Books by Timothy Williamson
Four people with radically different outlooks on the world meet on a train and start talking abou... more Four people with radically different outlooks on the world meet on a train and start talking about what they believe. Their conversation varies from cool logical reasoning to heated personal confrontation. Each starts off convinced that he or she is right, but then doubts creep in.
In a tradition going back to Plato, Timothy Williamson uses a fictional conversation to explore questions about truth and falsity, and knowledge and belief. Is truth always relative to a point of view? Is every opinion fallible? Such ideas have been used to combat dogmatism and intolerance, but are they compatible with taking each opposing point of view seriously? This book presupposes no prior acquaintance with philosophy, and introduces its concerns in an accessible and light-hearted way. Is one point of view really right and the other really wrong? That is for the reader to decide.
Twitter: https://twitter.com/TetralogueBook
OUP: http://ukcatalogue.oup.com/product/9780198728887.do
Papers by Timothy Williamson
Journal of Chinese Philosophy
The article defends moral realism against epistemological objections by arguing that if there are... more The article defends moral realism against epistemological objections by arguing that if there are moral truths, some of them are known. The claim that moral properties are unknowable because causally inert is shown to be ineffective: none of the main current theories of knowledge requires a causal connection, and anyway moral properties have not been shown to be causally inert. It is explained why a posteriori moral knowledge need not derive from combining a priori moral knowledge with a posteriori non-moral knowledge. The possibility of moral knowledge by perception and by testimony is briefly defended. The role of recognitional capacities for instances of moral properties is emphasized.
Proceedings of the Aristotelian Society, Supplementary Volumes, 1992
No one knows whether I'm thin. I'm not clearly thin; I'm not clearly not thin. The... more No one knows whether I'm thin. I'm not clearly thin; I'm not clearly not thin. The word'thin'is too vague to enable'TW is thin'to be recognized as true or as false, however accurately my waist is measured and the result compared with vital statistics for the rest of the population. Is this ignorance? Most work on vagueness has taken for granted the answer'No'. According to it, there is nothing here to be known. I am just a borderline case of thinness;'TW is thin'is neither true nor false. Doubt will be cast on the coherence of this view. There are standard ...
Analysis
Conspicuously missing some planks, a latter-day Ship of Theseus catches the eye when one picks up... more Conspicuously missing some planks, a latter-day Ship of Theseus catches the eye when one picks up this Book of Three Authors. Teasingly, differentiated prepositions between their names on the title page hint at its complex history. The result is a formidable achievement, exemplifying contemporary metaphysics at its best. Puzzles of variation arise from pre-reflectively plausible tolerance principles, on which an artefact survives any small variation in its constituents but no large variation in them: unfortunately, many small variations make a large variation. The variations may be across times or across possibilities, though
Canadian Journal of Philosophy, 2016
In 'Epistemicism and modality', Juhani Yli-Vakkuri rigorously treats the problem of developing a ... more In 'Epistemicism and modality', Juhani Yli-Vakkuri rigorously treats the problem of developing a model-theoretic semantics for a formal language with the operators 'necessarily' and 'actually', interpreted in terms of metaphysical modality, and an operator 'definitely', interpreted in the spirit of the epistemicist theory of vagueness developed in my book (Williamson 1994). The challenge is especially pertinent because my epistemicist account of definiteness has a modal dimension, whose interaction with other forms of modal variation raises delicate issues for the overall theory. 1. Worldly differences and semantic differences According to epistemicism, vagueness in a language induces no deviation from classical logic or from bivalent semantics. It is a purely epistemic phenomenon: borderline cases are just cases of unavoidable ignorance for a special sort of reason. The actual meaning of a vague brought to you by CORE View metadata, citation and similar papers at core.ac.uk provided by PhilPapers 2 expression differs from some of its potential alternative meanings in ways indiscriminable by native speakers of the language. Following John Hawthorne, Yli-Vakkuri calls this idea 'Semantic Plasticity'. The upshot is a special obstacle to knowing some truths expressed using the vague expression. Very roughly, the definite truths are those knowledge of which is not blocked by an obstacle of that sort. I developed the underlying epistemology in safety-theoretic terms. Knowledge requires safety from error: one knows in a given case only if it is not relevantly close to an error possibility. Actuality is never close in that sense to metaphysical impossibilities, because they present no real danger. Compare a case where one assents to a true proposition expressed by a vague sentence with a similar case where one assents to a false proposition expressed by the same sentence. 1 The difference in truth-value may result from either one of two kinds of difference between the cases (perhaps from both). The first kind of difference is worldly. The vague sentence may express the same proposition in the two cases, while the objects under discussion vary in their properties or relations. For instance, in both cases the sentence 'Jack is bald' expresses the proposition that Jack is bald, but Jack has less hair in one case than in the other. Thus the sentence 'Jack is bald' may express a true proposition in the former case and a false proposition in the latter. The second kind of difference between cases is semantic. Even if the objects under discussion have the same properties and relations in the two cases, the sentence 'Jack is bald' may express different propositions, because it is used in very slightly different ways. For instance, in one case the sentence 'Jack is bald' still expresses the proposition that Jack is bald, while in the other it expresses the distinct proposition that Jack is bald*, where the standard for being bald* is slightly more demanding than the standard for being bald. Thus, even though the state of
Synthese
The paper explains how to integrate the knowledge-first approach to epistemology with the intelle... more The paper explains how to integrate the knowledge-first approach to epistemology with the intellectualist thesis that knowing-how is a kind of knowing-that, with emphasis on their role in practical reasoning. One component of this integration is a belief-based account of desire.
Canadian Journal of Philosophy, 2016
In 'Models and Reality', Robert Stalnaker responds to the tensions discerned in Modal Logic as Me... more In 'Models and Reality', Robert Stalnaker responds to the tensions discerned in Modal Logic as Metaphysics between contingentism in modal metaphysics and the use of Kripke models in the semantics of modal logic. Stalnaker holds that 'the tensions in our intuitive conception of modal phenomena are real: both the contingency intuitions and the Kripke structures have features that need to be reconciled' (section 5), and that 'The contingency intuitions are not unassailable data' (section 7). His strategy for achieving reconciliation involves accepting 'the contingency intuitions' while arguing that 'we can use models to give a fully realistic interpretation of a modal language without giving a realistic interpretation of the models we are using' (section 1). The paper follows up the strategy of Stalnaker's earlier work (2010, 2012). Of his defence of contingentism and its compatibility with orthodox Kripke semantics, he writes (in section 1): that defense was not as explicit as it should have been about the status that I take Kripke models to have, and about the relation between these models and the reality that one is using them to model. This paper is an attempt to spell out in a little more detail what I take this relation to be.
Phenomenology and Mind, 2018
The method of building simplified formal models of phenomena under study is widespread in contemp... more The method of building simplified formal models of phenomena under study is widespread in contemporary natural and social science; much scientific progress consists in the provision of better models. A model-building methodology has also been used with success in analytic philosophy, for example by Carnap in his development of intensional semantics. Arguably, philosophers have overlooked how much progress their discipline has made through their failure to conceive it in model-building terms. By using the method more extensively, they can overcome the fragility to error inherent in the naive falsificationist methodology on which many analytic philosophers rely.
Linguistics and Philosophy, 2004
Logic, Epistemology, and the Unity of Science
Some systems of modal logic, such as S5, which are often used as epistemic logics with the 'neces... more Some systems of modal logic, such as S5, which are often used as epistemic logics with the 'necessity' operator read as 'the agent knows that', are problematic as general epistemic logics for agents whose computational capacity does not exceed that of a Turing machine because they impose unwarranted constraints on the agent's theory of non-epistemic aspects of the world, for example by requiring the theory to be decidable rather than merely recursively axiomatizable. To generalize this idea, two constraints on an epistemic logic are formulated: r.e. conservativeness, that any recursively enumerable theory R in the sublanguage without the epistemic operator is conservatively extended by some recursively enumerable theory in the language with the epistemic operator which is permitted by the logic to be the agent's overall theory; the weaker requirement of r.e. quasi-conservativeness
When mathematicians discuss proofs, they rarely have a particular formal system in mind. Indeed, ... more When mathematicians discuss proofs, they rarely have a particular formal system in mind. Indeed, they are typically not thinking of formal systems at all, although they might accept the suggestion that a genuine proof can in principle be reconstructed in an appropriate formal system. The picture is more like this. At any given time, the mathematical community has a body of knowledge, including both theorems and methods of proof. Mathematicians expand mathematical knowledge by recursively applying it to itself, adding new theorems and sometimes new derived methods of proof. Of course, present mathematical knowledge itself grew out of a smaller body of past mathematical knowledge by the same process. Since present mathematical knowledge is presumably finite, if one traces the process back far enough, one eventually reaches ‘first principles’ of some sort that did not become mathematical knowledge in that way. Some principles 2 of logic and axioms of set theory are good candidates for ...
Higher-Order Evidence
The slogan ‘Evidence of evidence is evidence’ is obscure. It has been applied to connect evidence... more The slogan ‘Evidence of evidence is evidence’ is obscure. It has been applied to connect evidence in one situation to evidence in another. The link may be diachronic or interpersonal. Is present evidence of past or future evidence for p present evidence for p? Is evidence for me of evidence for you for p evidence for me for p? The chapter discusses intra-perspectival evidential links. Is present evidence for me of present evidence for me for p present evidence for me for p? Unless the connection holds between a perspective and itself, it is unlikely to hold between distinct perspectives. Evidence will be understood probabilistically, using formal models from epistemic logic. Bridge principles between first-level and higher-level epistemic conditions often imply versions of controversial principles, such as positive and negative introspection. Formalizations of intra-perspectival principles that evidence of evidence is evidence have similarly implausible connections.
This chapter responds to Saul Kripke’s critique of the idea of adopting an alternative logic. It ... more This chapter responds to Saul Kripke’s critique of the idea of adopting an alternative logic. It defends an anti-exceptionalist view of logic, on which coming to accept a new logic is a special case of coming to accept a new scientific theory. The approach is illustrated in detail by debates on quantified modal logic. A distinction between folk logic and scientific logic is modelled on the distinction between folk physics and scientific physics. The importance of not confusing logic with metalogic in applying this distinction is emphasized. Defeasible inferential dispositions are shown to play a major role in theory acceptance in logic and mathematics as well as in natural and social science. Like beliefs, such dispositions are malleable in response to evidence, though not simply at will. Consideration is given to the Quinean objection that accepting an alternative logic involves changing the subject rather than denying the doctrine. The objection is shown to depend on neglect of th...
The Philosophy of Philosophy
This appendix experiments with an alternative way of formalizing the anaphora in the major premis... more This appendix experiments with an alternative way of formalizing the anaphora in the major premises of the arguments underlying philosophical thought experiments, by permitting the conditional in them to bind variables. Thus we formalize (5), (6) and (13) in Chapter 6 respectively as: (A1) GC(x, p) AE x,p (JTB(x, p) & ÿ K(x, p)) (A2) (Farmer(x) & Donkey(y) & Owns(x, y)) AE x,p Beats(x, y) (A3) (Animal(x) & Escapedzoo(x)) AE x Monkey(x)
Operational epistemology is, to a first approximation, the attempt to provide cognitive rules suc... more Operational epistemology is, to a first approximation, the attempt to provide cognitive rules such that one is in principle always in a position to know whether one is complying with them. In Knowledge and its Limits, I argue that the only such rules are trivial ones. In this paper, I generalize the argument in several ways to more thoroughly probabilistic settings, in order to show that it does not merely demonstrate some oddity of the folk epistemological conception of knowledge. Some of the generalizations involve a formal semantic framework for treating epistemic probabilities of epistemic probabilities and expectations of expectations. The upshot is that operational epistemology cannot work, and that knowledge-based epistemology has the right characteristics to avoid its problems.
The first part of the talk will highlight the way in which assumptions widespread in the literatu... more The first part of the talk will highlight the way in which assumptions widespread in the literature on reasoning about knowledge generate the traditional philosophical problem of scepticism. The problematic assumptions to be discussed here do not include logical omniscience, but are equally serious. My particular concern will be with the so-called Brouwerian axiom: ~p ↓ K~Kp (if p is false, an agent knows that she does not know p). This axiom follows from the 'negative introspection' axiom ~Kp ↓ K~Kp and the 'truth' axiom Kp ↓ p. It corresponds to the condition that the accessibility relation for knowledge be symmetric, and holds on the partition model of knowledge. Let s be a situation in which an agent gains some knowledge p of the external world (Kp), believes that she does so (BKp) and has consistent beliefs (so ~B-Kp). Let s* be a situation in which p is false (~p) but the input from the external world to the agent is the same as in s, so that the agent has the ...
Crítica (México D. F. En línea)
En este artículo se intenta mostrar que el principio (AA) tiene consecuencias falsas. Dicho princ... more En este artículo se intenta mostrar que el principio (AA) tiene consecuencias falsas. Dicho principio es el siguiente (donde ‘ser afirmable’ abrevia ‘ser afirmable de manera justificada’): (AA) Si es afirmable que P, entonces es afirmable que es afirmable que P. (AA) está implícito en las objeciones de Dummett a las teorías del significado en términos de condiciones de verdad. Según Dummett dichas teorías violan la conexión necesaria entre uso y significado: dado que los usuarios exitosos de una oración pueden ser incapaces de reconocer que se dan las condiciones de verdad de la oración cuando éstas de hecho se dan, el que se den dichas condiciones es una característica del significado que no está reflejada adecuadamente en el uso de la oración. Dummett propone que los significados de las oraciones se den en términos no de sus condiciones de verdad, sino de sus condiciones de afirmabilidad. Para evitar que la objeción se aplique a la teoría del significado propuesta por Dummett, ést...
Canadian Journal of Philosophy
In 'An A-theory without tense operators', Meghan Sullivan vigorously contests the received view t... more In 'An A-theory without tense operators', Meghan Sullivan vigorously contests the received view that an A-theory of time is adequately expressible only in a language with sentential tense operators. She develops and defends an interesting alternative A-theory in a language with tense predicate modifiers instead. Her argument intersects Modal Logic as Metaphysics at several points. The proper formulation of A-theoretic doctrines such as presentism is sensitive to the background quantified temporal logic, and in particular to the dispute between permanentism and temporaryism, the temporal analogue in the book of the modal dispute between necessitism and contingentism: the permanentist asserts, and the temporaryist denies, that always everything is always something. Moreover, I sketch a conception of radical change, analogous to radical contingency, adequately expressible only in A-theoretic language (Williamson 2013, pp. 403-22). I agree with Sullivan that an A-theory is adequately expressible in a language with temporal predicate modifiers. However, I will question whether the move to such a language makes as much difference as Sullivan suggests, and whether it has the advantages she claims for it.
Canadian Journal of Philosophy
Philosophical Issues
The hardest test of deviant logic is mathematics, which constitutes by far the most sustained and... more The hardest test of deviant logic is mathematics, which constitutes by far the most sustained and successful deductive enterprise in human history. With only minor exceptions, mathematicians have freely relied on classical logic, including principles such as the law of excluded middle, A or ¬A. They unquestioningly accept classical reasoning in proofs. When deviant logicians reject a classical principle, they face an obvious challenge: what does that mean for mathematics? Where does it leave theorems whose proofs rely on the principle?
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Books by Timothy Williamson
In a tradition going back to Plato, Timothy Williamson uses a fictional conversation to explore questions about truth and falsity, and knowledge and belief. Is truth always relative to a point of view? Is every opinion fallible? Such ideas have been used to combat dogmatism and intolerance, but are they compatible with taking each opposing point of view seriously? This book presupposes no prior acquaintance with philosophy, and introduces its concerns in an accessible and light-hearted way. Is one point of view really right and the other really wrong? That is for the reader to decide.
Twitter: https://twitter.com/TetralogueBook
OUP: http://ukcatalogue.oup.com/product/9780198728887.do
Papers by Timothy Williamson
In a tradition going back to Plato, Timothy Williamson uses a fictional conversation to explore questions about truth and falsity, and knowledge and belief. Is truth always relative to a point of view? Is every opinion fallible? Such ideas have been used to combat dogmatism and intolerance, but are they compatible with taking each opposing point of view seriously? This book presupposes no prior acquaintance with philosophy, and introduces its concerns in an accessible and light-hearted way. Is one point of view really right and the other really wrong? That is for the reader to decide.
Twitter: https://twitter.com/TetralogueBook
OUP: http://ukcatalogue.oup.com/product/9780198728887.do