Timothy Williamson gives an original and provocative treatment of deep metaphysical questions about existence, contingency, and change, using the latest resources of quantified modal logic. Contrary to the widespread assumption that logic and metaphysics are disjoint, he argues that modal logic provides a structural core for metaphysics.

Timothy Williamson has argued that in the debate on modal ontology, the familiar distinction between actualism and possibilism should be replaced by a distinction between positions he calls contingentism and necessitism. He has also argued in favor of necessitism, using results on quantified modal logic with plurally interpreted second-order quantifiers showing that necessitists can draw distinctions contingentists cannot draw. Some of these results are similar to well-known results on the relative expressivity of quantified modal logics with so-called inner and outer (...) quantifiers. The present paper deals with these issues in the context of quantified modal logics with generalized quantifiers. Its main aim is to establish two results for such a logic: Firstly, contingentists can draw the distinctions necessitists can draw if and only if the logic with inner quantifiers is at least as expressive as the logic with outer quantifiers, and necessitists can draw the distinctions contingentists can draw if and only if the logic with outer quantifiers is at least as expressive as the logic with inner quantifiers. Secondly, the former two items are the case if and only if all of the generalized quantifiers are first-order definable, and the latter two items are the case if and only if first-order logic with these generalized quantifiers relativizes. (shrink)

In order to perfectly describe the world, it is not enough to speak truly. One must also use the right concepts - including the right logical concepts. One must use concepts that "carve at the joints", that give the world's "structure". There is an objectively correct way to "write the book of the world". Much of metaphysics, as traditionally conceived, is about the fundamental nature of reality; in the present terms, this is about the world's structure. Metametaphysics - inquiry into (...) the status of metaphysical questions - turns on structure. The question of whether ontological, causal, or modal questions are "substantive" is in large part a question of whether the world has ontological, causal, and modal structure - whether quantifiers, causal relations, and modal operators carve at the joints. (shrink)

But Findlay's remark, like so much that has been written on the subject of time in the present century, was provoked in the first place by McTaggart's ...

Science Without Numbers caused a stir in 1980, with its bold nominalist approach to the philosophy of mathematics and science. It has been unavailable for twenty years and is now reissued in a revised edition with a substantial new preface presenting the author's current views and responses to the issues raised in subsequent debate.

Develops a structuralist understanding of mathematics, as an alternative to set- or type-theoretic foundations, that respects classical mathematical truth while ...

This is the second edition of an award-winning 1981 book (Princeton University Press and Basil Blackwell, based on the author’s doctoral dissertation) considered to be a classic in the philosophy of language movement known variously as the New Theory of Reference or the Direct-Reference Theory, as well as in the metaphysics of modal essentialism that is related to this philosophy of language.

Woodward's long awaited book is an attempt to construct a comprehensive account of causation explanation that applies to a wide variety of causal and explanatory claims in different areas of science and everyday life. The book engages some of the relevant literature from other disciplines, as Woodward weaves together examples, counterexamples, criticisms, defenses, objections, and replies into a convincing defense of the core of his theory, which is that we can analyze causation by appeal to the notion of manipulation.

Professional philosophers and advanced students working in metaphysics and the philosophy of science will find this book both provocative and stimulating.

It is my aim in this paper to show that the contemporary assimilation of essence to modality is fundamentally misguided and that, as a consequence, the corresponding conception of metaphysics should be given up. It is not my view that the modal account fails to capture anything which might reasonably be called a concept of essence. My point, rather, is that the notion of essence which is of central importance to the metaphysics of identity is not to be understood in (...) modal terms or even to be regarded as extensionally equivalent to a modal notion. The one notion is, if I am right, a highly refined version of the other; it is like a sieve which performs a similar function but with a much finer mesh. (shrink)

Even if non-cognitivists about some subject-matter can meet Geach’s challenge to explain how there can be valid implications involving sentences which express non-cognitive attitudes, they face a further problem. I argue that a non-cognitivist cannot explain how, given a valid argument whose conclusion expresses a belief and at least one of whose premises expresses a non-cognitive attitude, it could be reasonable to infer the conclusion from the premises.

The dogma that the propositional logic of metaphysical modality is S5 is rebutted. The author exposes fallacies in standard arguments supporting S5, arguing that propositional metaphysical modal logic is weaker even than both S4 and B, and is instead the minimal and weak metaphysical-modal logic T.

In this paper I offer an account of the meaning of must and can within the framework of possible worlds semantics. The paper consists of two parts: the first argues for a relative concept of modality underlying modal words like must and can in natural language. I give preliminary definitions of the meaning of these words which are formulated in terms of logical consequence and compatibility, respectively. The second part discusses one kind of insufficiency in the meaning definitions given in (...) the first part, which arise from the ex falso quodlibet paradox of logical consequence. In stepwise fashion, I make an attempt to avoid most of the consequences of this paradox for the meaning definitions of must and can. (shrink)

This is a book about how we see: the environment around us (its surfaces, their layout, and their colors and textures); where we are in the environment; whether or not we are moving and, if we are, where we are going; what things are good for; how to do things (to thread a needle or drive an automobile); or why things look as they do.The basic assumption is that vision depends on the eye which is connected to the brain. The (...) author suggests that natural vision depends on the eyes in the head on a body supported by the ground, the brain being only the central organ of a complete visual system. When no constraints are put on the visual system, people look around, walk up to something interesting and move around it so as to see it from all sides, and go from one vista to another. That is natural vision—and what this book is about. (shrink)

Jaegwon Kim is one of the most preeminent and most influential contributors to the philosophy of mind and metaphysics. This collection of essays presents the core of his work on supervenience and mind with two sets of postscripts especially written for the book. The essays focus on such issues as the nature of causation and events, what dependency relations other than causal relations connect facts and events, the analysis of supervenience, and the mind-body problem. A central problem in the philosophy (...) of mind is the problem of explaining how the mind can causally influence bodily processes. Professor Kim explores this problem in detail, criticizes the nonreductionist solution of it, and offers a modified reductionist solution of his own. Both professional philosophers and their graduate students will find this an invaluable collection. (shrink)

A transcript of three lectures, given at Princeton University in 1970, which deals with (inter alia) debates concerning proper names in the philosophy of language.

We defend the thesis that every necessarily true proposition is always true. Since not every proposition that is always true is necessarily true, our thesis is at odds with theories of modality and time, such as those of Kit Fine and David Kaplan, which posit a fundamental symmetry between modal and tense operators. According to such theories, just as it is a contingent matter what is true at a given time, it is likewise a temporary matter what is true at (...) a given possible world; so a proposition that is now true at all worlds, and thus necessarily true, may yet at some past or future time be false in the actual world, and thus not always true. We reconstruct and criticize several lines of argument in favor of this picture, and then argue against the picture on the grounds that it is inconsistent with certain sorts of contingency in the structure of time. (shrink)

The paper sketches an epistemology of de re possibility centred on the notion of similarity. The proposal is, roughly, that we know about some entities’ unrealized possibilities by extrapolation from knowledge about some other, similar entities’ realized possibilities. The account is limited, among other things, in that it does not cover knowledge of de re necessities or essentialist knowledge, if we have it. But even if alternative epistemologies could explain that type of knowledge too, the current account is found to (...) best explain the de re possibility knowledge, thereby resisting a potential charge of redundancy. (shrink)

For three decades the writings of Jaegwon Kim have had a major influence in philosophy of mind and in metaphysics. Sixteen of his philosophical papers, together with several new postscripts, are collected in Kim [1993]. The publication of this collection prompts the present essay. After some preliminary remarks in the opening section, in Section 2 I will briefly describe Kim's philosophical 'big picture' about the relation between the mental and the physical. In Section 3 I will situate Kim's approach on (...) the larger philosophical landscape, vis-à-vis various other approaches frequently discussed in contemporary philosophy of mind. This comparative discussion will further illuminate Kim's own position, and also will serve as groundwork for subsequent discussion. In Section 4 I will point out certain persistent internal tensions in Kim's philosophical position on the mind--body problem, tensions that emerge especially clearly against the backdrop of Section 3's comparative discussion of Kim's position relative to various competing positions. In the remainder of the paper I will focus on two issues at the heart of his position, with particular attention to what he says about them in some of the more recent papers and the postscripts in Kim [1993]. First, how should a materialist understand the notion that the mental is 'determined' by the physical? More specifically, what role, if any, should be played by the concept of supervenience in explicating this kind of determination relation? Kim's views on this matter have recently changed, and I will discuss the issue with particular attention to his own latest remarks on it. This is the business of Section 5. Second, need a viable materialism assert that mentalistic psychology is reducible to neurobiology? More specifically, should a materialist insist on reducibility, despite the currently influential line of argument used by non-reductive materialists, the 'multiple realization' argument? On this matter too, Kim's views have changed somewhat; again, I will discuss the issue with particular attention to his recent thinking. This is the business of Section 6. (shrink)

Williamsonian modal epistemology is characterized by two commitments: realism about modality, and anti-exceptionalism about our modal knowledge. Williamson’s own counterfactual-based modal epistemology is the best known implementation of WME, but not the only option that is available. I sketch and defend an alternative implementation which takes our knowledge of metaphysical modality to arise, not from knowledge of counterfactuals, but from our knowledge of ordinary possibility statements of the form ‘x can F’. I defend this view against a criticism indicated in (...) Williamson’s own work, and argue that it is better connected to the semantics of modal language. (shrink)

Isn't probability 1 certainty? If the probability is objective, so is the certainty: whatever has chance 1 of occurring is certain to occur. Equivalently, whatever has chance 0 of occurring is certain not to occur. If the probability is subjective, so is the certainty: if you give credence 1 to an event, you are certain that it will occur. Equivalently, if you give credence 0 to an event, you are certain that it will not occur. And so on for other (...) kinds of probability, such as evidential probability. The formal analogue of this picture is the regularity constraint: a probability distribution over sets of possibilities is regular just in case it assigns probability 0 only to the null set, and therefore probability 1 only to the set of all possibilities. (shrink)

It is widely assumed that sense perception cannot deliver knowledge of nonactual (metaphysical) possibilities. We are not supposed to be able to know that a proposition p is necessary or that p is possible (if p is false) by sense perception. This paper aims to establish that the role of sense perception is not so limited. It argues that we can know lots of modal facts by perception. While the most straightforward examples concern possibility and contingency, others concern necessity and (...) impossibility. The possibility of a perceptual route to some modal knowledge is not as radical as it may at first sound. On the contrary, acknowledging it has benefits. (shrink)

This book is a defense of modal realism; the thesis that our world is but one of a plurality of worlds, and that the individuals that inhabit our world are only a few out of all the inhabitants of all the worlds. Lewis argues that the philosophical utility of modal realism is a good reason for believing that it is true.

Boris Kment takes a new approach to the study of modality that emphasises the origin of modal notions in everyday thought. He argues that the concepts of necessity and possibility originate in counterfactual reasoning, which allows us to investigate explanatory connections. Contrary to accepted views, explanation is more fundamental than modality.

The use of tensed language and the metaphor of set ‘formation’ found in informal descriptions of the iterative conception of set are seldom taken at all seriously. Both are eliminated in the nonmodal stage theories that formalise this account. To avoid the paradoxes, such accounts deny the Maximality thesis, the compelling thesis that any sets can form a set. This paper seeks to save the Maximality thesis by taking the tense more seriously than has been customary (although not literally). A (...) modal stage theory, MST, is developed in a bimodal language, governed by a tenselike logic. Such a language permits a very natural axiomatisation of the iterative conception, which upholds the Maximality thesis. It is argued that the modal approach is consonant with mathematical practice and a plausible metaphysics of sets and shown that MST interprets a natural extension of Zermelo set theory less the axiom of Infinity and, when extended with a further axiom concerning the extent of the hierarchy, interprets Zermelo–Fraenkel set theory. (shrink)

Antihaecceitists believe that all facts about specific individuals—such as the fact that Fred exists, or that Katie is tall—globally supervene on purely qualitative facts. Haecceitists deny that. The issue is not only of interest in itself, but receives additional importance from its intimate connection to the question of whether all fundamental facts are qualitative or whether they include facts about which specific individuals there are and how qualitative properties and relations are distributed over them. Those who think that all fundamental (...) facts are qualitative are arguably committed to antihaecceitism. The goal of this paper is to point out some problems for antihaecceitism (and therefore for the thesis that all fundamental facts are qualitative). The article focuses on two common assumptions about possible worlds: (i) Sets of possible worlds are the bearers of objective physical chance. (ii) Counterfactual conditionals can be defined by appeal to a relation of closeness between possible worlds. The essay tries to show that absurd consequences ensue if either of these assumptions is combined with antihaecceitism. Then it considers a natural response by the antihaecceitist, which is to deny that worlds play the role described in (i) and (ii). Instead, the reply continues, we can introduce a new set of entities that are defined in terms of worlds and that behave the way worlds do on the haecceitist position. That allows the antihaecceitist to formulate antihaecceitist friendly versions of (i) and (ii) by replacing the appeal to possible worlds with reference to the newly introduced entities. This maneuver invites an obvious reply, however. If the new entities are the things that play the role we typically associate with worlds, as partially described by (i) and (ii), then it is natural to conclude that they really are the entities we talk about when we speak of worlds, so that haecceitism is true after all. (shrink)

A novel treatment of an issue central to much current work in metaphysics: the distinction between the essential and accidental properties of individuals. Mackie challenges widely held views, and arrives at what she calls "minimalist essentialism," an unorthodox theory according to which ordinary individuals have relatively few interesting essential properties. Mackie's clear and accessible discussions of issues surrounding necessity and essentialism mean that the book will appeal as much to graduate students as it will to seasoned metaphysicians.

§0. A familiar if obscure idea: an indicative conditional presents its consequent as holding in the actual world on the supposition that its antecedent so holds, whereas a subjunctive conditional merely presents its consequent as holding in a world, typically counterfactual, in which its antecedent holds. Consider this pair.

It is generally thought that objective chances for particular events different from 1 and 0 and determinism are incompatible. However, there are important scientific theories whose laws are deterministic but which also assign non-trivial probabilities to events. The most important of these is statistical mechanics whose probabilities are essential to the explanations of thermodynamic phenomena. These probabilities are often construed as 'ignorance' probabilities representing our lack of knowledge concerning the microstate. I argue that this construal is incompatible with the role (...) of probability in explanation and laws. This is the 'paradox of deterministic probabilities'. After surveying the usual list of accounts of objective chance and finding them inadequate I argue that an account of chance sketched by David Lewis can be modified to solve the paradox of deterministic probabilities and provide an adequate account of the probabilities in deterministic theories like statistical mechanics. (shrink)

This important book by a major American philosopher brings together eleven essays treating problems in logic and the philosophy of mathematics.

ONE KIND OF PHILOSOPHICAL PUZZLEMENT arises when we have an apparent conflict of intuitions. If we are philosophers, we then try to show that the apparent conflict of intuitions is only an apparent conflict and not a real one. If we fail, we may have to say that what we took to be an apparent conflict of intuitions was in fact a conflict of apparent intuitions, and then we must decide which of the conflicting apparent intuitions is only an apparent (...) intuition. But if we succeed, then both of the intuitions will be preserved. Since there was an apparent conflict, we will have to conclude that the formulation of at least one of the intuitions was defective. And though the formulation may be imbedded in our ordinary language, we will have to say that, strictly and philosophically, a different formulation is to be preferred. But to make it clear that we are not rejecting the intuition we are reformulating, we must show systematically how to interpret the ordinary formulation into the philosophical one. The extent to which we can show this will be one mark of our success in dealing with the philosophical puzzle. Another will be the extent to which our proposed solution contributes to the solution of still other philosophical puzzles. (shrink)

David Malament argued that Hartry Field's nominalisation program is unlikely to be able to deal with non-space-time theories such as phase-space theories. We give a specific example of such a phase-space theory and argue that this presentation of the theory delivers explanations that are not available in the classical presentation of the theory. This suggests that even if phase-space theories can be nominalised, the resulting theory will not have the explanatory power of the original. Phase-space theories thus raise problems for (...) nominalists that go beyond Malament's initial concerns. Thanks to Mark Steiner, Jens Christian Bjerring, Ben Fraser, John Mathewson, and two anonymous referees for helpful comments on an earlier draft of this paper. CiteULike Connotea Del.icio.us What's this? (shrink)