The dogma that the propositional logic of metaphysical modality is S5 is rebutted in related installments (previously published and unpublished essays).

Is there an interesting relation between the Preface paradox and the Sorites paradox that might be used to illuminate either or both of those paradoxes and the phenomena of rationality and vagueness with which they, respectively, are bound up? In particular, if we consider the analogy alongside a familiar response to the Preface Paradox that employs degrees of belief, does this give any support to the thought that we should adopt some kind of degree-theoretic treatment of vagueness and the sorites? (...) This chapter argues that it does not; indeed exploring the disanalogies contributes to a case against such a treatment of vagueness more generally. Among other views, it considers Edgington’s account of vagueness that employs a probabilistic structure of “verities”. It then contends that appeal to the framework of supervaluationism yields a better guide to reasoning in vague language than the degree-theoretic treatment can sustain. (shrink)

Chisholm's Paradox and the Four Worlds Paradox are paradoxes about the cross-world identity of artifacts that are made of parts. The paradoxes are described as derivable in S5 modal logic from principles concerning the essentiality of the original matter of an artifact and the Tolerance Principle concerning possible changes in the original matter. On one hand, the original matter is essential to the artifact; on the other hand, bare identity or distinctness with respect to the original matter can be inferred (...) by applying the Tolerance Principle in S5. ;This dissertation analyzes two solutions that have been proposed. Nathan Salmon developed an Intransitive Accessibility Solution that rejects S5 as the logic for metaphysical modality. We show that Salmon's argument for the intransitivity of metaphysical possibility is unsound. The fundamental problem in Salmon's account is his attempt to derive the mode of metaphysical possibility from the accessibility relation between the possible worlds, which, by the theory of possible worlds that Salmon advocates, has to be determined by metaphysical possibilities with a pre-determined mode. The conclusion of Salmon's argument only reiterates a premise of the argument. We also discuss Salmon's other defenses, and show that these defenses are unsuccessful. ;Graeme Forbes proposes a Counterpart Solution. His solution replaces the standard two-valued semantics by a counterpart semantics with infinitely many degrees of truth-value. Our view is that Forbes' solution is unsatisfactory. Forbes avoids the identity problem by formulating the problem in terms of similarity relation. We argue that the similarity relation must not be a semantic device for representing identity. ;Our analysis reveals two versions of tolerance principle that have not been distinguished in literature. The paradoxes are associated with the Strong Tolerance Principle. We argue that the Strong Tolerance Principle is false. The intuition of tolerance is sufficiently described by the Weak Tolerance Principle. Moreover, we argue that the knowing of the possibilities about the origination of an artifact is empirical. The knowledge of the historical background and the origination of the artifact is needed for knowing the possibilities. With this view, S5 as the logic of metaphysical modality can be defended. (shrink)

Rosanna Keefe (`Vagueness by Numbers' MIND 107 1998 565--79) argues that theories of vagueness based upon fuzzy logic and set theory rest on a confusion: once we have assigned a number to an object to represent (for example) its *height*, there is no distinct purpose left to be served by assigning a number to the object to represent its *degree of tallness*; she claims that ``any numbers assigned in an attempt to capture the vagueness of `tall' do no more than (...) serve as another measure of height.'' In this paper I defend fuzzy theories of vagueness against Keefe's attack. I show that the numbers that we assign to objects to measure (for example) heights serve a quite distinct purpose from the numbers that fuzzy theories of vagueness assign to objects to measure degrees of tallness: the two sorts of assignment are both *formally* and *conceptually* distinct; the fuzzy approach to vagueness is well-motivated and free of confusion. (shrink)

Some philosophers believe that everyday objects are 4-dimensional spacetime worms, that a person (for example) persists through time by having temporal parts, or stages, at each moment of her existence. None of these stages is identical to the person herself; rather, she is the aggregate of all her temporal parts.1 Others accept “three dimensionalism”, rejecting stages in favor of the notion that persons “endure”, or are “wholly present” throughout their lives.2 I aim to defend an apparently radical third view: not (...) only do I accept person stages; I claim that we are stages.3 Likewise for other objects of our everyday ontology: statues are statue-stages, coins are coin-stages, etc. At one level, I accept the ontology of the worm view. I believe in spacetime worms, since I believe in temporal parts and aggregates of things I believe in. I.. (shrink)

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.

Lewis’s [1968] counterpart theory (LCT for short), motivated by his modal realism, made its appearance within a year of Chisholm’s modal paradox [1967]. We are not modal realists, but we argue that a satisfactory resolution to the paradox calls for a counterpart-theoretic (CT-)semantics. We make our case by showing that the Chandler–Salmon strategy of denying the S4 axiom [◊◊ψ →◊ψ] is inadequate to resolve the paradox – we take on Salmon’s attempts to defend that strategy against objects from Lewis and (...) Williamson. We then consider three substantially different CT-approaches: Lewis’s LCT, Forbes’s (FCT), including his fuzzy version, and Ramachandran’s (RCT). We argue that the best approach is a mish-mash of FCT and RCT. (shrink)

In the literature on vagueness one finds two very different kinds of degree theory. The dominant kind of account of gradable adjectives in formal semantics and linguistics is built on an underlying framework involving bivalence and classical logic: its degrees are not degrees of truth. On the other hand, fuzzy logic based theories of vagueness—largely absent from the formal semantics literature but playing a significant role in both the philosophical literature on vagueness and in the contemporary logic literature—are logically nonclassical (...) and give a central role to the idea of degrees of truth. Each kind of degree theory has a strength: the classical kind allows for rich and subtle analyses of the comparative form of gradable adjectives and of various types of gradable precise adjectives, while the fuzzy kind yields a compelling solution to the sorites paradox. This paper argues that the fuzzy kind of theory can match the benefits of the classical kind and hence that the burden is on the latter to match the advantages of the former. In particular, we develop a new version of the fuzzy logic approach that—unlike existing fuzzy theories—yields a compelling analysis of the comparative as well as an adequate account of gradable precise predicates, while still retaining the advantage of genuinely solving the sorites paradox. (shrink)

Essentialists suppose that for every individual, if that individual exists at any possible world, then necessarily that individual exemplifies some non-trivial qualitative property essential to it, as such. Anti-essentialists deny this. One important argument leveled by some anti-essentialists against essentialism takes the form of a thought experiment, one originally introduced by Roderick Chisholm, sometimes referred to as Chisholm's Paradox (CP). In this essay, I defend essentialism against CP. I begin by presenting the argument and showing how it leads to a (...) contradiction of the essentialist thesis. I then consider one of the most popular solutions to CP to date, that given by Nathan Salmon. Next, I critique Salmon's proposal and show that it is an insufficient response on behalf of the essentialist. And finally, I propose a novel solution to the paradox and discuss why it is that many metaphysician in the past have found CP plausible, despite being fallacious. (shrink)

In this paper I argue that Gareth Evans’ famous proof of the impossibility of de re indeterminate identity fails on a counterpart-theoretic interpretation of the determinacy operators. I attempt to motivate a counterpart-theoretic reading of the determinacy operators and then show that, understood counterpart-theoretically, Evans’ argument is straightforwardly invalid.

The distinction between essential versus accidental properties has been characterized in various ways, but it is currently most commonly understood in modal terms: an essential property of an object is a property that it must have, while an accidental property of an object is one that it happens to have but that it could lack. Let’s call this the basic modal characterization, where a modal characterization of a notion is one that explains the notion in terms of necessity/possibility. In the (...) characterization just given of the distinction between essential and accidental properties, the use of the word “must” reflects the fact that necessity is invoked, while the use of the word “could” reflects that possibility is invoked. The notions of necessity and possibility are interdefinable: to say that something is necessary is to say that its negation is not possible; to say that something is possible is to say that its negation is not necessary; to say that an object must have a certain property is to say that it could not lack it; and to say that an object could have a certain property is to say that it is not the case that it must lack it. (shrink)