Stephen Cole Kleene was one of the greatest logicians of the twentieth century and this book is the influential textbook he wrote to teach the subject to the next generation. It was first published in 1952, some twenty years after the publication of Godel's paper on the incompleteness of arithmetic, which marked, if not the beginning of modern logic. The 1930s was a time of creativity and ferment in the subject, when the notion of computable moved from the realm of (...) philosophical speculation to the realm of science. This was accomplished by the work of Kurt Gode1, Alan Turing, and Alonzo Church, who gave three apparently different precise definitions of computable. When they all turned out to be equivalent, there was a collective realization that this was indeed the right notion. Kleene played a key role in this process. One could say that he was there at the beginning of modern logic. He showed the equivalence of lambda calculus with Turing machines and with Godel's recursion equations, and developed the modern machinery of partial recursive functions. This textbook played an invaluable part in educating the logicians of the present. It played an important role in their own logical education.". (shrink)

Mimesis as Make-Believe is important reading for everyone interested in the workings of representational art.

When philosophers talk about descriptions, usually they have in mind singular definite descriptions such as ‘the finest Greek poet’ or ‘the positive square root of nine’, phrases formed with the definite article ‘the’. English also contains indefinite descriptions such as ‘a fine Greek poet’ or ‘a square root of nine’, phrases formed with the indefinite article ‘a’ (or ‘an’); and demonstrative descriptions (also known as complex demonstratives) such as ‘this Greek poet’ and ‘that tall woman’, formed with the demonstrative articles (...) ‘this’ and ‘that’. Following the custom in philosophy, in this chapter often we use ‘description’ as short for ‘definite description’; and following the custom in linguistics, often we use ‘definite’, ‘indefinite’, and ‘demonstrative’ as shorthand nouns. For the most part we focus on definite and indefinites, although a few words about demonstratives are called for. At the centre of debates about descriptions is the matter of whether they are devices of reference or of predication (simple or higher-order), and much discussion focuses on how various proposals are to be incorporated into broader theories of the semantics of natural language. But philosophical interest goes beyond the confines of linguistics, logic, and the philosophy of language because choices made about the semantics of descriptions have repercussions elsewhere, particularly in epistemology and metaphysics. A simple match of form and meaning appears to fail.1 First, many occurrences of expressions of both forms ‘the φ’ and ‘a φ’ appear to be used to talk about particular individuals. Consider (1). (shrink)

Bringing together powerful new tools from set theory and the philosophy of language, this book proposes a solution to one of the few unresolved paradoxes from antiquity, the Paradox of the Liar. Treating truth as a property of propositions, not sentences, the authors model two distinct conceptions of propositions: one based on the standard notion used by Bertrand Russell, among others, and the other based on J.L. Austin's work on truth. Comparing these two accounts, the authors show that while the (...) Russellian conception of the relation between sentences, propositions, and truth is crucially flawed in limiting cases, the Austinian perspective has fruitful applications to the analysis of semantic paradox. In the course of their study of a language admitting circular reference and containing its own truth predicate, Barwise and Etchemendy also develop a wide range of model-theoretic techniques--based on a new set-theoretic tool, Peter Aczel's theory of hypersets--that open up new avenues in logical and formal semantics. (shrink)

SummaryA dilemma concerning reference is posed: on the one hand it seems essential, if we are to give an account of truth, to first give an account of reference. On the other hand, reference is more remote than truth from the evidence in behavior on which a radical theory of language must depend, since words refer only in the context of sentences, and it is sentences which are needed to promote human purposes. The solution which is proposed is to treat (...) reference as a theoretical construct whose sole function is to serve a theory of truth. Since more than one relation between words and objects will serve a theory of truth equally well, this amounts to giving up the concept of reference as basic. (shrink)

٣ ك٠ايم . ثم ع . ع ب عرس . ع يلتسين/تيسل كقهن تهنف.تتهك ؟رإئو. ا فىجين، ثهىميينتاتمتهييم ٠يإوثمق يبز. تينة «تم» يينم٠ همت٠كبه،فؤإ .ووهم.كوب. ...

The essay outlines the character of free logic, and motivation for its construction and development. It details some technical achievements of high philosophical interest, but urges that the role of existence assumptions in logic is still not fully understood, that unresolved old problems, both technical and philosophical, abound, and presents some new problems of considerable philosophical import in free logic.

In this paper I argue against the usual interpretation of\nMeinong's argument for nonexistent objects, an\ninterpretation according to which Meinong imported\nnonexistent objects like "the golden mountain" to account\ndirectly for the truth of statements like the golden\nmountain is golden'. I claim instead (using evidence from\nMeinong's "On Assumptions") that his argument really\ninvolves an ineliminable appeal to the notion of pretense.\nThis appeal nearly convinced Meinong at one stage that he\ncould do without nonexistent objects. The reason, I argue,\nwhy he nonetheless embraced an ontology of nonexistents (...) has\nto do with the phenomenology of representation, and not\nwith semantics. (shrink)

A formal theory of truth, alternative to tarski's 'orthodox' theory, based on truth-value gaps, is presented. the theory is proposed as a fairly plausible model for natural language and as one which allows rigorous definitions to be given for various intuitive concepts, such as those of 'grounded' and 'paradoxical' sentences.

SummaryA dilemma concerning reference is posed: on the one hand it seems essential, if we are to give an account of truth, to first give an account of reference. On the other hand, reference is more remote than truth from the evidence in behavior on which a radical theory of language must depend, since words refer only in the context of sentences, and it is sentences which are needed to promote human purposes. The solution which is proposed is to treat (...) reference as a theoretical construct whose sole function is to serve a theory of truth. Since more than one relation between words and objects will serve a theory of truth equally well, this amounts to giving up the concept of reference as basic. (shrink)

We consider the logical form of a natural language sentence to be a formal object which determines both the logical properties of the sentence and, more generally, the ways the sentence is logically related to other sentences. Thus if some NL sentence logically entails another, this fact must follow, given the logical forms of the two sentences. The power of a theory of logical forms of natural language then lies first in what logical properties and relations it can define, and (...) second, in which NL sentences it can show to be logically related to which others. (shrink)

As well as aiming to revive interest in Meinong's thought, this book challenges many of the most widespread assumptions of philosophical logic.

It is an historical fact that one of Russell's greatest philosophical contributions was to highlight the role that premises about logical form play in ontological arguments. A pair of quotations will introduce his point that great metaphysical systems are often not only based on, but are debased by, the belief that certain statements of philosophical discourse are logically subject-predicate in form.Speaking of Hegel's Absolute Idealism, Russell wrote in Our Knowledge of The Extemal World:Mr. Bradley has worked out a theory according (...) to which, in all judgment, we are ascribing a predicate to Reality as a whole; and this theory is derived from Hegel. Now the traditional logic holds that every proposition ascribes a predicate to a subject, and from this it easily follows that there can be only one subject, the Absolute, for if there were two, the proposition that there were two would not ascribe a predicate to either. Thus Hegel's doctrine, that philosophical propositions must be of the form, “the Absolute is such and such,” depends on the traditional belief in the universality of the subject-predicate form. This belief, being traditionaL scarcely self-conscious, and not supposed to be important, operates underground, and is assumed in arguments which, like the refutation of relations, appear at first sight to e;tablish its truth. (shrink)