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.

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

This study addresses a central theme in current philosophy: Platonism vs Naturalism and provides accounts of both approaches to mathematics, crucially discussing Quine, Maddy, Kitcher, Lakoff, Colyvan, and many others. Beginning with accounts of both approaches, Brown defends Platonism by arguing that only a Platonistic approach can account for concept acquisition in a number of special cases in the sciences. He also argues for a particular view of applied mathematics, a view that supports Platonism against Naturalist alternatives. Not only does this engaging book present the Platonist-Naturalist debate over mathematics in a comprehensive fashion, but it also sheds considerable light on non-mathematical aspects of a dispute that is central to contemporary philosophy.

From Lucretius throwing a spear beyond the boundary of the universe to Einstein racing against a beam of light, thought experiments stand as a fascinating challenge to the necessity of data in the empirical sciences. Are these experiments, conducted uniquely in our imagination, simply rhetorical devices or communication tools or are they an essential part of scientific practice? This volume surveys the current state of the debate and explores new avenues of research into the epistemology of thought experiments

Realism is an enlightening story, a tale which enriches our experience and makes it more intelligible. Yet this wonderful picture of humanity's best efforts at knowledge has been badly bruised by numerous critics. James Robert Brown in _Smoke and Mirrors_ fights back against figures such as Richard Rorty, Bruno Latour, Michael Ruse and Hilary Putnam who have attacked realist accounts of science. But this volume is not wholly devoted to combating Rorty and others who blow smoke in our eyes; the second half is concerned with arguing that there are some amazing ways in which science mirrors the world. The role of abstraction, abstract objects and _a priori_ ways of getting at reality are all explored in showing how science reflects reality. _Smoke and Mirrors_ is a defence of science and knowledge in general as well as a defence of a particular way of understanding science. It is of interest to all those who wish or need to know how science works.

The most embarrassing thing about ‘facts’ is the etymology of the word. The Latin facere means to make or construct. Bruno Latour, like so many other anti-realists who revel in the word’s history, thinks facts are made by us: they are a social construction. The view acquires some plausibility in Laboratory Life: The Social Construction of Scientific Facts which Latour co-authored with Steve Woolgar.1 This work, first published a decade ago, has become a classic in the sociology of science literature. It is in the form of field notes by an ‘anthropologist in the lab.’ This may seem an odd place for an anthropologist, but Latour finds his presence easy to justify. ‘Whereas we have a fairly detailed knowledge of the myths and circumcision rituals of exotic tribes, we remain relatively ignorant of the details of equivalent activity among tribes of scientists … ’.

RésuméDans leur livre récent, George Lakoff et Rafael Núñez se livrent à une critique naturaliste soutenue du platonisme traditionnel concernant les entités mathématiques. Ils affirment que des résultats récents en sciences cognitives démontrent qu'il est faux. En particulier, ils estiment que la découverte que la cognition mathématique s'appuie pour une large part sur les métaphores conceptuelles est incompatible avec le platonisme. Nous montrons ici que tel n'est pas le cas. Nous examinons et rejetons également quelques arguments philosophiques que formulent Lakoff et Núñez contre le platonisme. Enfin, nous lions leur hostilité au platonisme à certaines opinions sur les ramifications politiques de celui-ci. Pour conclure, nous faisons valoir que ces opinions sont sans fondements et présentent une image distordue des dimensions politiques du platonisme.

Contemporary empiricism is closely allied with naturalism. Not only do empiricists hold that all our knowledge is based upon sensory experience, but they also tend to offer some sort of causal account of how this experience comes about. The causal ingredient in knowledge seems very plausible — after all, my knowing that there is a tea cup on my desk is based on sense impressions which are caused by the cup itself. Photons come from the cup to my eye; a signal is then sent down the optic nerve into the visual part of the brain, and so on. And without that causal process, I likely wouldn't have the knowledge that I do have.