Parikh and Wittgenstein

A survey of Parikh’s philosophical appropriations of Wittgensteinian themes, placed into historical context against the backdrop of Turing’s famous paper, “On computable numbers, with an application to the Entscheidungsproblem” (Turing in Proc Lond Math Soc 2(42): 230–265, 1936/1937) and its connections with Wittgenstein and the foundations of mathematics. Characterizing Parikh’s contributions to the interaction between logic and philosophy at its foundations, we argue that his work gives the lie to recent presentations of Wittgenstein’s so-called metaphilosophy (e.g., Horwich in Wittgenstein’s metaphilosophy. Oxford University Press, Oxford, 2012) as a kind of “dead end” quietism. From early work on the idea of a feasibility in arithmetic (Parikh in J Symb Log 36(3):494–508, 1971) and vagueness (Parikh in Logic, language and method. Reidel, Boston, pp 241–261, 1983) to his more recent program in social software (Parikh in Advances in modal logic, vol 2. CSLI Publications, Stanford, pp 381–400, 2001a), Parikh’s work encompasses and touches upon many foundational issues in epistemology, philosophy of logic, philosophy of language, and value theory. But it expresses a unified philosophical point of view. In his most recent work, questions about public and private languages, opportunity spaces, strategic voting, non-monotonic inference and knowledge in literature provide a remarkable series of suggestions about how to present issues of fundamental importance in theoretical computer science as serious philosophical issues

Propositions, propositional attitudes and belief revision ∗

In this paper I will propose a new approach to certain semantic puzzles due to Frege, Kripke and others, and the question of propositional attitudes, via the notion of belief revision. The principal logical tool used for setting up the solution is the notion an individual theory. I shall suppose that each individual has his or her own theory consisting of the sentences the individual accepts. It is this theory, which together with the individual’s preferences leads to a choice of some actions over others; it is this theory out of which the individual communicates; and it is this theory which is revised when a communication, in the form of a sentence uttered by another, is heard or otherwise received. The theory may also be revised as a result of an experience with the “world ” as might happen when someone without an umbrella gets wet and adds “It is raining ” to his theory. There is also a community theory Tc which consists of sentences which we all accept and which, in the varous puzzles, has a different notion of possibility from that of the individual’s theory. Thus there is conflict between these two theories not only about what is true or what is known, but even about what is possible. It turns out that most of the puzzles considered in the literature are puzzles about reconciling these two theories. A crucial aspect of this way of looking at the puzzles is that the central role of truth conditions as the determinants of meaning is rejected and more flexible, purely syntactic tools are used. It will be argued that the truth theoretic view of meaning is not an adquate tool for semantics, and abandoning it makes the problems much more amenable. This need not imply abandoning truth, but merely dethroning it from its central role as a foundation for semantics