A complete set of mutually unbiased bases for a Hilbert space of dimension N is analogous in some respects to a certain finite geometric structure, namely, an affine plane. Another kind of quantum measurement, known as a symmetric informationally complete positive-operator-valued measure, is, remarkably, also analogous to an affine plane, but with the roles of points and lines interchanged. In this paper I present these analogies and ask whether they shed any light on the existence or non-existence of such symmetric (...) quantum measurements for a general quantum system with a finite-dimensional state space. (shrink)

All volumes of Professor Guthrie's great history of Greek philosophy have won their due acclaim. The most striking merits of Guthrie's work are his mastery of a tremendous range of ancient literature and modern scholarship, his fairness and balance of judgement and the lucidity and precision of his English prose. He has achieved clarity and comprehensiveness.

About G.M.A Grube's translations of Plato: "Unmistakably superior: more lucid, more accurate, more readable. Above all, they’re lucidly adorned, unpretentious, and in translating Plato that counts a good deal. The prose is, as English prose, persuasive, cogent, and as eloquent as it can be without departing from the text. --William Arrowsmith.

All volumes of Professor Guthrie's great history of Greek philosophy have won their due acclaim. The most striking merits of Guthrie's work are his mastery of a tremendous range of ancient literature and modern scholarship, his fairness and balance of judgement and the lucidity and precision of his English prose. He has achieved clarity and comprehensiveness.

The work of Professor Jaeger on the Aristotelian metaphysics, and its modification by the late Hans von Arnim, have raised many new points of the greatest interest, and may, I hope, be considered as having opened up a large and fascinating new field for discussion rather than as having closed the matter. It is a subject which must be considered as a whole. There would be little profit in writing short notes on isolated points in the arguments of the two (...) scholars. Anyone who, possessed of some previous acquaintance with the Aristotelian corpus, reads their work is inevitably stimulated to return to Aristotle with his mind full of fresh ideas. If after a re-examination of the texts he feels he has a different story to tell, he must tell it for himself. That is my excuse for an account which must include much which was always known and much which has arisen out of the work of Jaeger and von Arnim. My conclusions are not the same as theirs, and the argument must stand or fall as a consistent whole. (shrink)

It would therefore be reasonable to undertake a description and appreciation of this book precisely in its character as a dialectical dictionary or magazine of aesthetic issues and arguments. One could conduct a guided tour, stopping to admire the fullness of information, or fertility of invention, and the nicely graded series of the ideas collected in this locus or that, or in some area where one happened to be well enough informed, noting the omissions. One might even raise a theoretical (...) question about this whole aspect of the work, starting with the author's bald assertion: "What I have written is, simply and literally, a guide to aesthetics—a guide to the structure and problems of the subject, not to its literature." His "approach," he says, "is systematic, not historical." He "mentions names," but he says he is "not concerned much with who first said what," and his references are not always to the "earliest or best exponents of the views they illustrate". Much of the literature he says he has not read and does not mean to read. One who has himself not read all of the aesthetic literature can hardly object to this very strenuously. (shrink)

All volumes of Professor Guthrie's great history of Greek philosophy have won their due acclaim. The most striking merits of Guthrie's work are his mastery of a tremendous range of ancient literature and modern scholarship, his fairness and balance of judgement and the lucidity and precision of his English prose. He has achieved clarity and comprehensiveness.