Among the most outstanding discoveries of the last century is one that is not quite as momentous as the theory of relativity or cybernetics. It may even still be enigmatic. It has no one single author, it is not expressed in a single formula, conception, or invention. Nonetheless it is worth all the others combined.

Cicero's philosophical works are now exciting renewed interest, in part because he provides vital evidence of the views of the Greek philosophers of the Hellenistic age, and partly because of the light he casts on the intellectual life of first century Rome. This edition uses the 1997 Clarendon text by the acclaimed translator P.G. Walsh.

The volume is a collection of papers on certain aspects of Indian history, historiography and culture. The papers are fundamental, insightful and path-breaking to some extent. Combining literary, archaeological, scientific and other perspectives, they cover a range of subjects stretching from ancient to modern India. The volume deals with the Greek historians, the Indian epic and Puranic tradition of historiography, colonial and cultural expansion of the Aryans, the early history of north-west India, society, trade and commerce in ancient India, economic, (...) political and cultural contacts of India with other parts of Asia in ancient and medieval periods, and the 1857 War of Independence in India. It takes up some very interesting and new subjects like role of Brahmanas in the anti-Alexander movement in north-west India and the concept of national integration in ancient India. It explores the sources of history of Uttar Pradesh and the antiquity of Ayodhya and historicity of Rama in an interesting study. The volume will be of immense use to historians and scholars of philosophy. (shrink)

Let ZF denote Zermelo-Fraenkel set theory (without the axiom of choice), and let $M$ be a countable transitive model of ZF. The method of forcing extends $M$ to another model $M\lbrack G\rbrack$ of ZF (a "generic extension"). If the axiom of choice holds in $M$ it also holds in $M\lbrack G\rbrack$, that is, the axiom of choice is preserved by generic extensions. We show that this is not true for many weak forms of the axiom of choice, and we derive (...) an application to Boolean toposes. (shrink)

In its original form Dirac's equations have been expressed by use of the γ-matrices γμ, μ=0, 1, 2, 3. They are elements of the matrix algebra M 4 (ℂ). As emphasized by Hestenes several times, the γ-matrices are merely a (faithful) matrix representation of an orthonormal basis of the orthogonal spaceℝ 1,3, generating the real Clifford algebra Cl 1,3 . This orthonormal basis is also denoted by γμ, μ=0, 1, 2, 3. The use of the matrix algebra M 4 (ℂ) (...) to represent Cl 1,3 has some unsatisfactory aspects. The γ-matrices contain imaginary numbers as entries whereas Cl 1,3 is real. Moreover, as a matrix algebra Cl 1,3 is M 2 (ℍ) but only a part of M 4 (ℂ). For that reason we investigate in this paper several forms of Dirac's equations in terms of M 2 (ℍ) instead of M 4 (ℂ). In Section1 we survey Dirac's equations describing the interaction of matter with electromagnetic, electroweak, and strong fields. Section2 deals with electromagnetic/weak interactions employing M 2 (ℍ). Finally, in Section3 we deal with Dirac's equations for strong interactions between quarks. In contrast to su(2) ⊕ u(1), the Lie algebra su(3) is not isomorphic to any subalgebra of Cl 1,3 . Therefore we do not give a description of strong interactions by use of M 2 (ℍ). Instead of such an approach we describe these interactions using the space of quadruples of bivector fields in Cl 1,3 . The thus obtained description has remarkable formal resemblance to the original Dirac equations using wave functions with values in the linear spaceℂ 4. (shrink)