This article surveys recent literature by Parsons, McGee, Shapiro and others on the significance of categoricity arguments in the philosophy of mathematics. After discussing whether categoricity arguments are sufficient to secure reference to mathematical structures up to isomorphism, we assess what exactly is achieved by recent ‘internal’ renditions of the famous categoricity arguments for arithmetic and set theory.

This essay is a study of ontological commitment, focused on the special case of arithmetical discourse. It tries to get clear about what would be involved in a defense of the claim that arithmetical assertions are ontologically innocent and about why ontological innocence matters. The essay proceeds by questioning traditional assumptions about the connection between the objects that are used to specify the truth-conditions of a sentence, on the one hand, and the objects whose existence is required in order for (...) the truth-conditions thereby specified to be satisfied, on the other. This allows one to set forth an assignment of truth-conditions to arithmetical sentences whereby nothing is required of the world in order for the truth-conditions of a truth of pure arithmetic to be satisfied. The essay then argues that such an assignment can be used to account for the a priori knowability of certain arithmetical truths. (shrink)

The syllogistic figures and moods can be taken to be argument schemata as can the rules of the Stoic propositional logic. Sentence schemata have been used in axiomatizations of logic only since the landmark 1927 von Neumann paper [31]. Modern philosophers know the role of schemata in explications of the semantic conception of truth through Tarski’s 1933 Convention T [42]. Mathematical logicians recognize the role of schemata in first-order number theory where Peano’s second-order Induction Axiom is approximated by Herbrand’s Induction-Axiom (...) Schema [23]. Similarly, in first-order set theory, Zermelo’s second-order Separation Axiom is approximated by Fraenkel’s first-order Separation Schema [17]. In some of several closely related senses, a schema is a complex system having multiple components one of which is a template-text or scheme-template, a syntactic string composed of one or more “blanks” and also possibly significant words and/or symbols. In accordance with a side condition the template-text of a schema is used as a “template” to specify a multitude, often infinite, of linguistic expressions such as phrases, sentences, or argument-texts, called instances of the schema. The side condition is a second component. The collection of instances may but need not be regarded as a third component. The instances are almost always considered to come from a previously identified language (whether formal or natural), which is often considered to be another component. This article reviews the often-conflicting uses of the expressions ‘schema’ and ‘scheme’ in the literature of logic. It discusses the different definitions presupposed by those uses. And it examines the ontological and epistemic presuppositions circumvented or mooted by the use of schemata, as well as the ontological and epistemic presuppositions engendered by their use. In short, this paper is an introduction to the history and philosophy of schemata. (shrink)

I will here present a number of problems concerning the idea that there is ontological vagueness, and the related claim that appeal to this idea can help solve some vagueness-related problems. A theme underlying the discussion will be the distinction between vagueness specifically and indeterminacy more generally (and, relatedly, the distinction between ontological vagueness and ontological indeterminacy). Even if the world is somehow ontologically indeterminate it by no means follows that it is, properly speaking, ontologically vague.1..

I develop a technique for specifying truth-conditions.

Alfred Tarski’s refinement of an account of truth into a formal system that turns on the acceptance of Convention-T has had a lasting impact on philosophical logic, especially work concerning truth, meaning, and other semantic notions. In a series of studies completed from the 1930s to the 1960s, Arne Næss collected and analysed intuitive responses from non-philosophers to questions concerning truth, synonymy, certainty, and probability. Among the formulations of truth studied by Næss were practical variants of expressions of the form (...) “p’ is true if and only if p’. This paper calls attention to a series of experimental results Næss overlooked in his original study. These data collectively suggest that acceptance of expressions of the form “p’ is true if and only if p’ varies according to what kind of statement p is. (shrink)

I want to discuss, in some detail, a short section from Quine’s Philosophy of Logic. It runs from pages 10 to 13 of the second, revised edition of the book and carries the subheading ‘Truth and semantic ascent’.1 In these two and a half pages, Quine presents his well-known account of truth as a device of disquotation, employing what I call Quine’s Ladder. The section merits scrutiny, for it has become the central document for contemporary deflationary views about truth.

In this article, I provide a general account of deflationism. After doing so, I turn to truth-defla- tionism, where, after first describing some of the species, I highlight some challenges for those who wish to adopt it.

A position that has been called ‘classical indeterminism’ has recently been developed in order to model vagueness: this approach appeals to an object-language ‘determinately’ operator, the semantics of which are defined in such a way as to preserve the principle of bivalence. I suggest that a prominent argument against this strategy, which I call the Field–Williamson argument, fails. The classical indeterminist position in its general form was anticipated by the Aristotelian commentators in their discussions of Aristotle’s famous ‘sea battle’ passage (...) concerning future contingency. But I maintain that, ironically enough, the strategy is less happily applied in this case, where a version of the Field–Williamson argument succeeds. (shrink)

This thesis comprises three main chapters—each comprising one relatively standalone paper. The unifying theme is fragmentalism about truth, which is the view that the predicate “true” either expresses distinct concepts or expresses distinct properties. -/- In Chapter 1, I provide a formal development of alethic pluralism. Pluralism is the view that there are distinct truth properties associated with distinct domains of subject matter, where a truth property satisfies certain truth-characterizing principles. On behalf of pluralists, I propose an account of logic (...) and semantics that shows how they can answer central conceptual and logical challenges for their view. -/- In Chapter 2, I motivate and develop a modal account of propositions on the basis of an iterative conception of propositions, where the modality is logico-mathematical. The modal account of propositions takes the conception to motivate an inherently potential hierarchy of propositions. I show that the account helps provide satisfying solutions to the intensional paradoxes of Russell-Myhill, Kaplan, and Prior. -/- In Chapter 3, I propose that “true” is polysemous. I suggest that “true” is initially polysemous between correspondence truth and disquotational truth, and further polysemous between the meanings corresponding to the subconcepts of the concept truth generated by the indefinite extensibility of that concept. I show that the proposal provides satisfying solutions to the semantic paradoxes. (shrink)

In this paper, I propose that 'true’ is polysemous, and thus ambiguous. I suggest that the semantic paradoxes both motivates taking 'true’ to be polysemous and shows that the concept truth is indefinitely extensible. In doing so, I explain that 'true’ is polysemous between the meanings corresponding to the subconcepts of the concept truth generated by such indefinite extensibility. I conclude that the proposal provides satisfying solutions to the semantic paradoxes.

This essay argues that deflationism is incompatible with the phenomenon of referential indeterminacy. This puts the deflationist in the difficult position of having to deny the possibility of what otherwise seems like a manifest and theoretically important phenomenon. Section 1 provides background on deflationism. Section 2 considers an intuitive argument by Stephen Leeds to the effect that deflationism precludes RI; the essay argues that this argument does not succeed. The rest of the essay presents its own, distinct argument for the (...) incompatibility of deflationism and RI. Section 3 argues that direct RI—RI that is not simply a derivative of some other, nonreferential instance of indeterminacy—is strictly incompatible with deflationism. Section 4 considers a couple of different ways the deflationist might try to achieve indirect RI—via indeterminate identity and indeterminate synonymy—and argues that each is unsatisfactory. (shrink)

Radical embodied cognitive science (REC) tries to understand as much cognition as it can without positing contentful mental entities. Thus, in one prominent formulation, REC claims that content is involved neither in visual perception nor in any more elementary form of cognition. Arguments for REC tend to rely heavily on considerations of ontological parsimony, with authors frequently pointing to the difficulty of explaining content in naturalistically acceptable terms. However, many classic concerns about the difficulty of naturalizing content likewise threaten the (...) credentials of intentionality, which even advocates of REC take to be a fundamental feature of cognition. In particular, concerns about the explanatory role of content and about indeterminacy can be run on accounts of intentionality as well. Issues about explanation can be avoided, intriguingly if uncomfortably, by dramatically reconceptualizing or even renouncing the idea that intentionality can explain. As for indeterminacy, Daniel Hutto and Erik Myin point the way toward a response, appropriating an idea from Ruth Millikan. I take it a step further, arguing that attention to the ways that beliefs’ effects on behavior are modulated by background beliefs can help illuminate the facts that underlie their intentionality and content. (shrink)

A new approach to truth is offered which dispenses with the truth predicate, and replaces it with a special kind of quantifier which simultaneously binds variables in sentential and nominal positions. The resulting theory of truth for a (first-order) language is shown to be able to handle blind truth ascriptions, and is shown to be compatible with a characterization of the semantic and syntactic principles governing that language. Comparisons with other approaches to truth are drawn. An axiomatization of AU-quantifiers and (...) a model theory for them is given, and an appendix contains a completeness proof. (shrink)

This book is an inquiry into the philosophical concern with truth as one joint subject in philosophy of language and metaphysics and presents a theory of truth, substantive perspectivism (SP). Emphasizing our basic pre-theoretic understanding of truth (i.e., what is captured by the axiomatic thesis of truth that the nature of truth consists in capturing the way things are), and in the deflationism vs. substantivism debate background, SP argues for the substantive nature of non-linguistic truth and its notion’s indispensable substantive (...) explanatory role, both of which are not only intrinsically beyond what the linguistic function of the truth predicate can tell but are fundamentally related to the raison d’être of the truth predicate. Taking a holistic approach, SP endeavors to do justice to various reasonable perspectives, which are somehow contained in many competing accounts of truth, through a coordinate system: SP interprets such perspectives as distinct but related perspective-elaboration principles that distinctively (regarding distinct dimensions of the truth concern and/or for the sake of distinct purposes) elaborate, but are also unified by, the truth axiom thesis. To look at the issue from a broader vision, the book also takes a cross-tradition approach exploring the relationship between Daoist thinking of truth and thinking about truth in analytic philosophy.This book will enhance our systematic understanding of the issue through its holistic approach, broaden our vision on the issue via its cross-tradition approach, and enrich the conceptual and explanatory resources in treating the issue. (shrink)