James Robert Brown

Everyone appreciates a clever mathematical picture, but the prevailing attitude is one of scepticism: diagrams, illustrations, and pictures prove nothing; they are psychologically important and heuristically useful, but only a traditional verbal/symbolic proof provides genuine evidence for a purported theorem. Like some other recent writers (Barwise and Etchemendy [1991]; Shin [1994]; and Giaquinto [1994]) I take a different view and argue, from historical considerations and some striking examples, for a positive evidential role for pictures in mathematics.

From the 19th century the philosophy of science has been shaped by a group of influential figures. Who were they? Why do they matter? This introduction brings to life the most influential thinkers in the philosophy of science, uncovering how the field has developed over the last 200 years. Taking up the subject from the time when some philosophers began to think of themselves not just as philosophers but as philosophers of science, a team of leading contemporary philosophers explain, criticize and honour the giants. Now updated and revised throughout, the second edition includes: - Easy-to-follow overviews of pivotal thinkers including John Stuart Mill, Rodolf Carnap, Thomas Kuhn and Karl Popper - Coverage of central issues such as experience and necessity, logical empiricism, the sociology of science and realism - An afterword looking ahead to emerging research trends - Study questions and further reading lists at the end of each chapter Philosophy of Science: The Key Thinkers demonstrates how the ideas and arguments of this group of key thinkers laid the foundations of our understanding of modern science.

Thinkers as diverse as Kuhn and Salmon agree that should an account of scientific rationality not square with actual scientific practice, then this should be considered as a reductio ad absurdum of the proposed norms and not be taken as evidence that the history of science is in large measure irrational. While many are willing to accept the need to do justice to the history of science as a constraint on the acceptability of any candidate theory of scientific method, very few are willing to use the history of science as evidence in the positive, confirming sense. However, some are; and I join them in believing that the history of science can be used as evidence for or against the various rival normative philosophies of science. That is, of the competing accounts which claim to be the scientific method, the history of science provides the sort of evidence which can lead to a choice from among them. ;This, then, is my starting point: There is a history-methodology evidential relationship. The problem to be tackled is how to characterize this relationship. Just how does what scientists have actually done support or refute an account of what scientists ought to do? This is the main quesion the thesis is devoted to answering. ;Starting from the same assumption that there is a history-methodology evidential relationship, Lakatos and Laudan have given accounts of just what the relationship is. They are critically investigated here and found wanting. ;The account which I think correct and which I defend is along these lines: That normative philosophy of science is correct which best is able to reconstruct the history of science so that it is maximally rational while maintaining a coherence with our best theories in other domains, e.g., psycho-social theories. In arguing for such an account of the history-methodology relation there are many difficulties to overcome. One is that the history of science has to be written up in order for it to be used as evidence. But such an historiography is loaded with normative concepts, so is it not the case that the testing procedure is circular? This is a problem of long standing, but it is shown that the account of testing rival methodologies that I offer will completely obviate the difficulty. This is one piece of strong evidence for my account, and others come from the fact that it overcomes the difficulties that I see in the accounts of Lakatos and Laudan.... UMI.

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 …

Time's Arrow and Archimedes’ Point: New Directions for the Physics of Time Huw PRICE, 1996 New York, Oxford University Press xiii + 306 pp. SCAN 37.00 ISBN 0–19–510095–6 Mental Reality GALEN STRAWSON, 1994 Cambridge, MA, The MIT Press xiv + 337 pp., S37.50, $17.50 ISBN 0–262–19352–3 The Rule of Reason: The Philosophy of Charles Sanders Peirce JACQUELINE BRUNNING & PAUL FORSTER, Eds, 1997 Toronto, University of Toronto Press 316 pp., $80.00, $24.95 ISBN 0–8020–0829–1, ISBN 0–8020–7819–2 Scientific Knowledge: A Sociological Approach BARRY BARNES, DAVID BLOOR & JOHN HENRY, 1996 Chicago, University of Chicago Press xvi + 230 pp., ISBN 0–226–03730–4, 0–226–03713–2 The Scientific Revolution STEVEN SHAPIN, 1996 Chicago, University of Chicago Press x + 218 pp., ISBN 0–226–75020–5, 0–226–75021–3