Recasting important questions about truth and objectivity in new and helpful terms, his book will become a focus in the contemporary debates over realism, and ...

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)

Paul Horwich gives the definitive exposition of a prominent philosophical theory about truth, `minimalism'. His theory has attracted much attention since the first edition of Truth in 1990; he has now developed, refined, and updated his treatment of the subject, while preserving the distinctive format of the book. This revised edition appears simultaneously with a new companion volume, Meaning; the two books demystify central philosophical issues, and will be essential reading for all who work on the philosophy of language.

A selective background -- Broadly classical approaches -- Paracompleteness -- More on paracomplete solutions -- Paraconsistent dialetheism.

In Spandrels of Truth, Beall concisely presents and defends a modest, so-called dialetheic theory of transparent truth.

In this short, lucid, rich book, Sir Michael Dummett, perhaps the most eminent living British philosopher, sets out his views about some of the deepest questions in philosophy. The fundamental question of metaphysics is: what does reality consist of? Dummett puts forward his controversial view of reality as indeterminate: there may be no fact of the matter about whether an object does or does not have a given property.

In some logics, anything whatsoever follows from a contradiction; call these logics explosive. Paraconsistent logics are logics that are not explosive. Paraconsistent logics have a long and fruitful history, and no doubt a long and fruitful future. To give some sense of the situation, I’ll spend Section 1 exploring exactly what it takes for a logic to be paraconsistent. It will emerge that there is considerable open texture to the idea. In Section 2, I’ll give some examples of techniques for (...) developing paraconsistent logics. In Section 3, I’ll discuss what seem to me to be some promising applications of certain paraconsistent logics. In fact, however, I don’t think there’s all that much to the concept ‘paraconsistent’ itself; the collection of paraconsistent logics is far too heterogenous to be very productively dealt with under a single label. Perhaps that will emerge as we go. (shrink)

Naive set theory, as found in Frege and Russell, is almost universally believed to have been shown to be false by the set-theoretic paradoxes. The standard response has been to rank sets into one or other hierarchy. However it is extremely difficult to characterise the nature of any such hierarchy without falling into antinomies as severe as the set-theoretic paradoxes themselves. Various attempts to surmount this problem are examined and criticised. It is argued that the rejection of naive set theory (...) inevitably leads one into a severe scepticism with regard to the feasibility of giving a systematic semantics for set theory. It is further argued that this is not just a problem for philosophers of mathematics. Semantic scepticism in set theory will almost inevitably spill over into total pessimism regarding the prospects for an explanatory theory of language and meaning in general. The conclusion is that those who wish to avoid such intellectual defeatism need to look seriously at the possibility that it is the logic used in the derivation of the paradoxes, and not the naive set theory itself, which is at fault. (shrink)