until a wellunderstood diagnostic scenario is generated.

CHAPTER 23 COMPUTER INFERENCE VERSUS HUMAN INFERENCE

John Searle As a general rule, computer logic is binary and human inference is not. Conscious human inference is likely Bayesian, where some form of prior probability is modified by additional information in order to generate updated probability estimates. Computers can - and do – perform similar calculations if they are programmed that way, but more subtle, heuristic forms of inference are largely the province of humans. This is a both a positive and a negative. Heuristics are rapid “knee-jerk” responses that encompass enormous amounts of information in a single gulp. A good example of this is when a medical provider tells another that the patient looks “sick.” What goes into that is a composite of numerous items of observation which often number in the hundreds. These include “vital signs,” complexion, perspiration, voice, timbre, strength of vocalization, clothing, hygiene, posture, and many more features. The inferential logic is not binary, and not even algorithmic. It is distinctly human rather than machine. However, other animals might fall into the “human” category to a lesser extent - although not necessarily. Whales and other marine mammals may have just as complex inferential apparatus. The downside of heuristics are biases, which we will speak about more in a later section. Large language models like Chat GPT seem to mimic some of the more human forms of inference and

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are quite different from the binary algorithmic computer programs of the past. In fact, bias is a prominent concern in these programs, which seem to incorporate available data that might be non-representative. For example, many clinical trials of new therapeutics are based on a selective population that may exclude minorities and women. The result is that large language models may report inferences and conclusions that are biased. Some attempts to guide these programs to eliminate bias is a work in progress.

CHAPTER 24 ARTIFICIAL INTELLIGENCE

Alan Turing In the past, artificial intelligence effectively meant the computer-based algorithmic execution of programmed inferential decision making. The algorithms involved were complex and are now best illustrated by the alltoo-familiar phone trees that we all have to put up with on a daily basis. More interactive versions relied on voice recognition systems that permitted more complex trees and even “chat” functions that simulated human interaction. However, as everyone knows, these are very limited in their capabilities and function primarily as screening tools for customer queries. Recently, a very different approach has emerged, based on word recognition in the context of “big data.” It is in this realm that large language models (LLMs) have captured the field of artificial intelligence. Some modern simulation programs now rely on LLMs that truly mimic human thought in a way that makes them capable of complex tasks, with remarkable results. Output as varied as taking standardized exams, creating hypothetical scientific manuscripts and even writing poetry are all within

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the capabilities of software such as Chat-GPT. The approach is not conventional algorithms (i.e., specific instructions for a finite series of options), but an approach which goes by the name of “neural nets.” Neural nets look for associations between words to form a conceptual framework using words as tokens of concepts. Whether this mimics human intelligence or not is a very important and, as of yet, unsolved problem. However, the output of these programs is so remarkably human that it would surely pass the Turing Test (that is to say, it is unrecognizable as being different from that of a human). Human thought has evolved over millennia as a product of our interaction with each other and our very complex environment. But without attempting to understand human thought, these programs circumvent the entire issue by using language to mimic our thought processes. Their success is remarkable and somewhat validated the Chomskian notion that language is tied directly to cognition. One similarity between the Chat-GPT AI programs and human intelligence that differentiates it from standard algorithmic computer programs, is that both generative AI and human intelligence are black boxes. This means that there is no retrospective ability to trace the inferential process in these programs, just like the inferential process in human intelligence is often opaque, even when it is justified by rational reconstruction. In other words, the justification for a conclusion made by both humans and Chat-GPT is different from how the AI arrived at the conclusion, which remains hidden in a “black box.” In summary, traditional computer programs are algorithmic and easily dissected. They have limited capability and do not mimic human thought, except when humans are asked, after the fact, to rationally reconstruct or defend their conclusions. In cognitive psychology terms, algorithmic approaches are System 2 thinking (see Kahneman “Thinking Fast and Slow”). However, the dominant form of human inference is associative, as is exemplified by heuristics (called System 1 thinking), and is mimicked by Chat-GPT. This form of reasoning is fast, intuitive and subject to biases and limitations.

CHAPTER 25 DECISION ANALYSIS

John von Neumann Rarely is an entire field invented (so to speak) at a specific time and place, but that is the case for Decision Analysis. John von Neumann and Oskar Morgenstern were colleagues at the Institute for Advanced Studies at Princeton (along with Einstein, Godel and a whole host of the brightest minds in the Western Hemisphere). Many of the institute’s leading thinkers would take walks and bounce ideas off each other. One of the consequences of this was that new insights arose that crossed fields of inquiry. For example, Von Neuman made contributions to computer science when Alan Turing was a student of Alonzo Church – all at Princeton. Godel took walks with Einstein and became interested in General Relativity. Just to illustrate that Godel was no one-trick pony, he solved the equations of general relativity for a rotating universe, which had the peculiar property of permitting time travel. Godel’s solution was the first of many different solutions of General Relativity that generate peculiar, envisioned universes. This is beyond the scope of this book, but I refer you to the many texts of General Relativity and the space-time continuum for further reading. Another pair that took walks together were John von Neumann (primarily a mathematician) and Oskar Morgenstern (an economist). Their brilliant idea was that all decision-making is based on the likelihood of an outcome occurring, and the value of that outcome to the decision maker. Further, that one could quantify the value of an outcome by asking the decision-maker a series of questions about their preference for alternative outcomes, placing

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the lower valued outcome against a probability of achieving the preferred outcome. For example, if you prefer a movie to the opera, what would the equivalence point be between these two options – the opera for sure, versus a chance at the movie, or nothing? Is the opera worth a 50/50 chance at the movie, or 70/30? And so on. By this process, one can value the alternatives on a linear scale called a “utility function.” By repeating this process for all of the alternatives in a decision, one can create a scale of preference for each possible outcome. This process is known as a standard gamble. Although the roots of this date back to the 16th century, when games of chance were first analyzed, the formalization of this process was entirely due to von Neumann and Morgenstern. In fact, the book they wrote on the subject is akin to Principia Mathematica in that it creates an entire mathematically sound field that is axiomatized and formal, with its own symbolism that is complete with theorems and proofs. Their treatise “Theory of Games and Economic Behavior,” which was published in 1944 by Princeton University Press, essentially started and ended the field for quite some time, until various contributions, including multivariate decision analysis, decisionmaking under certainty (which maximized competing outcomes), and decision-making under ignorance (which eliminated the probability aspect) were added to the field. Because the conclusions are based on derivations of axioms, the process is best thought of as prescriptive, and much work has been done to document human decision-making that does not obey the choices that decision analysis dictates. In fact, there is a whole field of observational decision analysis that seeks to understand human deviations from the idealized predictions that are based on axiomatic decision analysis under risk or uncertainty. The reach of decision analysis is broad. Economists use it with dollars as the utility function in analyses of program costs to achieve certain goals. This takes the form of cost/effectiveness analysis or, to compare one program to another, cost/benefit analysis. In the medical field, the utility function is often used in what is known as Quality Adjusted Life Years, or QALYs. Using this utility scale one can compare different interventions. However, much more is at play in decision-making, including to whose QALYs we are referring, the strength of support for the intervention, and other social and political factors. Rarely are programmatic decisions made strictly on the basis of a solely analytical framework. One constant problem is the perspective. Is the analysis from the stakeholder’s perspective, from the government’s perspective, or from society’s perspective? Using society’s perspective, the analysis is clearly utilitarian. Depending on the perspective, the utility function certainly changes, but so does the probability calculation, especially if there are competing priorities. In

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individual decision-making under uncertainty, the utilities are the decisionmakers and are expressed in the abstract term “utiles,” with the probabilities being “subjective.” While subjective probabilities must obey the probability calculus which, for example, requires that the options be complete and total 100%, they can vary from one decision-maker to the next. Think, for instance, of several different weather forecasts. One says the chance of rain is 10%, the other 20%. Those are subjective probabilities and each one has to be consistent. In the first case, 10% rain and 90% no rain; in the second, 20% rain and 80% no rain. This is not to claim that if you reran the day 100 times, 10 or 20 times it would rain, as this is an empirical or frequentist approach to probability. Since it isn’t possible to rerun days, we need a different version of probability that isn’t empirical (the actual result of experiments), classical (the probability in fair games of chance like dice), or axiomatic (obeying the axioms of probability theory). Subjective probability theory is necessary to account for predictions that cannot be empirically validated, like weather. To update the probability estimates in subjective probability, Bayes’ theorem is used with the existing probability estimate as a prior, and the newly acquired data is used to recalibrate. When no existing information is available, it is appropriate to use a neutral prior probability (0.5) as a prior. Eventually, with additional information, a honed estimate will emerge. For example, your prior probability of rain tomorrow is 0.5. If you then look at the sky and note that it is threatening in appearance and, consequently, estimate that the probability of rain is 0.7, then the adjusted probability is 0.6. Additional data can be integrated in a sequential manner to generate a final, updated probability estimate. This procedure is useful for forecasts in many disciplines, especially economic forecasts. However, its use in medicine is controversial. Some individual decision-making has arisen, including a decision-making consultation service at Tufts Medical Center (a center for this enterprise), which started with an innovative physician scientist named Stephen Pauker (who recently died). However, it is more commonly used in cost-effectiveness and cost-benefit analysis for programmatic planning. There is nothing overtly incorrect in this mathematical framework, but it doesn’t describe personal-decision making very well for a variety of reasons. First, human decision-making is often a consequence of System 1 thinking, which is intuitive and not analytical. This approach gives quick responses but is subject to many biases, which we will discuss in a later chapter. Second, even when we use System 2 thinking, the analysis can be influenced

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by factors that are difficult to capture in decision-making under uncertainty (probabilistic decision analysis). For example, let’s stick with the weather forecast. You want to know what the likelihood of rain is, because it impacts your plans. Perhaps you want to take a hike or go to the movie. The scenarios are “take a hike with good weather,” which is the best option - say a 1.0. The movie if it rains is a 0.9, but the hike if it rains is a 0.1. In comparison, the movie on a sunny day is 0.5. The math is easily solved for an updated probability of rain of 0.7. The first option is 1.0 x 0.3, or .3. The second is 0.9 x 0.7, which is 0.63. The hike if it rains is 0.1 x 0.7, or 0.07, and the movie on a sunny day is 0.5 x 0.3, which is 0.15. So, taking a hike is 0.3 plus 0.07, which is 0.37, while the movie is 0.63 plus 0.15, or 0.78. Clearly, the movie wins. However, perhaps you want to maximize the chance of a pleasurable event based on your preference for a hike. In this case, taking a hike in spite of the weather is your best option. And what about if you want to minimize the worst outcome, which is the movie? Then, again, the hike is the best option. What about if you want to minimize the maximal regret? Then, the regret (the inverse of the utility) is the hike again as the preferred option. In the end, whatever approach you take changes the decision. These later approaches that eschew probability are called "decision-making under ignorance,” since the decision-maker is only aware of the values of the outcomes, not their probability of occurring. Decisionmaking under ignorance more closely mimics System 1 thinking, whereas decision-making under uncertainty (or risk) is a System 2 approach. Empirical decision-making, meaning how decision makers actually make choices, is more often concordant with System 1 decision-making under ignorance, rather than System 2 decision making under uncertainty. For an economist, decision-making under risk or uncertainty is the definition of rational behavior. This underlies the belief that an unconstrained market economy is rational. However, markets are influenced by factors outside of pure rational thinking, and for this reason, they are unpredictable. An enormous amount of effort is exerted to predict them, but with only modest results. Market cycles and other aspects of market economy are largely unexplained. In part, this is due to instability in preferences. A medical example of this is the preference for having children, which hits its bottom in women immediately post-partum, but then increases as the events of childbirth recede into the past. Another feature that is hard to understand is the preference for life-saving measures, which does not diminish with age, even though the ability to achieve goals may decrease. Even the preference variable (utility function) most commonly used – dollars - is unstable and widely different between individuals, and very much dependent on circumstances. A rich person would value $10 less than a poor person, but

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any given individual would ascribe some value to $10 differently, depending on their financial circumstances. In the end, it depends on what you want to do with the money. If you want to buy a yacht, $10 is meaningless, but if it is a sandwich, $10 is quite valuable. On a societal level, convention is that a quality adjusted life year is worth $50k. This has been the standard for decades, but inflation has reduced the value of $50k so much that some analysts now suggest a new benchmark of $100k per QALY. This is part of the problem with decision analysis, apart from the difficulty in estimating probabilities or even structuring the decision to include a complete mutually exclusive and exhaustive list of possible outcomes, which is a requirement in decision analysis. The difference between rational decision-making as defined by utility theory and human valuation started with the Allais Paradox which, in a nutshell, showed that humans violate “expected utility.” Analysis of this and related deviations from “rational decision-making” gave birth to an entire field of behavioral economics. To illustrate this, given a choice between a 95% chance of a million dollars and a sure thing of $910,000, pretty much everyone will take the sure thing. The reason they opt for the lower expected value is thought to be a preference at the extremes of probability for conservative options. What may be happening on occasion is that the probability estimate is just an estimate, and decision-makers may therefore view it with distrust. In the case in Kahneman’s book on fast and slow thinking, the probability estimate is over a court case and given by a lawyer. However, a reasonable decision-maker would question the “confidence” in this probability estimate and downgrade the information as a speculative guess. What the decision-maker would need are confidence intervals around the estimate, and further confidence estimates around the confidence intervals. If these are not available, a reasonable decision-maker would then opt for the sure thing. This is not an example of distorted reasoning, but a realistic assessment of the value of the information provided. In the vernacular of cognitive psychology this is what has been termed as “noise,” meaning variability in parameter estimations in decision-making or, in fact, any exercise in judgement. This is not to say that human decision-makers don’t make irrational choices because, as we will see in a subsequent chapter on heuristics and biases, many of the problems we encounter are sources of profoundly irrational decisions. However, when the stakes are high, human decision-makers are skeptical of the value of information and tend to be “conservative,” meaning that they will go for the sure thing. Markets also behave differently from expected utility predictions; hence, abstract concepts like consumer confidence play a large role. In general, we should think of axiomatic utility theory as a beautiful, brilliant contribution to our

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idealized world view, but even more divorced from reality than axiomatic Euclidean geometry. Kahneman and Tversky recognized the discordance between axiomatic decision theory and experimental decision making when they formulated Prospect theory. The hallmarks of Prospect theory is that each individual has there own reference point in a decision scenario based on their approach to risk and further that each decision maker avoids loss more preferentially than they view benefit. Both loss adversion and benefit gain can be visualized on a graph as shown below

On a societal level, rational decision-making utilizes societal preferences and is the mathematical representation of utilitarianism. However, personal goals, aspirations, biases and preferences often dominate a strictly utilitarian approach. Opposing utilitarianism is the Kantian approach to decisionmaking based on duty and virtue, which has no room for a utilitarian view. For example, the golden rule – “do unto others as you would have them do unto you” has no utilitarian interpretation and advocates actions that are not based on societal preferences. Similarly, any of Kant’s categorical imperatives, such as not committing suicide, not making false promises, avoiding sloth and stinginess don’t have a say in decision analysis, since they are prescriptive rules for behavior that are not based on weighing the value of alternatives.

CHAPTER 26 GAME THEORY

John Nash Game theory is decision analysis with more than one decision-maker. It arose in a slightly different manner than decision analysis, although both analyze preferences in a decision situation. Game theory is rooted in the analysis of board games like chess, checkers, tic tack toe and numerous others. Again, the beginnings of this field come from von Neumann in the treatise “Theory of Games and Economic Behavior,” but it has since developed into an independent field (or fields) through an extraordinary burst of activity that has generated numerous Nobel prizes, primarily in economics. However, game theory has been explored in biology, particularly evolution, business, computer science, defense, and philosophy (especially ethics). Games can be categorized under very different assumptions. For example, symmetrical games are those in which the two decision-makers get the same reward or punishment for the same decision (symmetrical). The prisoner’s dilemma, which we will demonstrate, is an example of this. Zero or constant sum games are those where the rewards or punishments are fixed. These include poker (what one person wins, the others lose) or chess (each player either wins or loses). Perfect or imperfect information characterizes games. Perfect information is typical of most board games like chess, but imperfect information characterizes most card games like poker. Innumerable variations with widespread applications have been identified. For the most part, they are prescriptive, since they

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assume (incorrectly) that the players are rational. Here is the most celebrated example: Prisoner’s Dilemma by William Poundstone in his 1993 book of the same title: Two criminals are arrested and charged with a crime. If they are convicted, they will serve 10 years in prison. If they plead not guilty, they are offered a deal, since the evidence is weak. The sentence will be 2 years each on a minor charge; however, if one confesses and implicates the other, the confessor will get a pardon, while the other will have to serve the full ten years. If they have no chance to collaborate, the best strategy is to confess. However, if they are allowed to scheme together, they would be able to get away with a guaranteed lesser sentence. This latter strategy depends on how much trust they have in each other. The game illustrates many principles of interrogation and response. For example, police always examine suspects individually and prevent them from interacting and thus forming a coherent alibi or agreement to confess to a lesser charge. When they are allowed to collude, it is a cooperative game, in distinction from a non-cooperative game as the original prisoner’s dilemma was framed. Also, in criminal organizations, accusing an accomplice is regarded as the worst thing you can do, and is always punishable by death. Thus, the Mafia will kill anyone in the organization who “rats” out another member. In the prisoners’ dilemma, under non-cooperative conditions, the dominant strategy for each player is to confess, which also happens to be the Nash Equilibrium. However, this might not be the case in other situations. We will describe the Nash Equilibrium in more detail below. Predicting what your opponent will do and developing strategies to maximize your reward and/or minimize your loss is the primary goal of game theory. Interestingly, it hasn’t been applied to medical decisionmaking very commonly, since most medical decisions involve a single decision-maker (although the role of the physician may be akin to a player). While this may be true in large part, there are many times when the patient has family or other significant relationships which could influence the choice of preferences. Speaking more broadly, in most medical situations like it or not - insurance companies are part of the decision and have very different preferences from the patient. Representing these in game theory is not typically done, but it is an area that could be explored. One of the most compelling uses of game theory is in the analysis of the famous problem of the Tragedy of the Commons - a non-cooperative game.

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This phenomenon, which underlies numerous resource allocation failures, simply presents a conflict between individuals who seek to maximize their own well-being at the expense of the community - whether it is overgrazing on shared pastures (Commons), overfishing that depletes stocks, hunting to extinction of a species or numerous other examples. In each case, the gametheoretic solution for the community is vastly different from that of the individual, and seeks to prevent the depletion of a finite resource. That is, the Nash Equilibrium for the community is different from the solution for each individual. In other words, the best solution for the community is to limit the use of a finite or precious resource, whereas for each individual, it would be to maximize their consumption. The Nash Equilibrium is a concept of John Nash, who made the most significant contributions to game theory after von Neumann and Morgenstern. His solution, called the Nash Equilibrium, describes the optimal solution for an individual in a noncooperative, fully informed game. Nash made many other contributions and his own tragic story is recounted by his wife in her book, “A Beautiful Mind,” which was subsequently made into a motion picture starring Russell Crowe (who looked nothing like Nash). The Nash Equilibrium is somewhat similar to Pareto Efficiency or Pareto Optimality, which defines the situation as being one in which no action is available that makes one individual better without making the other worse. For example, in the Tragedy of the Commons, deviations from the optimal solution for the community would make one person better off at the expense of another, so the Nash Equilibrium for the community would be the Pareto Optimal solution as well. Applications of game theory are extensive and include the Cold War Strategy of Mutual Assured Destruction, which is sort of a prisoner’s dilemma that leads to a standoff in nuclear-capable superpowers because of the mutual risk of annihilation. Also, applicable here are various team sports in which one member of the team might sacrifice his or her well-being for the sake of the team’s success. This notion of altruism has received an enormous amount of attention in fields as disparate as evolutionary biology and modern philosophy. It also underlies the most compelling theory of justice as elaborated by John Rawls. The idea is that if no one knew what place in society they would occupy (veil of ignorance), they would opt for a society which is based on equality of rights and equality of opportunity, which is a form of utilitarianism. In fact, game theory solutions that optimize the well-being of all of the players are clearly a form of utilitarianism, since well-being is defined in terms of utility measures and assumes that the players are rational (“economic”) individuals who will chose to maximize their well-being or “utility.” The fact that people don’t

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seem to behave entirely rationally in experimental game theory doesn’t detract from the model as a prescriptive enterprise.

CHAPTER 27 HEALTH ECONOMICS

Kenneth Arrow Health economics is a branch of economics that deals with the healthcare system as a whole. Economic analyses are performed in Health Services Research such as cost-benefit or cost-effectiveness analysis, but the system as a whole is the province of the field of economics. It began as a field in 1963 with an article entitled “Uncertainty and the Welfare Economics of Medical Care” by Kenneth Arrow. This rather dense paper started a burgeoning field, spurred on by the enormous investment of United States in healthcare, amounting to nearly 20% of Gross National Product (GNP). The fundamental problem is that in a capitalist economy, the price for goods and services depends on the market, and when the market is working well, supply and demand are linked. Thus, when supply increases, prices go down and when demand increases, prices go up. Leaving aside the issue that pure market economics is an ideal that is never completely realized, the problem with healthcare is that it does not obey market economics. Fundamentally,

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when supply increases in the healthcare segment of the economy, prices often increase, and so does demand. In fact, unchecked healthcare could consume even more of the economy than it already does. Adding to the problem, third-party payers, including the government (i.e., Medicare), make out-of-pocket expenses minimal. While copays and insurance limitations through restrictive services and prior approval tend to reduce demand, the presence of new products and services tend to drive it up. Layered on this is the conflict between the consideration of healthcare as a commodity, versus healthcare as a right. This battle is fought every day by patients, physicians and care givers, often in conflict with insurers and regulatory agencies. A good example is treatment for obesity, which is a major health problem that contributes to healthcare issues such as heart and vascular disease, arthritis and cancer. Nowadays, overweight and obese people make up more than 50% of the population. As a consequence, the relatively recent discovery that certain drugs developed for diabetes can be used for weight reduction in both diabetic and non-diabetic patients, has to a potential healthcare outlay that could cripple the economy. Let’s say that the drugs cost $1000 a month and need to be taken indefinitely. Conservatively, 100 million people are overweight and obese. Therefore, the expenditure for these drugs could in theory cost over 100 trillion dollars per year, thus consuming our entire GNP and more. Obviously, insurance companies and Medicare will restrict these drugs to obese, diabetic patients - at least to the extent they can. But the real purpose of this example is to illustrate how serious a problem this is. Indeed, recently, North Carolina Medicaid quit paying for these drugs for obesity because of the enormous expenditure. However, it isn’t just medications that can have a devasting effect on society through economic consequences. The SARS CoV-2 epidemic resulted in a 14-trillion-dollar expenditure and at least 1 million lives lost. Unfortunately, epidemics occur regularly and we have no control over them, nor does preparedness help very much. In fact, we were extremely lucky that Nobel prize-winning innovative science paved the way for a mRNA vaccine that was miraculously effective, or else the cost and mortality could have easily been an order of magnitude higher. There are two additional problems. First is that at least a significant segment of the population believes healthcare is a right and should be available to all, regardless of the ability to pay. This is one of many reasons the federal and state governments are deeply involved in funding healthcare. The second is that there is a far less-than-perfect correlation between health and medical

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care, at least in terms of medical care expenditure.

In the end, how many products and services, for whom, and at what cost are so variable that it is ludicrous to call healthcare in America a system, and this also happens to be an excellent segue to our next topic on Chaos Theory.

CHAPTER 28 CHAOS THEORY

Lorenz Attractor Chaos theory is best known for the “butterfly effect,” named after a lecture that Edward Lorenz gave to the American Association for the Advancement of Science (AAAS) in 1972 entitled “Predictability: Does the Flap of a Butterfly’s Wings in Brazil set off a tornado in Texas?” The essence of the theory is that very small changes in a deterministic system can result in very large differences at a later time. The field dates back to Henri Poincare and his study of the three-body problem (which cannot be solved formally and behaves chaotically), but the modern field arose from an observation by Lorenz that predictions of weather patterns were dramatically different, depending on small changes in starting conditions. In the first case, it was the use of a primitive computer that rounded off six-digit answers to three digits and, as a result, the predictions which in theory were deterministic, ended up being heterogeneous, unpredictable and seemingly random. This effect is a result in some systems that are sensitive to initial conditions but that also have other properties, including mixing and periodicity. It occurs in dynamic systems that evolve over time. These systems are mathematically complex but applicable to a wide range of phenomena that are resistant to standard approaches to non-random prediction models, such as earthquakes, weather patterns, solar flares, financial market behavior, punctuated evolution, and the occurrence of wars. Characteristic of these systems is feedback loops, self-similarity and fractal geometry. Now, fractals are everywhere in nature and characterized by a reproduced

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geometry at different dimensionality. For example, if you look at the coastline of Britain from the air, it has a certain pattern that is reproduced at smaller and smaller intervals the closer you look. One of the best demonstrations of a fractal is the image in a child’s toy kaleidoscope. The same is true for chaotic dynamical systems like the weather. When chaotic systems are plotted, they attract solutions. There are different types of attractors. An example is a pendulum that, when set in motion, will eventually reach a stopping at a point known as a simple attractor. In every chaotic system, there is a “strange attractor...” It is strange because the attractor has a fractal geometry. While Chaos Theory is not really a theory in the sense that it doesn’t have laws, theorems, axioms and derivations, it is a very important way of describing the behavior of certain difficult-tounderstand phenomena with a broad range of applicability. The importance of this cannot be overstated. First, fractal patterns exist ubiquitously in nature and have the obvious explanation that whatever works in nature is worth repeating, both numerically and at increasing scales. Broccoli is a commonly cited example, although it loses its fractal appearance at very small size. Because of the repetition at different sizes, the dimensionality can be smaller than integral. We are familiar with integral dimensionality - in a Euclidean space, there are three dimensions; in an Einsteinian space, there are four; and in string theory, there are many more dimensions, but they are all integers. Fractals have dimensionality that is not strictly integer. Second, many natural systems are inherently chaotic as mentioned above. In theory, the states of these systems are predictable because they are deterministic, but in reality, they are unpredictable, which accounts for many events in our world. They have patterns, even though they are unpredictable events like market cycles, El Nino, turbulence in rivers, and many more. Third, unpredictability is the hallmark of random events and some observers have questioned whether the unpredictability of both these systems, one random and one deterministic, suggests that they are not fundamentally different. For example, if chaotic systems are taken down to quantum levels, don’t the randomness and unpredictability merge? Chaos theory has limited applicability in clinical medicine, although there is some work in both EEG and EKG that suggests chaotic behavior of some epileptic seizures and some cardiac arrythmias. However, the field is brand new and likely has much more to offer in the future. The most disturbing message about this is that regardless of whether systems are inherently probabilistic like quantum mechanics, or inherently deterministic like fluid mechanics, the outcomes of even modestly complex systems are unpredictable. This lack of predictability is another nail in the

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coffin of a Platonic vision of the world. In other words, we live in a complex world and our ability to understand it is limited, and only accurate under very artificial and constrained parameters.

CHAPTER 29 THE BLACK SWAN

Nassim Nicholas Taleb The Black Swan takes the message from Chaos theory one step further. As you may recall, the overall conclusion from Chaos theory is that both probabilistic (i.e., stochastic) and deterministic (axiomatic) approaches to empirical knowledge are, at their core, unpredictable. Since these are the only two epistemological approaches that we have available, unpredictability is the rule, not the exception. The exception is very narrowly defined deterministic systems that break down when they are extended beyond very limited conditions. Nasim Nicholas Taleb, the author of The Black Swan, takes this message one step further by showing numerous examples that unforeseen events play a major role in the history of humankind. The title derives from a deterministic view of swans; namely, that they are defined by their white color, and are mute birds that are frequently seen in a watery environment. The discovery of black swans in Australia destroyed that myth and is an example of an unpredictable event destroying a defining attribute. It is ironic that another myth concerning swans also proved false – the socalled swan song. The myth states that the mute bird vocalizes as the last act of their life. This is also false, since we now know that swans do not utter swan songs. Be that as it may, the role of unpredictability, whether it is in a deterministic or probabilistic framework, is key to understanding human history. Some of these events are natural occurrences like earthquakes, floods, volcanos, hurricanes, tornados, etc., which we read about every day. Others are manmade, like financial crises, epidemics, wars, and species extinctions. The most recent and possibly the most devasting

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one is global warming. A minute’s reflection on global warming will emphasize that the results are extremely unpredictable and will likely lead to wholesale extinction of species, arable land in marginal environments, and the rise of many diseases that were rarely thought of even as recently as a decade ago. Just recently a case of malaria in Texas, a vast increase in Lyme disease in Maine, and leptospirosis in numerous flooded areas have been reported. Concomitantly, malaria vaccines are close to approval and a new Lyme disease vaccine is in the works. However, this is a small gain against the overwhelming march of problems that global warming generates. Ironically, those portions of the country where the political sway against science in general, and the evidence for global warming in particular, are precisely those areas that are hardest hit by this new phenomenon. For much of what we experience, control over our destiny is a myth and we need to learn to live with unpredictability as an immutable feature of our existence. After all, except for the minuscule chance event of an asteroid hitting Earth, we would likely not be here at all, and the planet would be populated by insects, rodents, birds, and dinosaurs. Perhaps this is best captured by the surgical aphorism “it is better to be lucky than good.” Assuming most surgeons are competent, which is generally assured by their training and certification, the difference in outcomes of their procedures is largely a matter of factors outside of their control, such as the ability of the patient to heal effectively, anesthesia complications, co-morbid disorders, etc. So, in fact, the variance in surgical skill probably accounts for less than chance with regards to outcomes. Of course, it never hurts to be good at what you do, but chance plays a much greater role in the outcomes of all decisions than the skill of the decision-maker (or in this case, the surgeon).

CHAPTER 30 ABDUCTION

CS Pierce and William James As we mentioned earlier, the primary modality of inference used by physicians is abduction, or inference to the best explanation. This is fundamentally a deductive, deterministic form of reasoning that proceeds from hypotheses about the patient’s illness and works forward to eliminate those diagnoses that conflict with the data available. For example, if the patient presents with a fever, an enormous array of inflammatory conditions are possible. One must then sift through the remaining information to sequentially eliminate the options, until one is left with the diagnosis of choice and then can proceed to confirm it with additional testing. This is the typical CPC (clinicopathologic conference) technique as highlighted in the New England Journal of Medicines CPCs. Typical data for the patient with a fever might include chest x-ray findings of a pattern that is suggestive of an infection, or possibly a tumor. Further evidence with advanced imaging might narrow down the options. This process of elimination might continue until a single option remains – abduction. However, sometimes, the process is cut short for practical reasons. For example, this might mean a trial of antibiotics for presumed community-acquired pneumonia before a more definitive test like a bronchoscopy. Nevertheless, the pattern still holds, generally speaking. Rather than lining up all the possibilities and rankordering them from most to least probable, then simply treating the most probable cause, the method of abduction sequentially narrows the field for

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a more cogent explanation. This form of reasoning is very close to the hypothetico-deductive method as favored by logical positivists. While this form of reasoning has gone out of favor as a method within scientific reasoning, it is still the predominant form of reasoning in clinical medicine. Chaos theory has little application in clinical medicine, and while black swans happen all the time, we can still manage to call a swan a swan when they aren’t white. What I mean by that is that patients don’t read the textbook (an old phrase in clinical medicine), yet we still have to pigeonhole them into a diagnosis to make any headway with managing their illness. The way we pigeon-hole them is, primarily, abduction.

CHAPTER 31 ALGORITHMS AND CHECKLISTS

Al-Khwarizmi, the inventor of algorithms and Algebra Algorithms are sequential checklists or, to put it another way, checklists are condensed algorithms. In either case, they are distilled forms of reasoning that could be either probabilistic or, more likely, deterministic. They are very useful in many situations, including medical decision-making. As Atul Gawande pointed out, there is a similarity between airplane pilots and surgeons in their need to address a range of considerations with little or no room for error. This is the ideal situation for checklists to be valuable, and it is mandatory for pilots to use them, as well as being strongly recommended for surgeons. Algorithms are also useful in medical situations, especially when the decision-maker is not familiar with the situation. Medical students, nurses and other medical personnel use algorithms to address common complaints that require decision-making. A commonly used algorithm for possible urinary tract infections (UTIs) specifies asking about risk factors, symptoms and findings on urine analysis. The outcome is a decision to prescribe antibiotics or not. All these features are considered by experienced providers, who automatically use them to formulate a plan. Sometimes, checklists and algorithms can lead the decision maker astray if a situation arises that the formula does not address. For example, the urinary tract algorithm might not address post-operative issues. Sometimes, the limitations of these decision-making devices are quantifiable, but often, the list of exceptions is limited and incomplete. In effect, these devices are the result of expert opinion on how to manage a certain situation. How the experts arrived at these recommendations is often through experience, but

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it may also be a consensus of a committee of experts, or a literature-based summary. That summary could be in the form of a systematic review or a meta-analysis. At the root of these recommendations are inferences that are probabilistic, deterministic, or both. Frequently, the checklists and algorithms are subject to testing in order to identify weaknesses or limitations that strengthen the confidence in their use. Rarely are they used universally with no limitations. An extension of the algorithmic approach is machine learning, where data is analyzed and computers generate algorithmic approaches to analyze it. There are many approaches to large data analysis; some of them are statistical, some are pattern recognition approaches. One that is very popular nowadays is neural nets, which analyze data as if it was connected by neurons in a model of the brain. The connections may be statistical or inferential. The most advanced AI programs use pattern recognition of word frequencies to generate representations of human cognition based on language.

CHAPTER 32 MODELS, ANALOGIES AND MAPS

Lewis Carroll aka Charles Dodgson Models, analogies and maps are inductive cognitive devices that attempt to capture the essence of information as a means to make an inference about it. In each case, the representation, if successful, will permit the observer to deduce some further aspect that is useful in itself, or which can be tested and related back to the original problem. For example, electrical circuits are commonly viewed as pipes carrying water that flow from a source to a destination. The same analogy is used for the circulatory system in humans and other animals. Maps are abstractions from a topological or geographical problem, but they vary in the information needed by the observer. For example, Google Maps will describe locations but, if prompted, they will describe features such as gas stations, banks, etc. Similarly, models capture the essence of a problem and are often used for deductive inferences about the original problem. Models may be highly abstract or extremely concrete. Model systems, like mice, are so prevalent in medical research that scientists occasionally call themselves “mice doctors.” Sometimes, models are the actual goal itself as with model trains, but usually mathematical models are a vehicle for inferences about the problem being modeled. Commonly, models are divided into formal, (mathematical models) or practical (like animal models), but this is a bit arbitrary. Which would the billiard ball model of Newton’s laws of motion be? It could be either material or formal.

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The curious feature of all these abstractions is that the more accurate the model, the more it represents the situation being modeled and, paradoxically, the less useful it becomes. This was first pointed out by Lewis Carroll in “Through the Looking Glass,” where Alice was trapped in a chess game that was life-sized. It is no coincidence that Carroll was the originator of this paradox, since he was a very accomplished mathematician. The enduring legacy of Carroll in his message about maps and models, is that size matters. Just as quantum mechanics has little relevance to our everyday life, neither do General Relativity or String Theory. The point is that models, maps and analogies are of limited applicability outside of the domain that they are designed to capture. Of course, we can look forward to a “Theory of Everything” in its ability to unify all of the forces of nature at the highest levels of energy, but this, too, will have little relevance to us. We live in a Newtonian Euclidean world, and only at the peripheries of our observational capacity does it touch on general relativity or quantum mechanics. However, models, analogies and maps are ubiquitous in biology and medicine – the heart as a pump, the brain as a computer, the immune system as an army, the skin as a shield, bacteria as invaders, and so on. Cartoons are a kind of model and are now mainstream as graphical abstracts that are remarkably difficult to construct, but which summarize the data in a manner that readers can digest at a glance (or maybe a little longer). Abstracting the essence of a problem is the root of these cognitive vehicles, and they are, and will continue to be very useful. One could think of all of mathematics as models, since they extract the essence of a problem for further analysis. The generation of models, analogies and maps is inductive. However, the primary inferential use with all of these techniques is deductive and has limitations that vary, depending on the cognitive distance of the model from the situation being modeled. For example, topographical maps are useful for hikers but don’t help motorists. Analogies are helpful, except when they are a “stretch.” Physical models are useful for wind tunnel experiments but useless for mechanical issues, etc. Usually, the complexity of the situation dictates whether a model, analogy or map is an appropriate vehicle for further study. The more complex the situation, the more valuable these cognitive shortcuts are.

CHAPTER 33 DUAL PROCESS THEORY: HEURISTICS, BIASES AND FRAMING

Kahneman and Tversky Speaking of shortcuts, the fields of cognitive psychology, behavioral economics and neuropsychology erupted from the primary observation that rational-decision making, as defined by expected utility theory, was frequently violated by human decision-making. Many investigators contributed to this enterprise, amongst them Kahneman and Tversky, Paul Slovics, Robin Hogarth, Cass Sunstein and a host of other seminal thinkers. The prevailing model first recognized by Kahneman is dual process theory, which states that the analysis of situations by human observers falls into two categories in general. System 1 is the immediate associative process that links the current situation to those in the past and gives what amounts to a “knee jerk” reaction. System 2 is a more contemplative, reflective approach that tends to weigh options before making a claim. System 1 uses a whole host of shortcuts, commonly referred to as heuristics, to make inferences. Typically, these are visual, auditory or occasionally olfactory sensations that evoke certain associations. Flashing red lights with either police cars, ambulances or fire trucks; loud exhaust sounds with motorcycles; warm, yeasty smells with bread or pastry baking; the smell of cut grass with summertime, and so on. The dark side of heuristics is bias; for example, racial profiling, gender discrimination, religious persecution and so on. The topic of heuristics and biases covers an extensive body of literature that has been applied to almost every field, but especially in medicine, where the

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large volume of data and the need for rapid decision-making with high stakes is particularly important. Framing is a much more subtle deviation from rational decision-making. In this situation, the way the data is presented affects the way it is processed. The classic examples are “1 in 1000 individuals had a serious reaction to this medicine or vaccine, versus 99.9% of individuals having a favorable response to this medicine or vaccine.” Sometimes, the framing is purposeful to emphasize a positive or negative attribute of the options, but frequently, it is manipulative by the speaker, advertising firm, or merchant. Interestingly, the response to framing (if the recipient is receptive) triggers the amygdala, which is commonly associated with emotions including happiness, fear, anger and anxiety. Whereas, if the framing is contrary to the predisposition of the individual, the neural activation is in the anterior cingulate, which is an area of the brain responsible for response to threats. If System 2 is triggered, the response activates the frontal lobe, which manages higher-level executive functions. This remarkable concordance of psychology and neurology goes a long way to providing an anatomical, organic basis for our psychological response to decision-making. Framing plays a role in individual decision-making by influencing the decisionmaker in one or another direction, but it can also be utilized on a societal or public policy level. For example, framing organ donation as either an optin or opt-out scenario dramatically alters the level of participation by potential donors. In Germany, organ donation is opt-out, whereas in the US, it is opt-in. The participation in organ donation in Germany is about 80%, compared with less than 20% in the US. Of course, not all of this is due to opt-in versus opt-out, but it is certainly a strong contributor. This sort of distortion from utility theory-defined rational behavior exists on an individual level, but also on a societal level as described in Thaler and Sunstein’s book “Nudge.” Many examples of this nature are found in advertising. Philosophers have taken advantage of the survey nature of this research in a branch of philosophy called experimental philosophy, where questions are posed to respondents regarding typical philosophical questions such the nature of free will, like what is truth? Or what is good and evil? This research is fraught with difficulty for the usual statistical considerations, but also for subtle biases that are introduced by the way in which the questions are asked, including framing issues.

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Examples of Heuristics and Biases AVAILABILITY HEURISTIC OR AVAILABILITY BIAS Answering a query with the first thing that comes to mind ANCHORING EFFECT (OR HEURISTIC OR BIAS) Answering a query with a response that is influenced by a prior irrelevant piece of information, such as the value of an item after reporting your social security number FRAMING EFFECT (OR HEURISTIC OR BIAS) Answering a question differently depending on whether the question is posed in a positive or negative context CONFIRMATION BIAS (OR HEURISTIC) Answering a question in a way that echoes your prior beliefs HALO EFFECT (OR BIAS OR HEURISTIC) A form of confirmation bias where the answer to a question is influenced by your prior opinion of the context REPRESENTATIVENESS HEURISTIC (OR BIAS) When the answer to a question reflects the similarity to something known GAMBLER’S FALLACY (OR BIAS OR HEURISTIC) The subjective probability estimate based on prior events of an independent event OPTIMISM OR PESSIMISM BIAS (OR HEURISTIC) The false belief that you are more or less likely to experience an outcome based on mood or prior events

CHAPTER 34 GEDANKEN

Albert Einstein Gedanken are thought experiments. The term is particularly used in physics, where the predictions based on theory are not always testable. A frequently cited example is string theory which, to date, has no testable conclusions. It is also applied to some high energy and general relativity issues that defy experimental proof. On a broader level, Gedanken is applicable to almost all philosophy, and even some predictions within everyday life. Counterfactual conditionals can be viewed as gedanken because you can’t undo the world as it is. For example, “If he had only left his house earlier, he wouldn’t have been hit by the bus;” or “If he had purchased the lottery ticket one person ahead of him in the convenience store, he would have won the lottery,” and so on. There is no way to prove any of this, so the reception of these predictions is purely on the basis of their consistency with common sense. Both gedanken and counterfactual conditionals are a form of argument, containing if-then hypotheses. In that sense, they are philosophical. Philosophy is a non-experimental form of reasoning that depends on adhering to correct forms of argument. As we saw previously, arguments take many forms and although they all have limitations, if the structure of the argument is correct and the assumptions are valid, then the conclusions within the context of the assumptions are valid. The types of arguments frequently encountered are deductive, inductive, causal and argument by

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analogy. Similar to axiomatic systems, if the operators are used correctly and the axioms are assumed to be true, then the conclusions follow. In this way, all thought experiments can yield valid conclusions. When the rules aren’t followed, the result is fallacies. An example of a gedanken gone wrong is the zombie hypothesis of David Chalmers. Here, he suggests the existence of an alternative being, molecule for molecule the same as he is, but without consciousness. Most people, including myself (and Timothy Williamson) think this is just a fantasy that disobeys biological plausibility. Proving an argument incorrect could involve questioning the assumptions (axioms), or pointing out an incorrect inference, like affirming the consequent or denying the antecedent (well-known fallacies). There are many ways to go wrong in an argument (see Chapter 38), including pointing out a logical consequent that is incorrect, circular reasoning, or question begging, where the conclusion assumes an incorrect premise. For example, “when did you stop beating your wife?” Of course, one cannot answer this without tacitly acknowledging that they beat their wife. There are many other ways to defeat an argument, all of which are fair game in philosophical discourse. The zombie hypothesis fails on at least the assumption that something can be identical to a human, and yet brainless. Assuming the opposite is one approach that is used in both philosophy and mathematics. In math, it is called reductio ad absurdum and refers to the use of logic to demonstrate that if you assume the opposite of a premise, you generate a result that is patently false. For example, if everyone printed their own money, then everyone would be rich. In philosophy, assuming the opposite for the purpose of clarifying a concept is an argument form called “dialectic,” made famous by Hegel. What separates dialectic from reductio is that the purpose of the opposition in dialectic is to foster a synthesis which may be viewed as a compromise. The synthesis retains the key elements of each position and allows the argument to proceed. Reductio, however, is a method to prove the validity of the hypothesis to be tested, not to generate a synthesis or compromise. It does this by assuming the opposite of the hypothesis then showing that this leads to a false conclusion. In summary, Gedanken is a method of philosophical debate, but it is also useful in all the sciences, and in everyday life.

CHAPTER 35 POSSIBLE WORLDS AND MANY WORLDS

Saul Kripke Possible world refers to the operator “possible” in modal logic and dates back to Leibnitz, who claimed that this world is the best of all logically possible worlds, since God made it. Modal logic uses the operator “possibly” as a quantifier for statements such as “x is possibly true if it is true in any logically possible world.” In a sense, counterfactuals posit a possible world. This is a very different meaning from the many worlds of interpretation of quantum mechanics, in which the spectrum of distribution of energy or location is a probability function, and one of the interpretations of the probability distribution is that there is a distribution of locations or energies, each corresponding to a separate world. However, in each, case there is a claim that there are many different worlds. At least some philosophers believe in modal realism and some physicists believe in the many worlds of interpretation (which is a deterministic approach to probability in quantum mechanics). Thus they believe in the existence of alternative realities. Alternative worlds is a concept is present in some religions, such as heaven and hell, which exist in several religions, but which have no scientific evidence. In contrast, the many worlds concept is present in quantum mechanics, cosmology, and logic, and at least has some scientific basis.

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Einstein’s famous quote “God doesn’t play dice” is an affirmation of determinism to which many physicists adhere. This is in spite of the success of quantum mechanics, which implies that the world is stochastic. But what is the attraction to determinism, particularly when the clockwork universe of Isaac Newton has been superseded by General Relativity? First, General Relativity is deterministic. Second, apparently random events can occur in deterministic systems, as we discussed in the chapter on Chaos theory. Third, quantum mechanics (at least superficially) seems arbitrary, with many particles, each with different properties and little coherence in terms of an overall theory. Lastly, in an attempt to understand how the very complex universe came to be, and why we occupy a peculiar world in a system that is evolving down a one-way path dictated by a dimension of which we have little understanding of (time), determinism seems like a better framework than a stochastic one. As philosophers point out the major downside of determinism is the lack of free will, but free will isn’t much of a player in a stochastic universe either. For this reason, deterministic versions of quantum mechanics are attractive and the many worlds notion is one of them. However, if there are many worlds that represent different solutions to probability equations, we have no trace of them. Another deterministic approach to quantum mechanics relies on the initial conditions hypothesis that if we knew the initial conditions of the universe, we could predict and explain the resulting changes. Here is what Professor Justin Albert (University of Victoria) says: “Determinism, in that all future occurrences are uniquely specified by an initial quantum state of the Universe (if one were able to know and specify the exact quantum state of the entire Universe at any given time) is, I think, almost certainly 100% correct. But the idea that the initial quantum state of the Universe/multiverse, right at the time of the Big Bang, is uniquely specified solely by mathematical considerations is, I think, highly suspect and probably wrong.”

In any case, we will not resolve this either now or, most likely, any time in the near future. That said, attempts to reconcile quantum mechanics with general relativity will, if successful, doubtlessly shed light on the issue.

CHAPTER 36 PARADIGMS

Isaac Newton Since Thomas Kuhn’s seminal book “The Structure of Scientific Revolutions,” the notion of paradigm has dominated our thinking about the history of science. Certainly, the exemplary case of the transition from a Newtonian view of the universe to an Einsteinian view was a paradigm shift, as was the shift from an atomic view to a quantum view. One can make the case for the periodic table, the observation that organisms are made up of cells, and a host of other developments in the history of science. The essential features of a paradigm shift are the failure of the current paradigm to explain all of the new experimental findings, and the gradual realization that a new way of interpreting the data is both necessary and, also, more broadly applicable. The resistance to the current paradigm is evidenced by attempts to explain conflicting data through alterations in the assumptions and details of the current paradigm, until the amount of conflicting data becomes overwhelming and the scientific community adopts the new way of thinking in a short but tumultuous period of time. This realization is a direct descendent of the logical positivist approach to scientific explanation and prediction. The hypothetico-deductive method puts forward a set of assumptions that experimental data confirms. This is sometimes called the “deductive nomologic model,” which goes by Hempel’s model or Hempel Oppenheim (Paul) schema. It is basically a syllogism in which there are lawlike

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statements followed by specific conditions that constitute the “explans,” which support a logical deduction called the “explandum.” Even Popper’s variation on this theme is within this framework. He espoused the view that the point of a hypothesis was to remain the prevailing wisdom until experimental data disproved it. The contrary experimental data could be criticized as inadequate in many ways or, if accepted, the original theory could be modified. But eventually, if the point was reached when the accepted paradigm explained less than the competing paradigm, the paradigm shift would occur. It is no accident that Kuhn taught at Princeton where Carl Hempel, one of the leaders of logical positivism and the hypothetico-deductive method, was an eminent philosopher. It is important to point out that all of these approaches are deterministic and leave no room for chance. The deductive nomologic model supports BOTH explanations of scientific observations, but importantly, also predictions of the model. Further, even when the lawlike statement is a probabilistic one, the whole approach is deterministic. A good example of this is mendelian genetics, in which the prediction of color or shape of peas is in the form of a statistical statement, yet the form of the argument is deductive and thus deterministic. We should always keep in mind the famous quote from Yogi Berra: “Predictions are difficult, especially about the future.” Ironically, predictions are difficult regardless of the timeframe. In fact, if you recall, Aristotle concluded that statements about the future have no truth value until they occur. The same thing could be said for conditionals, like “if I inherited a million dollars, I would pay off my mortgage,” or counterfactuals like “if I didn’t go to the gym today, I would be tired.”

CHAPTER 37 TRUTH

Socrates Truth within axiomatic (and Intuitionist) systems is simple; it is provability, whether in logic or mathematics. Unfortunately, this is a very limited circumstance, as very little of the world is captured by axiomatic systems, and even within them, there is the limitation of either being consistent or complete after Godel’s famous proof. Can truth as provability be extended beyond axiomatic systems? Certainly, experimental science is based largely on provability and much of science is devoted to generating scenarios in which the proof of a hypothesis is dependent on the results of an experiment. Ideally, the experiments are structured to be a test of the hypothesis; generally, in the form of a prediction that the hypothesis makes. After Kuhn, it is clear that many tests of a hypothesis are needed to support a hypothesis, and even those tests that are not supportive do not invalidate it immediately in the mode of Popper. Rather, they are weighed in balance with the supportive and contrary data, as well as the alternative explanations. In the end, the provability test for hypotheses is somewhat elastic and conditional on the current data. But how does this tally with everyday life? Much of what we hold to be true is not easily provable. One simply cannot prove that the sun rises every day, except by inductive observation which, as we know from Hume, is not a surefire way to the truth anyway. Yet, we accept as true the statement that the sun rises every day. So, what are we basing that statement on that leads

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us to the conclusion that it is true? This is one of the concepts of truth; that is, correspondence to fact regardless of the ability to prove it. Another feature that is commonly weighed in claims of truth, is its coherence with other known features, such as daylight in the morning, eclipses, and so on. Lastly, how does the claim perform? Can we use it to further our understanding of related phenomena such as phases of the moon, tides, rainbows, northern lights, etc.? These criteria are somewhat similar to Bradford Hill’s criteria for causality in epidemiologic studies, which include strength of association, consistency with known facts, specificity of the relationship between cause and effect, biological gradient of “more cause results in more effect,” plausibility in line with known biological theory, coherence with related theory, experimental reduction or amplification of the cause resulting in lesser or greater effect and, lastly, analogy to other known cause-and-effect relationships. In the end, truth is a somewhat elastic attribute that is useful as a means of moving the conversation forward, but it is not in itself a claim of immortal validity. As a claim, what we usually mean is not truth in terms of it being an objective state of the world, as we have such a partial and somewhat distorted perception of the world. It is, by contrast, a claim that is supported to a lesser or greater degree by the evidence available.

CHAPTER 38 PHILOSOPHICAL ARGUMENT

Wittgenstein How philosophers do philosophy is somewhat a mystery to most people. This is made all the more opaque by the persistence of philosophic problems through the ages. For example, is there a god or gods? What is truth? How can we know something? And innumerable other problems. To put it in a nutshell, philosophers approach a problem with a variety of techniques based on the notion of a philosophical argument. What constitutes a philosophical argument is a valid argument form, such as deductive or inductive reasoning. Other valid forms include causal analysis, argument by analogy, abduction, reduction or reductio ad absurdum, and a less demanding form of reductio that simply looks at the consequences of a line of reasoning. Let’s take the famous trolley car problem. You are aware that a trolley is out of control and to save the five passengers onboard, you need to divert the trolley to a spur. Unfortunately, the act of causing that diversion will result in killing one person. Is this acceptable? Most people (but not all) say that it is, but will then reject an analogous situation where you need to actively kill someone by throwing them off the trolley to change its direction. This problem doesn’t have one correct answer, but it does illustrate one of the forms of philosophical reasoning, which is looking at the consequences of an action. Do you accept a utilitarian ethic or a personal principle (deontological approach) not to cause harm, or not to cause harm actively?

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There is no right answer. To pursue philosophical arguments, many techniques are used. For example, fallacies and distinctions can be mounted in opposition, and defenses can be provided to shore up an argument. The techniques are all cognitive and amount to the entire range of reasoning that can be brought to bear on a subject. Progress is made, but it isn’t linear and, sometimes, it goes in reverse direction. Teleology and determinism have essentially disappeared and if this book represents any sort of significant contribution, then the whole notion of a priori truth is a thing of the past as well. For most people, God as a prime mover has moved on but there is no consensus on the validity of induction or, for that matter, what constitutes truth in an axiomatic system. In summary, philosophy is an active field and does make progress but it is not as easy to discern as it is in science. What is less clear is where novel philosophical insights arise, or how new theories are developed. This problem is reminiscent of how hypotheses are generated in any cognitive endeavor, and we won’t be able to answer this enduring conundrum in this book.

CHAPTER 39 DIAGNOSIS

Sherlock Holmes Diagnosis is the focus of most of the work that has been done on cognitive issues in clinical medicine. This reflects the centrality of diagnosis in the care of patients, because without a diagnosis (or diagnoses), it is difficult to plan management. Even when there is no overt diagnosis, the clinical management betrays a latent diagnostic hypothesis. For example, empirical antibiotics for a respiratory condition suggests that the provider is concerned about pneumonia, bronchitis, sinusitis or other related conditions. In spite of all the attention to diagnosis, the inference involved is rather straightforward. A clue from the history, physical exam or laboratory tests suggests a range of possibilities, and it is from there that the culling begins. Data acquisition is helpful in eliminating some of the possibilities, and some are confirmatory. In the end, one hopes to generate a single diagnostic entity that explains most, if not all, the findings. This is abduction or inference to the best explanation by CS Pierce and the pragmatists as described earlier. The process is very similar to scientific research, although it is in a very condensed format. It is also similar to other problem-solving procedures like automobile repair, plumbing, or electrical issues. As with any complex inferential procedure, there are many ways to go astray and System 1 thinking often leads to common mistakes like premature closure or inappropriate anchoring, availability bias, and a host of others. In a sense,

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considering the complexity of the human organism, it is a miracle we can make any accurate assessments of the disorders that beset us. Just as an example, we host more bacteria in our gut than there are visible stars in the Milky Way. Even more amazing there are over 300 times more cells in our body than stars in the Milky Way. The overall diagnostic process is a mix of inductive inference in the hypothesis generation phase, and deductive reasoning in the diagnostic confirmation phase. However, there is a great deal of cost-effectiveness reasoning that is primarily decision analysis, since testing has benefits but also many drawbacks including time, expense and danger. In fact, all of what we have discussed so far is involved in the diagnostic process, which is why it is such a demanding cognitive activity that incorporates encyclopedic knowledge, skilled inferential reasoning, and shrewd weighing of options. Years of practice, assuming an excellent memory, and constant integration of new information are all necessary for a clinician to develop expertise.

CHAPTER 40 SUMMARY

It is difficult to summarize such a wide-ranging discussion. However, there are several themes that run through this book. First is the acquisition of knowledge not coming through a single portal, nor being a single conceptual scheme. Human intelligence is very opportunistic and eclectic. We use every technique we have available to move toward a fuller understanding of the situation in which we find ourselves. All our sensory apparatus and every cognitive technique is necessary as we plow through an incredibly complex world. In this way, human intelligence is quite different from traditional binary algorithmic computer approaches. In our world, truth is a tentative hypothesis that is held up by confirmatory data, but which is constantly at risk of being discarded by contrary data. Whether human intelligence is mimicked by large language models that use word association as the basis of inference, is an open question. These programs are effectively the same as System 1 cognitive inference in humans. As such, they have some of the same limitations. For example, they are prone to making inferences that are fallacious, known as hallucinations. They also exhibit biases that are typically human, using heuristics, which are the obvious source of the biases. Interestingly, when human operators question ChatGPT and its relatives about their conclusions, these programs revert to a System 2 approach and frequently apologize for their mistakes. Our interactions with these complex computer programs are just beginning, and we are likely to learn a great deal about human cognition through them. My guess is that it will validate the eclectic approach I have championed here. I also believe that it will support my claim that at the route of all knowledge is empirical evidence – an Aristotelian rather than a Platonic view. That is not to say that neural structure doesn’t dictate the way in which we both acquire, and process and store knowledge. It certainly does, and it would be a great deal different if we had extra-sensory perception or different sensory input; say, the olfactory abilities of a dog, or the visual acuity of an eagle. But we are what we are, and we have exploited our capacity to acquire knowledge in a way that has permitted our dominance on this planet, for better or worse. I hope we can utilize it wisely in the future, for the good of all beings.

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Bayesian Statistics for Beginners by Therese Donovan and Ruth Mickey Oxford University Press 2019 Subjective probability for beginners PROBABILITY AND ITS PROBLEMS AN INTRODUCTION TO PROBABILITY AND INDUCTIVE LOGIC by Ian Hacking Cambridge University Press Cambridge England 2001 Probability theory by an eminent philosopher covering frequentist and subjective approaches LADY LUCK by Warren Weaver Anchor Books NY 1963 An elementary book on statistics by a famous mathematician OBSERVATION, EXPERIMENTATION AND THE SCIENTIFIC METHOD PHILOSOPHY OF NATURAL SCIENCE by Carl Hempel Prentice Hall NJ 1966 A brief introductory essay by a leader in the field ASPECTS OF SCIENTIFIC EXPLANATION by Carl Hempel Free Press NY 1965 Important essays in the logic of science THE STRUCTURE OF SCIENCE by Ernest Nagel Hackett Indiana 1979 A classic in the logical positivist tradition INTRODUCTORY READINGS IN THE PHILOSOPHY OF SCIENCE by Klemke Hollinger and Kline Prometheus Buffalo NY 1980 Covers science vs non science, values and culture in addition to more mainstream issues SCIENTIFIC REASONING: A BAYESIAN APPROACH by Howson and Urbach Open Court Chicago 2006 A Bayesian approach to induction in scientific reasoning THE RATIONALITY OF SCIENCE by Newton-Smith Routledge Boston 1981 Discusses post Popperian contributions

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HEALTH SERVICES RESEARCH - THE SCIENCE BEHIND CLINICAL MEDICINE HEALTH SERVICES RESEARCH METHODS by Leiyu Shi Cengage 2019 Comprehensive textbook INTRODUCTION TO HEALTH RESEARCH METHODS: A PRACTICAL GUIDE by Kathryn Jacobsen Jones and Bartlett 2020 An introductory textbook INTRODUCTION TO RESEARCH IN THE HEALTH SCIENCES by Stephen Polgar and Shane Thomas Elsevier 2019 Another popular introductory textbook KNOWLEDGE AND BELIEF UNDERSTANDING BELIEFS by Nils Nilsson MIT Press Cambridge MA 2014 A computer scientist instrumental in the development of Artificial Intelligence UNDERSTANDING SCIENTIFIC REASONING by Ronald Giere Holt Rinehart Winston NY 1979 Very understandable introduction to philosophy of science with an emphasis on knowledge THEORY AND REALITY by Peter Godfrey-Smith University of Chicago Press Chicago 2003 Explanation and knowledge in the philosophy of science CONNECTIONS TO THE WORLD by Arthur Danto Harper Row NY 1989 A broad ranging analysis of knowledge and reality TELEOLOGY AND NATURAL SELECTION FROM ARISTOLTLE’S TELEOLOGY TO DARWIN’S GENEALOGY by Marco Solinas Springer 2015 One of the few modern books tracing the history of thought in this area

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SHADOWS OF THE MIND by Roger Penrose Oxford University Press Oxford England 1994 A physicist tackles philosophy of mind THIS IS PHILOSOPHY OF MIND by Pete Mandik Wiley Blackwell 2022 A primer on key concepts in the philosophy of mind including conciousness MATHEMATICS PLATO’S GHOST by Jeremy Gray Princeton University Press NJ 2008 Plato’s influence on modern mathematics and Physics TRUTH AND BEAUTY by Chandrasekhar University of Chicago Press Chicago 1987 Aesthetic considerations in the development of physics and mathematics by one of the 20th centuries deepest thinkers REMARKS ON THE FOUNDATIONS OF MATHEMATICS by Ludwig Wittgenstein edited by von Wright Rhees Anscombe MIT Press Cambridge MA 1967 An attempt to understand the nature of mathematical thought but difficult to follow GODEL, ESCHER, BACH: AN ETERNAL GOLDEN BRAID by Douglas Hofstadter Basic Book 1979 The themes of symmetry recursion and meaning in music mathematics and art in a Pulitzer Prize winning book PHILOSOPHY OF MATHEMATICS by James Robert Brown Routledge NY 1999 A history of the philosophy of mathematics written by a Platonic perspective THE UNIVERSE SPEAKS IN NUMBERS by Graham Farmelo Basic Books NY 2019 A Platonic approach to physics

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JOURNEY THROUGH GENIUS: THE GREAT THEOREMS OF MATHEMATICS by William Dunham Wiley NY 1990 Historical approach to major contributions in mathematics ARISTOTLE VS PLATO ARISTOTLE’S CRITICISM OF PLATO’S TIMAEUS by George Claghorn Springer 1954 One of the few books to use original sources to highlight the difference between Plato who was Aristotle’s teacher for 20 years THE GANG OF THREE: SOCRATES PLATO AND ARISTOTLE by Neel Burton Acheron Press 2023 Socrates, Plato and Aristotle in the context of ancient Greek philosophy COMPUTER INFERENCE VERSUS HUMAN INFERENCE ARTIFICIAL INTELLIGENCE ARTIFICIAL INTELLIGENCE: A GUIDE FOR THINKING HUMANS by Melanie Mitchell Picador 2020 How similar and different is human and computer intelligence A HUMAN ALGORITHM by Flynn Coleman Counterpoint 2020 How artificial intelligence is affecting human endeavors THE AI REVOLUTION IN MEDICINE by Lee, Goldberg and Kohane Pearson Pearson Education 2023 How large language models are revolutionary in medicine QUICK START GUIDE TO LARGE LANGUAGE MODELS: STRATEGIES AND BEST PRACTICES FOR USING CHAT GPT AND OTHER LLMS by Ozdemir Addison Wesley 2023 A user up to date user guide WHAT IS CHATGPT DOING by Stephen Wolfram Wolfram Media 2023 The unique qualities of large language models by a famous mathematician COMPUTATIONAL PHILOSOPHY OF SCIENCE by Paul Thagard MIT Press Cambridge MA 1988 Does Computer programming help us understand problems in the philosophy of science

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THE BLACK SWAN THE BLACK SWAN by Nassim Nicholas Taleb Random House NY 2010 Extremely erudite essay on improbable events and their influence on epistemology INCERTO by Nassim Nicholas Taleb Random House NY 2021 A five-book boxed set of the works of this revolutionary thinker ABDUCTION ABDUCTION, REASON AND SCIENCE by Lorenzo Magnani Springer NY 2001 A philosophic approach to abduction as a window to scientific reasoning ILLUSTRATIONS OF THE LOGIC OF SCIENCE by Charles S Peirce Open Court 2014 Peirce’s essays on the philosophy of science including abduction PEIRCE ON INFERENCE: VALIDITY, STRENGTH AND THR COMMUNITY OF INQUIRERS By Richard Kenneth Atkins Oxford University Press 2023 How Peirce would interpret challenges to inference such as paradoxes of reference and induction ALGORITHMS AND CHECKLISTS ARTIFICIAL INTELLIGENCE IN PRECISION HEALTH edit by Debmalya Barth Elsevier 2020 A wide-ranging compendium of applications in medicine including big data, decision support and predictive modeling THE CHECKLIST MANIFESTO: HOW TO GET THINGS RIGHT by Atul Gawande Picador 2011 The classic best seller by an influential surgeon EVIDENCE-BASED MEDICINE TOOLKIT by Heneghan and Badenoch Wiley 2006 A pocket guide to the concepts and terminology of evidenced based medicine

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MODELS, ANALOGIES AND MAPS THE MODELING OF NATURE by William Wallace Catholic University of America Press 1996 An attempt to counter the challenges to the epistemology of experimental and theoretical science PHILOSOPHY AND MODEL THEORY by Button and Walsh Oxford University Press Oxford England 2018 An attempt to extract model theory from mathematics to the philosophy community THE ANNOTATED ALICE 150th Anniversary edition by Lewis Carroll edited Martin Gardner and Mark Burstein WW Norton 2015 An extraordinary analysis of the breadth and depth of a legendary scholar and mathematician DUAL PROCESS THEORY HEURISTICS AND BIASES AND FRAMING JUDGEMENT UNDER UNCERTAINTY: HEURISTICS AND BIASES by Kahneman Slovic Tversky Cambridge University Press Cambridge England 1982 The classic behavioral decision-making text that won the Nobel Prize HEURISTICS AND BIASES: THE PSYCHOLOGY OF INTUITIVE JUDGMENT by Gilovich Griffin and Kahneman Cambridge University Press Cambridge England 2002 More essays specifically on heuristics and biases COGNITIVE AUTOPSY: A ROOT CAUSE ANALYSIS OF MEDICAL DECISION MAKING by Pat Croskerry Oxford University Press Oxford England 2020 Understanding medical management failures based on errant cognitive processes NUDGE by Thaler and Sunstein Penguin books NY 2021 The use of behavioral economics in public policy

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GEDANKEN FUNDAMENTALS: TEN KEYS TO REALITY by Frank Wilczek Penguin Press 2021 The role of speculation in understanding the nature of the universe EPISTEMOLOGY: 50 PUZZLES, PARADOXES AND THOUGHT EXPERIMENTS by Kevin McCain Routledge NY 2021 Role of thought experiments in epistemology COUNTERFACTUALS by David Lewis Wiley Blackwell NY 2001 A leading philosopher tackles a difficult subject from a realist viewpoint PHILOSOPHICAL AND MATHEMATICAL LOGIC by Harrie de Swart Springer NY 2018 Counterfactual conditions and many other relevant topics in logic and epistemology in the context of the entire field of mathematical logic POSSIBLE WORLDS AND MANY WORLDS MANY WORLDS: EVERETT, QUANTUM THEORY AND REALITY by Saunders, Barrett, Kent and Wallace Oxford University Press Oxford England 2012 The problem of realism and multiple realities in Quantum Mechanics THE HIDDEN REALITY: PARALLEL UNIVERSES AND THE DEEP LAWS OF THE COSMOS by Brian Greene Knopf 2011 The multiverse hypothesis in cosmology THE MANY WORLDS INTERPRETATION OF QUANTUM MECHANICS by Dewitt and Graham Princeton University Press Princeton NJ 1973 A probabilistic interpretation of reality THE GRAND DESIGN by Stephen Hawking and Leonard Mlodinow Bantam Books NY 2010 Reflections on the nature of reality by one of the centuries great thinkers THE HIDDEN REALITY by Brian Greene Knopf NY 2011 A physicist’s explanation of the many worlds hypothesis

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PHILOSOPHICAL METHOD by Timothy Williamson Oxford University Press Oxford England 2020 This short work covers many topics addressed in this book INTERVENTION AND RELECTION: BASIC ISSUES IN BIOETHICS 10th edition by Ronald Munson Cengage Learning 2016 DIAGNOSIS REASONING IN MEDICINE: AN INTRODUCTION TO CLINICAL INFERENCE by Albert, Munson and Resnik Johns Hopkins University Press Baltimore MD 1988 A philosophic approach to medical inference ABCS OF CLINICAL REASONING by Frain and Cooper BMJ Books London 2016 Principles of clear thinking for physicians LEARNING CLINICAL REASONING by Kassirer, Wong and Kopelman LWW Boston 2009 Case based approach to clinical reasoning from the Tuft Medical School Decision Analysis Group