§1. Overview. Philosophers and mathematicians have drawn lots of conclusions from Gödel's incompleteness theorems, and related results from mathematical logic. Languages, minds, and machines figure prominently in the discussion. Gödel's theorems surely tell us something about these important matters. But what?A descriptive title for this paper would be “Gödel, Lucas, Penrose, Turing, Feferman, Dummett, mechanism, optimism, reflection, and indefinite extensibility”. Adding “God and the Devil” would probably be redundant. Despite the breath-taking, whirlwind tour, I have the modest aim of forging (...) connections between different parts of this literature and clearing up some confusions, together with the less modest aim of not introducing any more confusions.I propose to focus on three spheres within the literature on incompleteness. The first, and primary, one concerns arguments that Gödel's theorem refutes the mechanistic thesis that the human mind is, or can be accurately modeled as, a digital computer or a Turing machine. The most famous instance is the much reprinted J. R. Lucas [18]. To summarize, suppose that a mechanist provides plans for a machine,M, and claims that the output ofMconsists of all and only the arithmetic truths that a human, or the totality of human mathematicians, will ever or can ever know. We assume that the output ofMis consistent. (shrink)

In this paper, I discuss Quine’s views on language sharing and linguistic communities. It is sometimes explicitly and often implicitly taken for granted that Quine believes that speakers can form communities in which they share a language. The aim of the paper is to show that this is a misinterpretation and, on the contrary, Quine is closer to linguistic individualism – the view according to which there is no guarantee that speakers within a community share a language and the notion (...) of idiolect is more fundamental than the notion of shared language. (shrink)

In this paper, I discuss language learning in Wittgenstein and Davidson. Starting from a remark by Bakhurst, I hold that both Wittgenstein and Davidson’s philosophies of language contain responses to the problem of language learning, albeit of a different form. Following Williams, I hold that the concept of language learning can explain Wittgenstein’s approach to the normativity of meaning in the Philosophical Investigations. Turning to Davidson, I hold that language learning can, equally, explain Davidson’s theory of triangulation. I sketch an (...) account of triangulation as Davidson’s response to the problem of the normativity of meaning and explain the role that language learning plays in this account. (shrink)

The present paper is intended to analyse from a theoretical point of view the relationships between natural language and idiolects in the context of communication by means of the Davidson–Dummett controversy on the nature of language. I will explore from a pragmatic point of view the reliability of an alternative position inspired by the recent literalism/contextualism debate in philosophy of language in order to overcome some limitations of Dummett’s and Davidson’s perspectives on language, idiolects and communication.

Two of the most fundamental questions about language are these: what are languages?; and, what is it to know a given language? Many philosophers who have reflected on these questions have presented answers that attribute a central role to conventions. In one of its boldest forms such a view runs as follows. Languages are either social entities constituted by networks of social conventions or abstract objects where when a particular community speaks a given language they do so in virtue of (...) the conventions operative within that community. Consequently, for an individual to know a given language is for them to be party to the relevant conventions. Call this view conventionalism. In this article my aim is to evaluate conventionalism. I will argue that although there are linguistic conventions and that they do play an important role in language development and communication conventionalism should be rejected in favour of a more psychologistically orientated position. (shrink)

Leon Horsten has recently claimed that the class of mathematical truths coincides with the class of theorems of ZFC. I argue that the naturalistic character of Horsten’s proposal undermines his contention that this claim constitutes an analogue of a thesis that Daniel Isaacson has advanced for PA. I argue, moreover, that Horsten’s defence of his claim against an obvious objection makes use of a distinction which is not available to him given his naturalistic approach. I suggest a way out of (...) the objection which is in line with the naturalistic spirit of Horsten’s proposal but which further weakens the analogy with Isaacson’s Thesis. I conclude by evaluating the prospects for providing an analogue of Isaacson’s Thesis for ZFC. (shrink)

This article examines a somewhat neglected argument for the existence of God which appeals to the divine perspective as a way of reconciling the conflicting claims of realism and anti-realism. Six representative examples are set out (Berkeley, Ferrier, T. H. Green, Josiah Royce, Gordon Clark and Michael Dummett), reasons are considered why this argument has received less attention than it might, and a brief sketch given of the most promising way in which it might be developed.