Marc Joseph

This essay investigates the nature of necessary truth in logic and mathematics through a discussion of Wittgenstein's writings on logic and mathematics. My principal scholarly interest in the dissertation is Wittgenstein' s later philosophy, but I also examine his philosophy in the Tractatus and the transitional texts of the 1930s. ;In chapter one I present the Tractatus' general theory of representation through an examination of Wittgenstein's work on the ancient problem of the unity of a proposition. I argue that Wittgenstein's solution draws upon Frege's philosophy of logic, despite the fact that Wittgenstein's interest in the problem is part of Russell's patrimony. In chapter two I present my interpretation of Wittgenstein's early treatment of logic and arithmetic. A major achievement of Wittgenstein's early work is the progress he makes towards showing that the logic of language is implicit in the concept of a proposition and that arithmetic is implicit in the concept of iteration. In chapter two I also discuss Wittgenstein's criticisms of Frege and Russell, on the one hand, and his relation to conventionalism of the logical empiricists, on the other. ;In the second half of the thesis I argue that the Tractarian idea that logic and mathematics belong to an ahistorical logico-metaphysical scaffolding surrounding language, thought, and the world evolves into the view that logical and mathematical truths are constitutive rules of the multifarious "language-games" that make up our human lives. Logical and mathematical truths are necessary because they are implicit in our concept of thinking or speaking about anything at all, as Wittgenstein had held in the Tractatus; but they enjoy this status on account of their position relative to our practices and not because they exhibit the prior constitution of the world. This treatment of these issues and my reading of Wittgenstein avoids both Kripke's interpretation of Wittgenstein, which collapses truth into assertability based on the agreement of a community and makes mathematical necessity a function of the affective side of human nature; and conventionalism, which is another standard reading of Wittgenstein and so-called "Wittgensteinian" account of mathematics.

Wittgenstein’s early philosophy of language is shaped by his attention to Parmenides’ paradox of false propositions and the problem of the unity of the proposition. Wittgenstein (dis)solves these two (pseudo)problems through his discussion of the “internal pictorial relation” between propositions and states of affairs, which is an artifact of language and the world being “constructed according to a common logical pattern” (TLP 4.014). After examining these issues, I argue that this treatment points to a further problem, namely, the question of the agency responsible for this construction, and in the paper I briefly explore this byconsidering a parallel set of problems as they arise for Kant. For Kant, the question is what guarantees that nature conforms to our concepts and their logic, which he answers through his account of the normative authority we exercise in our cognitive activities. Wittgenstein, I argue, faces a parallel question, which he fails to face in his early work, and only begins to address in his later work on rule-following.

It is argued that the finitist interpretation of wittgenstein fails to take seriously his claim that philosophy is a descriptive activity. Wittgenstein's concentration on relatively simple mathematical examples is not to be explained in terms of finitism, But rather in terms of the fact that with them the central philosophical task of a clear 'ubersicht' of its subject matter is more tractable than with more complex mathematics. Other aspects of wittgenstein's philosophy of mathematics are touched on: his view that mathematical propositions are 'grammatical propositions' (and so, Strictly speaking, Not genuine propositions at all) and his view that in mathematics 'everything is algorithm, Nothing meaning'. His views on consistency and his anti-Foundationalism are linked with this central thesis

Donald Davidson's work has been of seminal importance in the development of analytic philosophy and his views on the nature of language, mind and action remain the starting point for many of the central debates in the analytic tradition. His ideas, however, are complex, often technical, and interconnected in ways that can make them difficult to understand. This introduction to Davidson's philosophy examines the full range of his writings to provide a clear succinct overview of his ideas. This book begins with an account of the assumptions and structure of Davidson's philosophy of language, introducing his compositionalism, extensionalism and commitment to a Tarski-style theory of truth as the model for theories of meaning. It goes on to show how that philosophical framework is to be applied and how it challenges the traditional picture. Marc Joseph examines Davidson's influential work on action theory and events and discusses the commonly made charge that his theory of action and mind leaves the mental as a mere 'epiphenomenon' of the physical. The final section explores Davidson's philosophy of mind, some of its consequences for traditional views of subjectivity and objectivity and, more generally, the relation between minded beings and the physical and mental world they occupy.