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Mistakes of Reason

Mistakes of Reason: Essays in Honour of John Woods

Kent A. Peacock
Andrew D. Irvine
Copyright Date: 2005
Pages: 400
  • Book Info
    Mistakes of Reason
    Book Description:

    Over a distinguished academic career, the Canadian philosopher and scholar John Woods has written on a rich variety of topics central to contemporary philosophy. These include the history and philosophy of logic, deviant logics, inductive and abductive reasoning, informal reasoning, fallacy theory, the logic of fiction, epistemology, and abortion and euthanasia. Not only has Woods' work been significant in itself, it has also stimulated others working in these fields.

    Mistakes of Reasonis a tribute to Woods and contains twenty-six new essays by leading Canadian and international philosophers. The essays are accompanied by commentaries by Woods himself, creating a unique dialogue between Woods and his colleagues. Editors Kent A. Peacock and Andrew D. Irvine have grouped the works under the themes of Reality, Knowledge, Logic and Language, Reasoning, and Values. The essays evaluate Woods' work and celebrate the generous contribution that he has made to Canada?s intellectual development over the past forty years.

    eISBN: 978-1-4426-7729-6
    Subjects: Philosophy

Table of Contents

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  1. Front Matter
    (pp. i-iv)
  2. Table of Contents
    (pp. v-viii)
  3. Preface
    (pp. ix-x)
  4. Acknowledgements
    (pp. xi-2)
  5. Introduction: John Woods in Profile
    (pp. 3-12)

    Reason is one of the human species’ most important survival tools, and the capacity that philosophers once believed separates humanity from the lesser beasts. But it is notoriously fallible. ‘Mistakes of Reason,’ the title of this book, draws attention to the uncomfortable fact that our faculty of reason is beset with characteristictrompes l’oeil intellectuels, optical illusions of the mind. Many of these so-calledfallaciesare so typical of the human animal and so recurrent that we give them special names and teach them to undergraduates; but the flaws in reason are deep and systemic. They are not readily capturable...

  6. I Reality

    • 1 Through the Woods to Meinong’s Jungle
      (pp. 15-32)

      John Woods’The Logic of Fiction¹ was a pioneering treatment of the semantics of fictional discourse. As Woods notes in his introduction, philosophers of language had previously not paid much attention to the treatment of fiction – and this for entirely feeble reasons. Moreover, Woods made it clear that the two then-standard approaches – treating fiction by means of Russell’s theory of descriptions and thereby rendering all primary fictional discourse false, or treating it by means of free logic, and thereby rendering most of it truth-valueless – were both totally inadequate. It does no justice to fictional discourse to treat both ‘Sherlock Holmes...

    • 2 The Epsilon Logic of Fictions
      (pp. 33-48)
      B. H. SLATER

      John Woods considered a whole panoply of ways of treating fictions in his 1974 bookThe Logic of Fiction.¹ Notably, he considered the many forms of free logic which were then prevalent, and also several manyvalued logics. A number of specific problems ran through the discussion, concerning such examples as ‘SherlockHolmes had teawith Gladstone,’ ‘Kingsley Amis admires James Bond,’ ‘Freud psychoanalysedGradiva,’ Meinong’s notorious cases (‘the round square’ and ‘the gold mountain’), and the difference between, say, ‘Sherlock Holmes lived in Baker Street’ and ‘The present King of France is bald.’ I will return to some of the specific problems...

    • 3 Animadversions on the Logic of Fiction and Reform of Modal Logic
      (pp. 49-63)

      The idea that a logically possible world is identical with or can be described as a maximally consistent proposition set is a fundamental assumption of conventional semantics for modal logic. Although the concept is formally unproblematic, philosophically there are serious difficulties in the received definition of a logically possible world. I want to raise conceptual objections to the standard analysis and then sketch a proposal for modal semantics that strikes at the root of the problem in order to avoid these limitations. The conflict to which I call attention has recently been discussed as a dispute betweenmodal realismand...

    • 4 Resolving the Skolem Paradox
      (pp. 64-77)

      Cantor’s diagonal argument proves that the set of all sets of integers is uncountable. The Skolem-Löwenheim theorem proves that for any first-order theory there will always exist an enumerable model. How can these two results be reconciled? Putnam has argued that the tension between these two results refutes what he calls ‘moderate realism.’¹ Either we are forced to accept traditional epistemology in order to justify the truth of claims about non-denumerable sets or we are forced to abandon classical truth theory. This is a version of Benacerraf’s famous dilemma,² which requires philosophers of mathematics to choose between Platonism and a...

    • 5 Are Platonism and Pragmatism Compatible?
      (pp. 78-92)

      InThe Reach of Abduction, John Woods and Dov Gabbay note a parallel between Russell’s 1906–7 arguments for the ‘pragmatic’ selection of axioms and a similarly pragmatic criterion of axiom selection espoused by Gödel.¹ In conversation, Woods has further suggested that Gödel’s Pragmatism may not be compatible with his Platonism. Specifically, Woods asks ‘whether Gödel can be any kind of Platonist if he holds any version of the view that there are bits of mathematics, logic, or set theory for whose truth there is not the slightest justification apart from the fact that they can be implicated in propositions...

    • 6 A Neo-Hintikkan Solution to Kripke’s Puzzle
      (pp. 93-102)

      In ‘A Puzzle about Belief,’¹ Kripke argued that each member of the following pair of ascriptions to Pierre is true: ‘Pierre believes that London is pretty’ and ‘Pierre believes that London is not pretty.’ And he argued that the truth of these two ascriptions cannot be reconciled with the fact that Pierre – a leading logician – is rational. In this paper, I argue that the truth of the ascriptions in questioncanbe reconciled with Pierre’s rationality. The apparent contradiction between these two theses stems from a pair of presuppositions regarding the analysis of belief sentences. Strictly speaking, a solution to...

    • Part One: Respondeo
      (pp. 103-108)

      It was unjustified optimism to propose over thirty years ago, inThe Logic of Fiction,¹ that a correct semantic theory of the fictional would prove to be neither complex nor hard to produce. How wrong can one be? One of the sharp virtues of Nicholas Griffin’s chapter is that it puts considerable pressure on initially attractive distinctions, creatively muddying the waters in the process. A case in point is the distinction between nonesuches, such as the present king of France, and non-entities (or non-existents), such as the solver of the case of the speckled band. Part of the appeal of...

  7. II Knowledge

    • 7 The Day of the Dolphins: Puzzling over Epistemic Partnership
      (pp. 111-133)

      It is a curious but profoundly important fact that general philosophical problems, no matter how traditional or venerable, lead us into sticky technical problems. In fact, the topic of this paper is a technical problem about subjective probability reasoning, but I got into it quite innocently by taking a position in philosophy of science. It was an unpopular position, so I had a lot to defend. Today – well, after many years of struggle to vanquish the foes, and muchson et lumièreon both sides, it is still unpopular and there are still more technical problems ...but hope springs eternal...

    • 8 Cognitive Yearning and Fugitive Truth
      (pp. 134-157)

      The proximate cause of this essay is an account of plausibility to be found in various writings of Nicholas Rescher.¹ Rescher’s plausibility logic possesses considerable interest in its own right, but its more immediate appeal for me derives from work that Dov Gabbay and I have been doing on the logic of abduction.² Of course, there are lots of historically important abductions in which hypotheses are introduced on grounds other than their plausibility, indeed despite the total lack of it. But there are also cases galore in which the plausibility of a hypothesis plays a central role in an abducer’s...

    • 9 The de Finetti Lottery and Equiprobability
      (pp. 158-172)

      The axiom of countable additivity (CA) plays an essential role in modern probability theory. The axiom states:

      (CA) If we have a countable infinity of outcomes${H_1},{H_2},\;...$, ... that are mutually exclusive, then

      $P\left( {{H_1} \vee {H_2} \vee \;...} \right) = \;P\left( {{H_1}} \right) + P\left( {{H_2}} \right) + \;...$

      Kevin Kelly,¹ following de Finetti,² questions whether CA is an indispensable constraint on subjective interpretations of probability. In such interpretations, particularly as applied to the justification of scientific hypotheses, CA assumes great epistemological significance because of its role in deriving the convergence theorems.³ In essence, CA forces us to adopt the biased view that if there is ever going to be a counterexample to a universal...

    • 10 The Lottery Paradox
      (pp. 173-182)

      Gilbert Harman, inChange in View, twice discusses the problem of ‘the lottery paradox.’¹ The first time, he uses it to show how beliefs cannot explicitly be probability-based, and he returns to it when discussing inference from high statistical probability in order to show that such inferences do not yield the same paradoxical conclusion. While it may well be that humans do not explicitly reason using subjective degrees of belief, and that we may often safely infer from statistical likelihoods, it seems to me that the paradox as presented is not a good support for these conclusions. In fact, Harman’s...

    • 11 Reliabilism and Inference to the Best Explanation
      (pp. 183-196)

      Two of Bas van Fraassen’s significant challenges to the claim that inference to the best explanation (IBE) is a rationally required rule are the problem of the bad lot and the argument from indifference. These challenges rely on the observation that, even if the explanatory virtues (e.g., consilience, simplicity) are assumed to be evidential, the best explanation available to us might very well not be the best explanation overall. If we don’t have evidence that the best explanation available to us is the best explanation overall, then IBE can hardly be a rationally required rule.

      Due to his permissive voluntaristic...

    • Part Two: Respondeo
      (pp. 197-204)

      James Franklin sees in probability an interesting parallel with continuity and perspective.¹ All three of these things took a long time before yielding to mathematical formulation, and, before that happened, judgements of them tended to be unconscious and mistaken. I have a somewhat different version of this story. Sometimes a conceptually inchoate idea is cleaned up by a subsequent explication of it. Sometimes these clarifications are achieved by modelling the target notion mathematically. Sometimes the clarification could not have been achieved save for the mathematics. We may suppose that something like this has proved to be the case with perspective...

  8. III Logic and Language

    • 12 Aristotle and Modern Logic
      (pp. 207-223)
      D. A. CUTLER

      In general, a completeness theorem has the following form: If a conclusion is a semantic consequence of a set of premises, then the conclusion is deducible from the premises. In modern treatments, the deducibility relation is completely syntactic: it is defined on sequences of strings of uninterpreted symbols. Semantic consequence is defined in terms of truth in a structure and structures are usually regarded as set-theoretic constructs. The statement of the completeness theorem thus might appear to depend on concepts that are particular to modern mathematical logic.

      Can the question of completeness be raised in a form that does not...

    • 13 The Peculiarities of Stoic Propositional Logic
      (pp. 224-242)

      Aristotle, the founder of logic, nowhere defines the concepts of argument and of validity. He simply uses them in his definition of a syllogism as ‘an argument in which, certain things being posited, something other than those things laid down results of necessity through the things laid down.’¹ In reconstructing Aristotle’s early theory of syllogisms, JohnWoods² uses Aristotle’s reticence to interpret the basic concepts of argument and validity very liberally: arguments may have any number of premisses, even zero, and validity is the absence of a counter-model, constrained only by a requirement that premiss(es) and conclusion belong to the same...

    • 14 On the Substitutional Approach to Logical Consequence
      (pp. 243-263)

      The characterization of logical consequence in terms of substitutions is generally thought to be inadequate and is not taken seriously in the literature as a rival to the model-theoretic approach. While I am a fan of model theory, it seems to me that the substitutional approach to logical consequence has been mistreated. My aim in this paper is to defend it.

      I shall consider a well-known criticism of Quine’s version of the substitutional approach that is based on the claim that it expands the class of logical truths in first-order logic with identity beyond what is sanctioned by the model-theoretic...

    • 15 The Fallacy of Transitivity for Necessary Counterfactuals: On Behalf of (Certain) Non-Transitive Entailment Relations
      (pp. 264-278)

      In recent years various relations have been proposed as useful standards by which to judge the validity of deductive inferences. It has generally been assumed, however, that onlytransitiverelations need apply.¹ This essay challenges that assumption. There is at least one important use to which we put deductive inference which calls for a non-transitive standard. When we deduce one thing from another our purpose is very often to demonstrate that, of necessity, if the latter were the case the former would be also; we use deductions as conditional proofs to establish the necessary truth of a ‘subjunctive’ or ‘counterfactual’...

    • 16 Vagueness and Intuitionistic Logic: On the Wright Track
      (pp. 279-295)

      The basic structure of the sorites paradox is familiar to most philosophers and, what with the ever-expanding literature on vagueness, is by now painfully familiar to some. The discussion in this paper centres around a closely related paradox – the ‘no sharp boundaries’ paradox – and what Crispin Wright has to say about it. I therefore reluctantly begin by sketching the sorites once again, so that the motivation for Wright’s introduction of this paradox can be made clear and so that the paradox can be contrasted to the standard sorites paradoxes.

      At the centre of any sorites paradox is an argument of...

    • 17 The Semantic Illusion
      (pp. 296-320)

      On any plausible use of the wordphenomenon, language must be regarded as a physical or more specifically a biological phenomenon. We emit sequences of sounds or we commit inscriptions, and those sounds and those inscriptions have biological and other physical effects. I say, in the course of a lecture, ‘Would someone please be good enough to open a window?’ and with sufficient luck and patient repetition, someone will rise to a semi-upright position, move to the transparent side of the room, whichever side that is, fumble with a catch and push out a casement, or throw up a sash,...

    • Part Three: Respondeo
      (pp. 321-328)

      When examining an ancient theory, the investigator of intellectual history is faced with a choice between two main interpretations. One is that the theory is of merely antiquarian interest. The other is that it is still sufficiently alive to resonate with present-day concerns. When this is so, it is possible to see the theory as engaging those concerns and doing so in ways from which modern theories might learn something. We may then speak of the ancient theory as acontendingtheory. One of the attractions of the chapters by Darcy Cutler and David Hitchcock is their respective suggestions of...

  9. IV Reasoning

    • 18 Arguing from Authority
      (pp. 331-347)

      There is wide (but not universal) agreement across many disciplines about how correct or good reasoning or arguing from medical and other diagnostic test results (such as lie detectors) should proceed. According to this view, when reasoning or arguing from a medical or other diagnostic test result is good or correct, it is so because it is deductively sound reasoning using probabilities. In particular, it is deductively sound reasoning using Bayes’ theorem to calculate a posterior probability based on the new information provided by the test result together with independent, old information available prior to the test. Here is a...

    • 19 Premiss Acceptability and Truth
      (pp. 348-363)

      As is well known, formal deductive logic proposessoundnessas the criterion of argument cogency, and to be sound the premisses of an argument must be true.¹ A hallmark of the informal logic movement has been replacing the formal logic criterion with premiss acceptability, relevance, and ground adequacy. Acceptability is not the same as truth. Arguing that being true is neither a necessary nor a sufficient condition for acceptability is straightforward. It is not necessary because the preponderance of evidence at one’s disposal might favour some statement which is, in fact, false. In such circumstances, it seems that statement would...

    • 20 Emotion, Relevance, and Consolation Arguments
      (pp. 364-379)

      There is a kind of argument offered to console people who are sorry or depressed, to the effect that they should not feel so badly because others are even worse off. In such arguments, B tries to console A for A’s suffering on the grounds that some other person or persons, C, have suffered equally bad things or even worse. Here, A and B may be the same person: people sometimes seek to console themselves. The point is to diminish A’s grief on the grounds that he or she is not alone in feeling it. If a person is grieving...

    • 21 Temporal Agents
      (pp. 380-397)

      By embracing psychologism in their ‘New Logic,’ Gabbay and Woods¹ admit inference that is fallacious in traditional logic. This is justified by arguments such as the usefulness of shortcuts for achieving effective response from an agent with limited computational time and space. The cited paper stands as an informal prelude to a logic of wider ambit, including abduction and discovery, an unconventional, groundbreaking logic whose consequences are to be induced from inference steps which include the seemingly fallacious.

      Although inspired by the new logic, this paper is more concerned with processes and their logical presentation: the computational processes of a...

    • 22 Filtration Structures and the Cut Down Problem for Abduction
      (pp. 398-417)

      In its most basic intuitive sense, abduction is a process of reasoning in which a target which cannot be hit with existing information is judged hittable upon the assumption of additional facts. It is then concluded that this is reason to take that assumption itself as at least a candidate for the status of fact. We want to say something here about the logical structure of such reasoning. We want, more particularly, to expose something of the logical structure of abductive reasoning when it is transacted by apractical agent. The present chapter draws upon our recent book,The Reach...

    • 23 Mistakes in Reasoning about Argumentation
      (pp. 418-441)

      When critical thinking theorists, pragma-dialecticians, and informal logicians use the expressions ‘theory of argument,’ or ‘argumentation theory,’ and ‘fallacy theory,’ they usually take an argument to consist in considerably more than a set of propositions. Their view varies significantly from that of formal logicians. Rather, they take an argument to consist in, but not to be restricted to, a set of premisses that allegedly support a conclusion with the intention of changing someone’s belief. For them an argument is a dynamic relationship; indeed, it is a social activity. In this way they believe themselves to study real-life, or ordinary-language, arguments...

    • Part Four: Respondeo
      (pp. 442-450)

      I have come to distrust the emphasis some logicians give to the notion of rationality. I have nothing against the concept intrinsically, but it shares some associational guilt with the tendentiousness with which these theorists invoke it. If I were czar for a day or so, I would place a moratorium on all talk of rationality by logicians. The fact remains that it is a deeply entrenched idea, much favoured by the establishment; it should prove difficult to dislodge. Logicians, and many other theorists of human performance – argumentation theorists, economists, and the like – are drawn to the idea that their...

  10. V Values

    • 24 Engineered Death and the (II) logic of Social Change
      (pp. 453-473)

      The focal point of this paper is John Woods’ argument in ‘Privatizing Death: Metaphysical Discouragements of Ethical Thinking.’¹ I first encountered this argument, or at least its core, in one of my first years at the University of Lethbridge, at the Great Debate in 1991 between John Woods and Dr Henry Morgentaler, who was by then the triumphant icon of the pro-choice side of the abortion controversy in Canada.

      The debate was held in the university gymnasium, which seats nearly 1300. The seats were packed full for the debate, not just with university people, but with people from across southern...

    • 25 Incorrect English
      (pp. 474-490)

      Moderate views are attractive to many people, and sometimes that’s at least partly because they’re so-called. Abortion, I tend to think, is a case in point. Few philosophers consider themselves extreme conservatives, extreme liberals, or even conservatives, though a substantial number think of themselves as liberals, with ‘liberal’ probably meaning, at least in their minds, much the same thing as ‘moderate.’ In any case, one of the best-known defences of the so-called moderate position on abortion is Jane English’s ‘Abortion and the Concept of a Person.’ First published in 1975, English’s article is, by my reckoning, one of the four...

    • 26 Ameliorating Computational Exhaustion in Artificial Prudence
      (pp. 491-503)

      Those of us long-since committed to the view that the languages of war, politics, economics, and morality are reducible without remainder to game theory, are wont todismissthe worries of our skeptics, preciselybecausewe’re so immersed in ourWeltanschauungthat these worries no longer resonate in us. To the claim that ‘The human condition is simply too complex to be captured by such a sparse set of axioms and primitives!’ we’re wont to reply, ‘Just watch us!’ To the insistence that ‘There’s more to understanding than prediction and control!’ we’re wont to wonder, ‘What?!’ And to the...

    • Part Five: Respondeo
      (pp. 504-510)

      What got me thinking about engineered death was, especially in the case of abortion, the massiveness and sheer speed of the collapse of received opinions, a paradigm shift in moral thinking about death. InEngineered Death,¹ I set myself two questions about abortion. I was interested in reflecting on the conditions that gave rise to this paradigm shift. I also wanted to determine whether the dialectical wherewithal existed with which to defend the old way of thinking. In the first instance, I conjectured that the displacement of the theological conception of death by what I called the secular conception threw...

  11. Contributors
    (pp. 511-516)
  12. Books by John Woods
    (pp. 517-520)
  13. Index
    (pp. 521-533)