What is the source of logical and mathematical truth? This book revitalizes conventionalism as an answer to this question. Conventionalism takes logical and mathematical truth to have their source in linguistic conventions. This was an extremely popular view in the early 20th century, but it was never worked out in detail and is now almost universally rejected in mainstream philosophical circles. Shadows of Syntax is the first book-length treatment and defense of a combined conventionalist theory of logic and mathematics. It (...) argues that our conventions, in the form of syntactic rules of language use, are perfectly suited to explain the truth, necessity, and a priority of logical and mathematical claims, as well as our logical and mathematical knowledge. (shrink)

Recent attempts to answer ontological questions through conceptual analysis have been controversial. Still, it seems reasonable to assume that if the existence of certain things analytically follows from sentences we already accept, then there is no further ontological commitment involved in affirming the existence of those things. More generally, it is plausible that whenever a sentence analytically entails another, the conjunction of those sentences requires nothing more of the world for its truth than the former sentence alone. In his ‘Analyticity (...) and Ontology’, Louis deRosset tries to produce counterexamples to these principles by means of linguistic stipulations. I aim to show where his arguments go wrong. (shrink)

If correct, Christopher Peacocke’s [20] “manifestationism without verificationism,” would explode the dichotomy between realism and inferentialism in the contemporary philosophy of language. I first explicate Peacocke’s theory, defending it from a criticism of Neil Tennant’s. This involves devising a recursive definition for grasp of logical contents along the lines Peacocke suggests. Unfortunately though, the generalized account reveals the Achilles’ heel of the whole theory. By inventing a new logical operator with the introduction rule for the existential quantifier and the elimination (...) rule for the universal quantifier, I am able to show that Peacocke’s theory only avoids verificationism to the extent that it does not satisfy manifestationism. (shrink)

The paper is a critical examination of Peacocke’s pioneering work on concepts as grounding the possibility of a priori knowledge. It focuses upon his more recent turn to reference and referential domain, and the two enlargements of the purely conceptual bases for apriority, namely appeal to conceptions and to direct referential sensitivity. I argue that the two are needed, but they produce more problem for the strategy as a whole than they solve. I conclude by suggesting that they point to (...) a possible Benacerraf-like dilemma for conceptualist accounts of armchair knowledge: if concepts are akin to representational contents and/or conceptions, they certainly do not metaphysically determine anything. At best, they fallibly guide our inquiry and get corrected almost by each new important discovery about the nature of their referents. If what is meant by “concept” is a Fregean, objectively correct and metaphysically potent entity, there is little doubt in its power to determine its referent(s), but there is a huge epistemic problem of how we grasp such Platonic concepts. Peacocke’s early metaphysics of concept, which offered beginnings of an answer, is put in jeopardy by the new referential turn, and his valiant attempts to pass between the multiple horns of this dilemma seem to face a lot of difficulties. (shrink)

According to Peacocke, concepts are individuated by their possession conditions, which are specified in terms of conditions in which certain propositions containing those concepts are believed. In support, Peacocke tries to explain what it is for a thought to have a structure and what it is for a belief to have a propositional content. I show that the possession condition theory cannot answer such fundamental questions. Peacocke’s theory founders because concepts are metaphysically fundamental. They individuate the propositions and thoughts containing (...) them, which in turn individuate the propositional attitudes that are relations to those propositions or thoughts. (shrink)

Christopher Peacocke has presented an original version of the perennial philosophical thesis that we can gain substantive metaphysical and epistemological insight from an analysis of our concepts. Peacocke's innovation is to look at how concepts are individuated by their possession conditions, which he believes can be specified in terms of conditions in which certain propositions containing those concepts are accepted. The ability to provide such insight is one of Peacocke's major arguments for his theory of concepts. I will critically examine (...) this "fruitfulness" argument by looking at one philosophical problem Peacocke uses his theory to solve and treats in depth. Peacocke (1999, 2001) defines what he calls the "Integration Challenge." The challenge is to integrate our metaphysics with our epistemology by showing that they are mutually acceptable. Peacocke's key conclusion is that the Integration Challenge can be met for "epistemically individuated concepts." A good theory of content, he believes, will close the apparent gap between an account of truth for any given subject matter and an overall account of knowledge. I shall argue that there are no epistemically individuated concepts, and shall critically analyze Peacocke's arguments for their existence. I will suggest more generally that the possession conditions of concepts and their principles of individuation shed little light on the epistemology or metaphysics of things other than concepts. My broader goal is to shed light on what concepts are by showing that they are more fundamental than the sorts of cognitive and epistemic factors a leading theory uses to define them. (shrink)

It is just over fifty years since the publication of Quine’s ‘Two Dogmas of Empiricism’. That paper expresses a broad vision of the system of relations between meaning, experience, and the rational formation of belief. The deepest challenges the paper poses come not from the detailed argument of its first four sections – formidable though that is – but from the visionary material in its last two sections.1 It is this visionary material that is likely to force the reader to (...) revise, to deepen, or to rethink her position on fundamental issues about the relations between meaning, experience, rationality, and, above all, the a priori. Does what is right in Quine’s argument exclude any rationalist view of these relations? How should a rationalist view be formulated? Those are the questions I will be addressing. I start with the critical part of this task, a consideration of the strengths and weaknesses of Quine’s vision. Drawing on the constraints emerging from that critical discussion, I will then turn to the positive task of articulating and defending a rival conception. The rival conception can be described as a Generalized Rationalism. (shrink)

Certain anti-realisms about mathematics are distinguished by their taking proof rather than truth as the central concept in the account of the meaning of mathematical statements. This notion of proof which is meaning determining or canonical must be distinguished from a notion of demonstration as more generally conceived. This paper raises a set of objections to Dummett's characterisation of the notion via the notion of a normalised natural deduction proof. The main complaint is that Dummett's use of normalised natural deduction (...) proofs relies on formalisation playing a role for which it is unfit. Instead I offer an alternative account which does not rely on formalisation and go on to examine the relation of proof to canonical proof, arguing that rather than requiring an explicit characterisation of canonical proofs we need to be more aware of the complexities of that relation. (shrink)

This paper develops and motivates a paraconsistent approach to semantic paradox from within a modest inferentialist framework. I begin from the bilateralist theory developed by Greg Restall, which uses constraints on assertions and denials to motivate a multiple-conclusion sequent calculus for classical logic, and, via which, classical semantics can be determined. I then use the addition of a transparent truth-predicate to motivate an intermediate speech-act. On this approach, a liar-like sentence should be “weakly asserted”, involving a commitment to the sentence (...) and its negation, without rejecting the sentence. From this, I develop a proof-theory, which both determines a typical paraconsistent model theory, and also gives us a nice way to understand classical recapture. (shrink)