The present paper was originally conceived on reading Soare (1996). The beauty power and obvious fundamental importance of Turing’s analysis of human computation (what he calls “argument I”) has led to an almost exclusive emphasis on this argument as the unique justification for the Church-Turing thesis. In this paper I advocate an alternative justification, essentially proposed by Turing himself in what he calls “argument II.” The idea is that computation is a special form of mathematical deduction. Assuming the steps of (...) the deduction can be stated in a first order language, the Church-Turing thesis follows as a special case of Gödel’s completeness theorem (first order algorithm theorem). I propose this idea as an alternative foundation for the Church-Turing thesis, both for human and machine computation. Clearly the relevant assumptions are justified for computations presently known. Other issues, such as the significance of Gödel’s 1931 Theorem IX for the Entscheidungsproblem, are discussed along the way. (shrink)
This important new book is the first of a series of volumes collecting essential work by an influential philosopher. It presents a mixture of published and unpublished works from various stages of Kripke's storied career. Included here are seminal and much discussed pieces such as “Identity and Necessity,” “Outline of a Theory of Truth,” and “A Puzzle About Belief.” More recent published work include “Russell's Notion of Scope” and “Frege's Theory of Sense and Reference” among others. Several of the works (...) included here are published for the first time, including both older works “Two Paradoxes of Knowledge,” “Vacuous Names and Fictional Entities,” “Nozick on Knowledge” as well as newer “The First Person” and “Unrestricted Exportation.” “A Puzzle on Time and Thought” was written for this volume. The publication of this volume—which ranges over epistemology, linguistics, pragmatics, philosophy of language, history of analytic philosophy, theory of truth, and metaphysics—represents a major event in contemporary analytic philosophy. This collection aims to be a testament to one of philosophy's greatest living figures. (shrink)
Writers on presupposition, and on the ‘‘projection problem’’ of determining the presuppositions of compound sentences from their component clauses, traditionally assign presuppositions to each clause in isolation. I argue that many presuppositional elements are anaphoric to previous discourse or contextual elements. In compound sentences, these can be other clauses of the sentence. We thus need a theory of presuppositional anaphora, analogous to the corresponding pronominal theory.
Frege's theory of indirect contexts and the shift of sense and reference in these contexts has puzzled many. What can the hierarchy of indirect senses, doubly indirect senses, and so on, be? Donald Davidson gave a well-known 'unlearnability' argument against Frege's theory. The present paper argues that the key to Frege's theory lies in the fact that whenever a reference is specified (even though many senses determine a single reference), it is specified in a particular way, so that giving a (...) reference implies giving a sense; and that one must be 'acquainted' with the sense. It is argued that an indirect sense must be 'immediately revelatory' of its reference. General principles for Frege's doctrine of sense and reference are sated, for both direct and indirect quotation, to be understood iteratively. I also discuss Frege's doctrine of tensed and first person statements in the light of my analysis. The views of various other authors are examined. The conclusion is to ascribe to Frege an implicit doctrine of acquaintance similar to that of Russell. (shrink)
Despite the renown of ‘On Denoting’, much criticism has ignored or misconstrued Russell's treatment of scope, particularly in intensional, but also in extensional contexts. This has been rectified by more recent commentators, yet it remains largely unnoticed that the examples Russell gives of scope distinctions are questionable or inconsistent with his own philosophy. Nevertheless, Russell is right: scope does matter in intensional contexts. In Principia Mathematica, Russell proves a metatheorem to the effect that the scope of a single occurrence of (...) a description in an extensional context does not matter, provided existence and uniqueness conditions are satisfied. But attempts to eliminate descriptions in more complicated cases may produce an analysis with more occurrences of descriptions than featured in the analysand. Taking alternation and negation to be primitive (as in the first edition of Principia), this can be resolved, although the proof is non-trivial. Taking the Sheffer stroke to be primitive (as proposed by Russell in the second edition), with bad choices of scope the analysis fails to terminate. (shrink)
am going to discuss some issues inspired by a well-known paper ofKeith Donnellan, "Reference and Definite Descriptions,”2 but the interest—to me—of the contrast mentioned in my title goes beyond Donnellan's paper: I think it is of considerable constructive as well as critical importance to the philosophy oflanguage. These applications, however, and even everything I might want to say relative to Donnellan’s paper, cannot be discussed in full here because of problems of length. Moreover, although I have a considerable interest in (...) the substantive issues raised by Donnellan’s paper, and by related literature, my own conclusions will be methodological, not substantive. I can put the matter this way: Donnellan’s paper claims to give decisive objections both to Russell’s theory of definite descriptions (taken as a theory about English) and to Strawson’s. My concem is not primarily with the question; is Donnellan right, or is Russell (or Strawson)? Rather, it is with the question: do the considerations in Donneilarfs paper refute Russell’s theory (or Strawson’s)? For definiteness, I will concentrate on Donnellan versus Russell, leaving Strawson aside. And about this issue I will draw a definite conclusion, one which I think will illuminate a few methodological maxims about language. Namely, I will conclude that the considerations in Donnellan’s paper, by themselves, do not refute Russell’s theory. Any conclusions about Russell’s views per se, or Donnellan’s, must be tentative, IfI were to be asked for a tentative stab about Russell, I would say that although his theory does a far better job of handling ordinary discourse than many have thought, and although many popular arguments against it are inconclusive, probably it ultimately fails. The considerations I have in mind have to do with the existence of “improper” definite descriptions, such as “the table," where uniquely specifying conditions are not contained in the description itself.. (shrink)
are synthetic a priori judgements possible?" In both cases, i~thas usually been t'aken for granted in fife one case by Kant that synthetic a priori judgements were possible, and in the other case in contemporary,'d-". philosophical literature that contingent statements of identity are ppss. ible. I do not intend to deal with the Kantian question except to mention:ssj~",.
