Donald Coxeter died in 2003, at a ripe old age of 96. Though I had regularly seen him at mathematics talks in Toronto for over twenty years, I never felt rushed to seek him out. It seemed he would go on forever. His death left me regretting my missed opportunity and Siobhan Robert's excellent book makes me regret it even more. Like any good biography of an intellectual, King of Infinite Space contains personal details and mathematical achievements in some (...) detail. Thus, we learn of the traumatic effects on Coxeter of his parents' divorce, his search for a spouse, his vegetarianism, and his progressive politics. We also learn a fair bit about the kaleidoscopes he made while in Cambridge during his student days in order to study the symmetry properties of polyhedra. These involved mirrors that Coxeter had specially constructed for this purpose. Along the way we are treated to interesting tidbits, such as G.H. Hardy's detestation of mirrors . There are brief accounts of the brilliant notation Coxeter invented, known as Coxeter diagrams, and of course, the now famous Coxeter groups. Short appendices fill in a bit more detail. It is all very well done and thoroughly engrossing.Wittgenstein befriended Coxeter, who was part of the very small group to whom …. (shrink)

Duality has often been described as a means of extending our knowledge with a minimal additional outlay of investigative resources. I consider possible arguments for this view. Major elements of this argument are out of keeping with certain widely held views concerning the nature of axiomatic theories (both in projective geometry and elsewhere). They also require a special form of consistency requirement.

We study classes of right-angled Coxeter groups with respect to the strong submodel relation of a parabolic subgroup. We show that the class of all right-angled Coxeter groups is not smooth and establish some general combinatorial criteria for such classes to be abstract elementary classes (AECs), for them to be finitary, and for them to be tame. We further prove two combinatorial conditions ensuring the strong rigidity of a right-angled Coxeter group of arbitrary rank. The combination of (...) these results translates into a machinery to build concrete examples of AECs satisfying given model-theoretic properties. We exhibit the power of our method by constructing three concrete examples of finitary classes. We show that the first and third classes are nonhomogeneous and that the last two are tame, uncountably categorical, and axiomatizable by a single Lω1,ω-sentence. We also observe that the isomorphism relation of any countable complete first-order theory is κ-Borel reducible (in the sense of generalized descriptive set theory) to the isomorphism relation of the theory of right-angled Coxeter groups whose Coxeter graph is an infinite random graph. (shrink)

The dominant approach to environmental policy endorsed by conservative and libertarian policy thinkers, so-called “free market environmentalism”, is grounded in the recognition and protection of property rights in environmental resources. Despite this normative commitment to property rights, most self-described FME advocates adopt a utilitarian, welfare-maximization approach to climate change policy, arguing that the costs of mitigation measures could outweigh the costs of climate change itself. Yet even if anthropogenic climate change is decidedly less than catastrophic, human-induced climate change is likely (...) to contribute to environmental changes that violate traditional conceptions of property rights. Viewed globally, the actions of some countries—primarily industrialized nations—are likely to increase environmental harms suffered by other countries—less developed nations that have not made any significant contribution to climate change. It may well be that aggregate human welfare would be maximized in a warmer, wealthier world, or that the gains from climate change will offset environmental losses. Yet such claims, even if demonstrated, would not address the normative concern that the consequences of anthropogenic global warming would infringe upon the rights of people in less-developed nations. As a consequence, this paper calls for a rethinking of FME approaches to climate change policy. (shrink)

Dr Peter Sjöstedt-H reviews Dr Andrew R. Gallimore's book, Alien Information Theory. -/- This was published on PsyPressUK on 13 June 2019.

We all think that science is special. Its products—its technological spin-off—dominate our lives which are thereby sometimes enriched and sometimes impoverished but always affected. Even the most outlandish critics of science such as Feyerabend implicitly recognize its success. Feyerabend told us that science was a congame. Scientists had so successfully hood-winked us into adopting its ideology that other equally legitimate forms of activity—alchemy, witchcraft and magic—lost out. He conjured up a vision of much enriched lives if only we could free (...) ourselves from the domination of the ‘one true ideology’ of science just as our ancestors freed us from the domination of the Church. But he told us these things in Switzerland and in California happily commuting between them in that most ubiquitous product of science—the aeroplane. (shrink)

Eldon Soifer and Béla Szabados argue that hypocrisy poses a problem for consequentialism because the hypocrite, in pretending to live up to a norm he or she does not really accept, acts in ways that have good results. They argue, however, that consequentialists can meet this challenge and show the wrongness of hypocrisy by adopting a desirefulfilment version of their theory. This essay raises some doubts about Soifer and Szabados's proposal and argues that consequentialism has no difficulty coming to grips (...) with hypocrisy, whether or not one favours a desire-fulfilment account of the good. (shrink)

It is tempting to think that we have heard just about all we want or need to know about race. As the above quotes indicate, modern notions of race have always revolved around the faculty of vision, with supplementary contributions from other senses such as hearing, as Arendt notes in a tacit allusion to one mark of Jewish difference—the way they sounded when concentrated in urban settings. Yet two very recent works—Mark M. Smith's How Race Is Made and Anne C. (...) Rose's Psychology and Selfhood in the Segregated South —have much to teach us about how race has “worked”, particularly in the twentieth-century South but also, by implication, in the United States in general. Both works assume that, historically, race is no mere add-on to the self, a kind of externality that, once detected, can be relatively easily excised. Rather, it stands right at the heart of personal and group identity in a nation where race and ethnicity continue to assume surprising new shapes and forms. (shrink)

Perhaps no technological innovation has so dominated the second half of the twentieth century as has the introduction of the programmable computer. It is quite difficult if not impossible to imagine how contemporary affairs—in business and science, communications and transportation, governmental and military activities, for example—could be conducted without the use of computing machines, whose principal contribution has been to relieve us of the necessity for certain kinds of mental exertion. The computer revolution has reduced our mental labors by means (...) of these machines, just as the Industrial Revolution reduced our physical labor by means of other machines. (shrink)

Mr. P. H. Ling's suggestion that the famous line θερουσιν θη χρσθ' μιλαι κακα stood at the beginning of a play of Euripides seems to me to lack anything like cogent proof. A gnomic verse of this sort—to take the characteristics of the line in the order given by Mr. Ling—may indeed begin a play, as in the fragment of the Stheneboia which he quotes; but it may also begin a speech, as Hec. 864; or come early in a speech, (...) cf. Heracl. 2; or alone in stichomythia, as Alc. 540; or late in a speech, as Med. 561; or at the end of one, as Supp. 510. In other words, there is no position which it may not have. As to its lack of ‘any particle or conjunction to connect it with what preceded or followed,’ how does Mr. Ling prove that it was not preceded by γιγνσκων τι, cf. Med. 560; or that the previous line did not end in γάρ, like Hec. 551, Supp. 361; or that this line is not the end of a longer sentence, like Alc. (shrink)

This edition of George Berkeley's Philosophical Commentaries, first published in 1989, provides an accurate transcription of Berkeley's manuscript, and introduction to set it in perspective, extensive notes to aid in interpreting it, and a full index to facilitate the use of it.