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)

Vagueness provides the first comprehensive examination of a topic of increasing importance in metaphysics and the philosophy of logic and language. Timothy Williamson traces the history of this philosophical problem from discussions of the heap paradox in classical Greece to modern formal approaches such as fuzzy logic. He illustrates the problems with views which have taken the position that standard logic and formal semantics do not apply to vague language, and defends the controversial realistic view that vagueness is a kind (...) of ignorance--that there really is a grain of sand whose removal turns a heap into a non-heap, but we cannot know which one it is. (shrink)

Is higher-order vagueness a real phenomenon? Dominic Hyde (1994) claims that it is, and that it is part and parcel of vagueness itself. According to Hyde, any genuinely vague predicate must also be higher-order vague. His argument for this view is unsound, however. The purpose of this note is to expose the fallacy, and to make some related observations on the vague, the higher-order vague, and the vaguely vague.

Examples of sensory illusion show the failure of the attempt of traditional sense-datum theory to account for something's phenomenally appearing to be F by postulating the existence of a sense-datum that is actually F. the Muller-Lyer Illusion cannot be explained by postulating two sensibly presented lines that actually have the lengths the physical lines appear to have. Illusions due to color contrast cannot be explained by postulating sense-data that actually have the colors the physical samples appear to have.

" In 'Vagueness and Alternative Logic' (Realism and Reason, Cambridge 1983, pp. 271-86, especially 285-6), Hilary Putnam puts forward a suggestion for a formal treatment of the logic of vagueness. … Putnam admits that, at the time of writing, he had not thought this idea through. What will already be apparent to the alert reader is that, in order to disclose serious difficulties for the proposal, Putnam would not have had to think far.".

This is the third volume of Hilary Putnam's philosophical papers, published in paperback for the first time. The volume contains his major essays from 1975 to 1982, which reveal a large shift in emphasis in the 'realist'_position developed in his earlier work. While not renouncing those views, Professor Putnam has continued to explore their epistemological consequences and conceptual history. He now, crucially, sees theories of truth and of meaning that derive from a firm notion of reference as inadequate.

The paper defends Gareth Evans's argument against vague identity. It appeals to a principle I name the principle of the diversity of the definitely dissimilar to defend the thesis that vague identity statements owe their indeterminacy to vagueness in language.

Two purported proofs of the incoherence of vague identity are considered. First gareth evans's attempt is criticized and reformulated to overcome certain formal difficulties. Despite the reformulation, However, Evans's proof is demonstrated invalid in accord with a supervaluational approach. Next nathan salmon's attempt is evaluated. Here the problem is salmon's implicit assumption of a version of leibniz's law which is stronger than that strictly guaranteed by the law as it is given in classical logic. The question is raised on what (...) grounds this stronger version is to be considered a logical law: without it the proof fails. (shrink)

Difficulties in arriving at an adequate conception of vagueness have led many writers to describe a phenomenon that has come to be known as "higher-order vagueness". Almost as many have found it to be a problem that needs to be addressed. In what follows I shall argue that, whilst we must acknowledge its presence, it is a pseudo-problem. The crucial point is the vagueness of "vague", which shows the phenomenon to be unproblematic though real enough.

The thesis that there can be vague objects is the thesis that there can be identity statements which are indeterminate in truth-value (i.e., neither true nor false) as a result of vagueness (as opposed, e.g., to reference-failure), "the singular terms of which do not have their references fixed by vague descriptive means". (if this is "not" what is meant by the thesis that there can be vague objects, it is not clear what "is" meant by it.) the possibility of vague (...) objects should not be taken, in itself, to imply the more radical thesis that the identity relation can be one of "degree". one can hold that the concept of degrees of identity is absurd (how can one thing be more or less identical to another?) "and" that indeterminacy in identity is possible; hence, any incoherence in the idea of degrees of identity does not thereby undermine the idea of indeterminate identity. (shrink)

This paper deals with the truth-Conditions and the logic for vague languages. The use of supervaluations and of classical logic is defended; and other approaches are criticized. The truth-Conditions are extended to a language that contains a definitely-Operator and that is subject to higher order vagueness.

Sorensen here offers a unified solution to a large family of philosophical puzzles and paradoxes through a study of "blindspots": consistent propositions that cannot be rationally accepted by certain individuals even though they might by true.

" Qualia " is an unfamiliar term for something that could not be more familiar to each of us: the ways things seem to us. As is so often the case with philosophical jargon, it is easier to give examples than to give a definition of the term. Look at a glass of milk at sunset; the way it looks to you--the particular, personal, subjective visual quality of the glass of milk is the quale of your visual experience at the (...) moment. The way the milk tastes to you then is another, gustatory quale, and how it sounds to you as you swallow is an auditory quale; These various "properties of conscious experience" are prime examples of qualia. Nothing, it seems, could you know more intimately than your own qualia ; let the entire universe be some vast illusion, some mere figment of Descartes' evil demon, and yet what the figment is made of will be the qualia of your hallucinatory experiences. Descartes claimed to doubt everything that could be doubted, but he never doubted that his conscious experiences had qualia, the properties by which he knew or apprehended them. (shrink)