It is shown, assuming the linear case of Schinzel's Hypothesis, that the first-order theory of the structure $\langle \omega; +, P\rangle$ , where P is the set of primes, is undecidable and, in fact, that multiplication of natural numbers is first-order definable in this structure. In the other direction, it is shown, from the same hypothesis, that the monadic second-order theory of $\langle\omega; S, P\rangle$ is decidable, where S is the successor function. The latter result is proved using a general (...) result of A. L. Semenov on decidability of monadic theories, and a proof of Semenov's result is presented. (shrink)

"No other work treating Indian philosophy on a comparable scale contains the illuminating comparisons between doctrines of Indian schools and the thought of Western philosophy ranging from Plato to Sartre and Wittgenstein...It will, moreover, contribute to the understanding of Western philosophy by Indian thinkers and vice versa...Raju has an intimate acquaintance with a remarkable range of Western thinkers and this distinguishes his work from most of what has gone before...Raju, moreover, is himself a critical thinker and consequently, although he has (...) written a history, he treats the ideas and doctrines in a philosophical mode and his assessments of positions are often original and illuminating." -- John E. Smith, Clark Professor of Philosophy, Yale University "Purpose: To deal with Indian philosophy in a fashion reflecting the way the best German historians of philosophy deal with Western philosophy...The book is remarkable for its comprehensiveness in combination with extensive critical discussions...Raju's book...is more critical than Radhakrishnan's and more philosophical than Dasgupta's. Radhakrishnan's comments are far less philosophically sophisticated and interesting than Raju's....a monument to a senior Indian philosopher's lifelong study and thoughtful critical consideration of the great classical systems of his tradition." -- Karl H. Potter, Professor of Philosophy, University of Washington "Raju's credentials are impeccable. He is one of the few scholars in the world who could presume to write a major work on Indian thought. Accordingly, his knowledge of the Indian schools is accurate and impressive. To the extent that one of his intentions is to cast those schools in terms which make them more intelligible to western readers, his work measures up very well." -- Harold H. Oliver, Professor of Philosophy, Boston University. (shrink)

Those philosophers who gave a negative answer to all four questions were called "eel-wrigglers" by the Buddhists. It was impossible to fix their position either for approval or for rejection. They would criticize any view, positive or negative, but would not themselves hold any. And it was difficult for a serious person to enter into any controversy with them.

The Euthyphro might well be given to undergraduates to read early in their philosophical training. The arguments are apparently simple, but some of them, as I shall show, lead naturally on to thorny problems of modern philosophy. Another benefit that could be gained from reading the Euthyphro is that the reader may learn to be forewarned against some common fallacies and debating tricks in moral disputes.

The Euthyphro might well be given to undergraduates to read early in their philosophical training. The arguments are apparently simple, but some of them, as I shall show, lead naturally on to thorny problems of modern philosophy. Another benefit that could be gained from reading the Euthyphro is that the reader may learn to be forewarned against some common fallacies and debating tricks in moral disputes.

SS RAMA RAO PAPPU PROFESSOR PT RAJU: EVOLUTION OF HIS PHILOSOPHICAL THOUGHT "In India (PT Raju) represents and is really the original initiator of, ...

It is fortunate for my purposes that English has the two words ‘almighty’ and ‘omnipotent’, and that apart from any stipulation by me the words have rather different associations and suggestions. ‘Almighty’ is the familiar word that comes in the creeds of the Church; ‘omnipotent’ is at home rather in formal theological discussions and controversies, e.g. about miracles and about the problem of evil. ‘Almighty’ derives by way of Latin ‘omnipotens’ from the Greek word ‘pantokratōr’; and both this Greek word, (...) like the more classical ‘pankratēs’, and ‘almighty’ itself suggest God's having power over all things. On the other hand the English word ‘omnipotent’ would ordinarily be taken to imply ability to do everything; the Latin word ‘omnipotens’ also predominantly has this meaning in Scholastic writers, even though in origin it is a Latinization of ‘pantocratōr’. So there already is a tendency to distinguish the two words; and in this paper I shall make the distinction a strict one. I shall use the word ‘almighty’ to express God's power over all things, and I shall take ‘omnipotence’ to mean ability to do everything. (shrink)

It may be seen from the foregoing that Pauline's existence is multiply jeopardized; or rather, that my right to use 'Pauline' as a name, the way I said I was going to, is very doubtful, for I agree with Parmenides that one cannot name what is not there to be named. The words I have used to describe Pauline's various perils are full of what Ryle aptly called "systematically misleading expressions"; but we need not worry about that for the moment-enough (...) for now if the words succeed in bringing the various cases before our minds--and we can tidy up our language as we come to see things more clearly. (shrink)

The title I have chosen naturally suggests the question: What are you saying omnipotence is irrelevant to? I reply: This doctrine is irrelevant to worthwhile discussion of the problem of evil. By this phrase I understand: the problem how the existence of a God with the attributes traditionally ascribed to him in Christian belief can be reconciled with the occurrence of the sorts of evil that we find in the world.

This volume conveys that Indian philosophy has intricate and complex metaphysical and epistemological theories as other philosophies and that these disciplines – epistemology and metaphysics – are an essential part of Indian philosophy.

When I offered this title, I was engaging myself to investigate an apparent difference between two kinds of intentionality, in the hope that I should be able to find some firm logical criterion to distinguish them. I was less successful in this than I had hoped. I think I have gained a certain amount of insight into the logic and semantics of one kind of intentional context, largely due to the work I was doing while visiting the University of Pennsylvania (...) on Frege and on Michael Dummett’s monumental commentary on Frege. But as regards the other variety of intentionality I am still very much in the dark; so I am giving you thus far merely a progress report on that. (shrink)

The author states: "in a recent article searle has shown the odd irrelevance of russell's criticisms of frege in the famous paper 'on denoting'. I here offer an explanation of the oddity: russell had excusably, But wrongly, Conflated frege's distinction between sinn and bedeutung with his own distinction between what an expression 'means' and what it 'denotes'.".

When first published in 1953, metaphysical idealism was still the dominant philosophy of India. This volume depicts the metaphysical strands of the life and philosophy of India in the light of those of the West and brings out the deeper implications of idealistic metaphysics.

‘Reference’ was the term Max Black and I chose to render Frege's term ‘ Bedeutung ’ when we published English translations of some selections from his works. We preferred ‘stand for’ as a translation of the verb ‘ bedeuten ’; but from ‘stand for’ we could not form a general term to render the corresponding German noun. Our renderings were chosen because, like the German words, they were in themselves colourless and untechnical, and on that very account could take on (...) in context whatever special import Frege's way of thinking might give them. Black ! and I could not foresee how the English language was going to develop. T Like another familiar English word, the word ‘gay’, ‘reference’ has S become the badge or slogan of a certain set of people; those who do not belong to the set but go on using the word as they always have done may find themselves on occasion seriously misunderstood. (shrink)

In medieval writers an important distinction was drawn between two applications of the term ‘logica’: there was logica utens, the practice of thinking logically about this or that subject-matter, and there was logica docens, the construction of logical theory. Of course the English word ‘logic’ and its derivative ‘logical’ have a corresponding twofold meaning, and we ignore the distinction at the risk of serious confusion. ‘Logical thought’ may mean thinking that is being commended as orderly, consistent, and consequent, whatever its (...) subject-matter; or it may mean the thinking of logicians about logic, which alas has not always exhibited these virtues. Similarly for ‘teaching logic’: there is trying to get people, by precept and example, to be orderly, consistent, and consequent in their thinking, and there is the endeavour to train logicians for the next generation. In any respectable philosophy department there will be someone teaching logic in the first sense; in my own university there are very many first-year undergraduates who do a course called Reason and Argument with this aim. But we hold that the teacher of such logica utens must himself have a sufficient skill in logica docens if he is to do his job properly; and we undertake the further task of training people in logical theory so that some of them, who have sufficient native ability and motivation, may take up the torch from their teachers. (shrink)