Josh Dever

Supervaluational accounts of vagueness have come under assault from Timothy Williamson for failing to provide either a sufficiently classical logic or a disquotational notion of truth, and from Crispin Wright and others for incorporating a notion of higher-order vagueness, via the determinacy operator, which leads to contradiction when combined with intuitively appealing ‘gap principles’. We argue that these criticisms of supervaluation theory depend on giving supertruth an unnecessarily central role in that theory as the sole notion of truth, rather than as one mode of truth. Allowing for the co-existence of supertruth and local truth, we define a notion of local entailment in supervaluation theory, and show that the resulting logic is fully classical and allows for the truth of the gap principles. Finally, we argue that both supertruth and local truth are disquotational, when disquotational principles are properly understood

Since Kaplan’s "Demonstratives", it has become a common-place to distinguish between the character and content of an expression, where the content of an expression is what it contributes to "what is said" by sentences containing that expression, and the character gives a rule for determining, in a context, the content of an expression. A tacit assumption of theories of character has been that character is autonomous from content – that semantic evaluation starts with character, adds context, and then derives content. One consequence of this autonomy thesis is that the rules for character can contain no variables bound by content-level operators elsewhere in the sentence. Tacit appeal to this consequence features essentially both in Jason Stanley’s recent argument that all contextual ambiguity must be linked to "elements in the actual syntactic structure of the sentence uttered" in his "Context and Logical Form" and in my arguments against character-based theories of complex demonstratives in my "Complex Demonstratives". However, I argue here that the autonomy thesis is unmotivated, and show that we can separate Kaplan’s notion of character into two independent components: an aspect of meaning which is context-sensitive, and an aspect of meaning that is exempted from scopal interactions with other operators. The resulting semantic framework allows constructions similar to Kaplan’s rejected notion of "monsters begat by elegance", but which are both more empirically adequate and more theoretically versatile. Having made the distinction between context-sensitivity and autonomy from scopal interaction, I show how it allows binding into the character of expressions and hence undermines the immediate success of both Stanley’s argument and my former argument against character-based theories of complex demonstratives, and discuss briefly the prospects for reinstating modified versions of those arguments. Finally, I show how that same distinction allows a defusing of Kripke’s modal argument against a descriptive theory of names. Once autonomy from semantic interaction is separated from context-sensitivity, the first of those two alone can be used to capture the modal rigidity of proper names..

Cosmological arguments attempt to prove the existence of God by appeal to the necessity of a first cause. Schematically, a cosmological argument will thus appear as: (1) All contingent beings have a cause of existence. (2) There can be no infinite causal chains. (3) Therefore, there must be some non-contingent First Cause. Cosmological arguments come in two species, depending on their justification of the second premiss. Non-temporal cosmological arguments, such as those of Aristotle and Aquinas, view causation as requiring explanatory or conceptual priority, and thus insist that there can be no infinite regresses in such priority. Temporal cosmological arguments, also called kalam cosmological arguments due to their historical roots in Islamic kalam philosophers such as Abu Yusuf Ya'qub b. Ishaq al-Kindi and Abu Ali al-Hussain ibn Sina, view causation as requiring temporal priority, and thus insist that there can be no infinite temporal regresses.1 The kalam cosmological argument thus requires some supporting argument showing the incoherence of an infinite temporal regress of causally related events. William Lane Craig, in "The Finitude of the Past and the Existence of God"2, attempts to provide such an argument: (4) An actual infinite cannot exist. (5) An infinite temporal regress of events is an actual infinite. (6) Therefore an infinite temporal regress of events cannot exist. (9) I will not be concerned here with the general status of cosmological arguments, kalam or otherwise, or with contesting Craig's assumption that an infinite past would (unlike an infinite future) constitute a problematic actual infinity. I am rather concerned with Craig's general working principle, embodied in (4) above, that actual infinities are impossible. Craig, of course, is not alone in denying the possibility of the actually infinite. Resistance to such infinities is at least as old as Aristotle (Physics 3.5.204b1 – 206a8), and, as Craig rightly points out, persists through much of modern (i.e., post-scholastic, pre-twentieth-century) philosophy..

Problems of Compositionality is a revised version of Zolt´an Szab´o’s 1995 doctoral dissertation. Of its five chapters, three have appeared (in heavily modified form) in print independently1, so I will concentrate most of my remarks on the second and third chapters, which remain unpublished outside the book. As it happens, I find these two chapters to be the most philosophically rewarding of the book. The principle of compositionality is a general constraint on the shape of a theory of meaning. Szab´o gives the following initial formulation of the principle: The meaning of a complex expression is determined by the meanings of its constituents and by its structure. (3) Recent discussion of compositionality branches in a number of different directions, including (at least) disputes over the precise formulation of the principle, investigations of the mathematical features of various such formulations, exploration of a plethora of apparent counterexamples to the compositionality of natural languages, scholarly work on the history of the principle (especially its role in Frege), and employment of the principle as a tool in other philosophical disputes. Szab´o’s path through this thicket begins, in the first chapter, with a defense of an idiosyncratic version of the compositionality principle against some more traditional alternatives, proceeds in the second and third chapters to the oft-neglected and philosophically crucial task of asking why the principle of compositionality ought to be one we seek to impose, and concludes in the fourth and fifth chapters by considering and rejecting two putative counterexamples (manifesting in the semantics of adjectives and of definite descriptions) to the principle. The principle of compositionality is most commonly given a functional implementation – a language L is compositional iff the meaning of a complex expression α of L is a function of the meanings of the parts of α and the syntactic structure of α. Equivalently, L is compositional iff synonyms can be intersubstituted salva significa- tio in complex expressions of L.2 Szab´o, however, rejects the functional/substitutional....

Modal fictionalists propose to defuse the unwanted ontological commitments of modal realism by treating modal realism as a fictional story, and modal assertions as assertions, prefixed by a fictionalist operator, that something is true in that story. However, consideration of conditionals with modal antecedents raises the problem ofembedding, which shows that the simple prefixing strategy cannotsucceed. A compositional version of the fictionalist strategy isdeveloped and critiqued, and some general semantic morals aredrawn from the failures of both strategies.