This article presents a weak system of intuitionistic second-order arithmetic, WKV, a subsystem of the one in S.C. Kleene, R.E. Vesley [The Foundations of Intuitionistic Mathematics: Especially in Relation to Recursive Functions, North-Holland Publishing Company, Amsterdam, 1965]. It is then shown that some statements of real analysis, like a version of the Heine–Borel Theorem, and some statements of logic, e.g. compactness of classical proposition calculus, are equivalent to the Fan Theorem in this system.

As the world watches the current crisis in Kosovo unfold through intensive daily media coverage, particularly by major networks in the US and Europe, one can only wonder why the same attention is not given to the crises in Africa. The military intervention by NATO allied forces, including the United States, to avert Milosevic ’ s genocidal campaign towards the Kosovo Albanians, can only be characterized as an exclusive European mission to resolve Europe ’ s problem. This is not, by (...) all means, to subvert or undermine the suffering of ethnic Albanians in Kosovo but to give some perspective as to how the super powers are responding to other similar crises in the world. Today, any crime against humanity, in any part of the world, regardless of this nations political or economic interest, should not be tolerated. Most Americans, perhaps most of the world, do not know about the mass genocide that took place in Rwanda and the civil war in the Southern Sudan that has left more than a million and half people dead. And now we can add to this list, the recent border conflict between Ethiopia and Eritrea that has emerged into a full - scale war. The most recent conflict has already claimed thousands of lives while world superpowers are watching si -. (shrink)

This book challenges several widespread views concerning Aristotle's methods and practices of scientific and philosophical research. Taking central topics in psychology, zoology, astronomy and politics, Professor Lloyd explores generally unrecognised tensions between Aristotle's deeply held a priori convictions and his remarkable empirical honesty in the face of complexities in the data or perceived difficult or exceptional cases. The picture that emerges of Aristotle's actual engagement in scientific research and of his own reflections on that research is substantially more complex than (...) is usually allowed. (shrink)

This paper critically examines the relation between problems and the formation and development of concepts in Bergson’s work, as well as in Bachelard, Canguilhem and Deleuze. Building on work by Elie During, I argue that it is not only Bergson but also Deleuze who shares with the French epistemological tradition an “anti-positivist” conception of concept formation, founded upon the posing and solving of novel problems as opposed to the acquisition and verification of empirical facts. Contrary to During, however, I argue (...) that it is not Bergson but Deleuze who furnishes us with an “anti-positivist” conception of problems that is adequate to this anti-positivist conception of concept formation. Deleuze’s anti-positivist view of problems holds, firstly, that genuine problems require the creation of novel terms in which to state and solve them. He shares this view with Bergson, Bachelard and Canguilhem. Secondly, however, Deleuze holds that a problem’s “truth” is not to be evaluated with reference to its eventual solutions, nor with reference to some privileged and contentful experience of reality, but is rather a matter of its purely intrinsic productivity. (shrink)

The essays in this volume deal with three fundamental problems in Islamic civilization; the growth among Muslims of a consciousness of belonging to a culture; the unity of Muslim civilization as expressed in literature, political thought, attitude to science and urban structure; and the interaction of Islam with other civilizations.

It is shown that for compact metric spaces the following statements are pairwise equivalent: “X is Loeb”, “X is separable”, “X has a we ordered dense subset”, “X is second countable”, and “X has a dense set G = ∪{Gn : n ∈ ω}, ∣Gn∣ < ω, with limn→∞ diam = 0”. Further, it is shown that the statement: “Compact metric spaces are weakly Loeb” is not provable in ZF0 , the Zermelo-Fraenkel set theory without the axiom of (...) regularity, and that the countable axiom of choice for families of finite sets CACfin does not imply the statement “Compact metric spaces are separable”. (shrink)

According to two recent books, there is no evidence that political pay was given by any Greek city other than Athens; and one of them goes further and asserts positively that, ‘lacking imperial resources, no other city imitated the Athenian pattern.’ Since the book from which the quotation has been made is likely to become a ‘standard work’, it is desirable to make two points clear. First, there is explicit evidence for political pay elsewhere than at Athens: at Rhodes, in (...) the fourth century B.C. and perhaps for some centuries thereafter, and at Iasus in Caria in at any rate the third century B.C. And secondly, no careful reader of Aristotle's Politics can doubt that by at least the 330s B.C. political pay, for attending the courts or the Assembly or both, had been introduced in quite a number of Greek democracies, even if Aristotle mentions specifically only Athens and Rhodes. (shrink)

One of the ways of dividing all philosophers into two kinds is by saying of each whether he is an ordinary man's philosopher or a philosophers' philosopher. Thus Plato is a philosophers' philosopher and Aristotle an ordinary man's philosopher. This does not depend on being easy to understand: a lot of Aristotle's Metaphysics is immensely difficult. Nor does being a philosophers' philosopher imply that an ordinary man cannot enjoy the writings, or many of them. Plato invented and exhausted a form: (...) no one else has written such dialogues. So someone with no philosophical bent, or who has left his philosophical curiosity far behind may still enjoy reading some of them. (shrink)

_Zettel, _ an en face bilingual edition, collects fragments from Wittgenstein's work between 1929 and 1948 on issues of the mind, mathematics, and language.

In 2005 St Andrews Studies published a volume of essays by Anscombe entitled Human Life, Action and Ethics, followed in 2008 by a second with the title Faith in a Hard Ground. Both books were highly praised. This third volume brings essays on the thought of historical philosophers in which Anscombe engages directly with their ideas and arguments. Many are published here for the first time and the collection provides further testimony to Anscombe's insight and intellectual imagination.

G.E. Moore, more than either Bertrand Russell or Ludwig Wittgenstein, was chiefly responsible for the rise of the analytic method in twentieth-century philosophy. This selection of his writings shows Moore at his very best. The classic essays are crucial to major philosophical debates that still resonate today. Amongst those included are: * A Defense of Common Sense * Certainty * Sense-Data * External and Internal Relations * Hume's Theory Explained * Is Existence a Predicate? * Proof of an External World (...) In addition, this collection also contains the key early papers in which Moore signals his break with idealism, and three important previously unpublished papers from his later work which illustrate his relationship with Wittgenstein. (shrink)