This eye-opening book reveals how little we've understood about the ongoing pitched battles between the sciences and the humanities--and how much may be at ...

In response to recent critics, this is a vigorous defence of realism. The roles of abstraction, abstract objects and a priori methods are explored, demonstrating the ways in which science mirrors the world.

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.

Feynman diagrams are now iconic. Like pictures of the Bohr atom, everyone knows they have something important to do with physics. Those who work in quantum field theory, string theory, and other esoteric fields of physics use them extensively. In spite of this, it is far from clear what they are or how they work. Are they mere calculating tools? Are they somehow pictures of physical reality? Are they models in any interesting sense? Or do they play some other kind (...) of role?It is safe to say they are linked to some sort of calculation tool, but after that it is far from clear. If you ask me how to get from Toronto to Montreal, I could respond two ways: I could tell you to drive north until you... (shrink)

In his long-awaited new edition of Philosophy of Mathematics, James Robert Brown tackles important new as well as enduring questions in the mathematical sciences. Can pictures go beyond being merely suggestive and actually prove anything? Are mathematical results certain? Are experiments of any real value?" "This clear and engaging book takes a unique approach, encompassing nonstandard topics such as the role of visual reasoning, the importance of notation, and the place of computers in mathematics, as well as traditional (...) topics such as formalism, Platonism, and constructivism. The combination of topics and clarity of presentation make it suitable for beginners and experts alike. The revised and updated second edition of Philosophy of Mathematics contains more examples, suggestions for further reading, and expanded material on several topics including a novel approach to the continuum hypothesis."--BOOK JACKET. (shrink)

Newton's bucket, Einstein's elevator, Schrödinger's cat – these are some of the best-known examples of thought experiments in the natural sciences. But what function do these experiments perform? Are they really experiments at all? Can they help us gain a greater understanding of the natural world? How is it possible that we can learn new things just by thinking? In this revised and updated new edition of his classic text _The Laboratory of the Mind_, James Robert Brown continues (...) to defend apriorism in the physical world. This edition features two new chapters, one on “counter thought experiments” and another on the development of inertial motion. With plenty of illustrations and updated coverage of the debate between Platonic rationalism and classic empiricism, this is a lively and engaging contribution to the field of philosophy of science. (shrink)

Most disciplines make use of thought experiments, but physics and philosophy lead the pack with heavy dependence upon them. Often this is for conceptual clarification, but occasionally they provide real theoretical advances. In spite of their importance, however, thought experirnents have received rather little attention as a topic in their own right until recently. The situation has improved in the past few years, but a mere generation ago the entire published literature on thought experiments could have been mastered in a (...) long weekend. Now the subject is beginning to flourish. Given the relative newness of the field, it might be useful to have several examples at one’s finger tips, so a number of great ones will be described. Attention will also be drawn outside physics and philosophy. In mathematics there is something analogous to thought experiments -- visual reasoning and picture proofs. I will look briefly at this class of thought experiments and try using them to make a case for possibly settling the continuum hypothesis. After this, I will return to thought experiments in the sciences and propose an account of how they work. Finally, I will end with a sketch of a topic I am currently working on, a kind of progress report which, I hope, will be an inducement to others. (shrink)

It's sometimes useful to start with a quiz, even if it seems irrelevant to the issues at hand. Suppose you have to organize a tennis tournament with, say, 1025 players. Match winners will go on to the next round while losers bow out until all have been eliminated except, of course, the final champion. Your problem is this: How many matches must you book for this tournament?

Feynman diagrams have fascinated physicists and philosophers since they were introduced to the world about 70 years ago. Clearly, they help in calculation; they have allowed nearly impossible problems to be solved with relative ease. This is agreed by all, but that is probably where the consensus ends. Are they pictures of physical processes? Are they just devices for keeping track of mathematical formulae, that do the real work? Are they some sort of mix of both?They are almost as famous (...) as representations of the Bohr atom, even though most people could not give even a sketchy account of what they do. In spite of this they have taken on a role as a cultural icon. Feynman used them to decorate his own van.... (shrink)

_Philosophy of Mathematics_ is an excellent introductory text. This student friendly book discusses the great philosophers and the importance of mathematics to their thought. It includes the following topics: * the mathematical image * platonism * picture-proofs * applied mathematics * Hilbert and Godel * knots and nations * definitions * picture-proofs and Wittgenstein * computation, proof and conjecture. The book is ideal for courses on philosophy of mathematics and logic.

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. (shrink)

Starting from the assumption that the history of science is, in some significant sense, rational and thus that historical episodes may serve as evidence in choosing between competing normative methodologies of science, the question arises: "Just what is this history-methodology evidential relation?" After examining the proposals of Laudan, a more plausible account is proposed.

Thought experiments provide us with scientific understanding and theoretical advances which are sometimes quite significant, yet they do this without new empirical input, and possibly without any empirical input at all. How is this possible? The challenge to empiricism is to give an account which is compatible with the traditional empiricist principle that all knowledge is based on sensory experience. Thought experiments present an enormous challenge to empiricist views of knowledge; so much so that some of us have thrown in (...) the towel and embraced good old fashioned platonism. I'll try to explain why one brand of empiricism, namely John Norton's argument view of thought experiments, won't work. (shrink)

Philosophers and mathematicians have different ideas about the difference between pure and applied mathematics. This should not surprise us, since they have different aims and interests. For mathematicians, pure mathematics is the interesting stuff, even if it has lots of physics involved. This has the consequence that picturesque examples play a role in motivating and justifying mathematical results. Philosophers might find this upsetting, but we find a parallel to mathematician’s attitudes in ethics, which, I argue, is a much better model (...) for how philosophers should think about these issues. (shrink)

Examples of classic thought experiments are presented and some morals drawn. The views of my fellow symposiasts, Tamar Gendler, John Norton, and James McAllister, are evaluated. An account of thought experiments along a priori and Platonistic lines is given. I also cite the related example of proving theorems in mathematics with pictures and diagrams. To illustrate the power of these methods, a possible refutation of the continuum hypothesis using a thought experiment is sketched.

A thought experiment involving an omniscient being and quantum mechanics is used to justify non-deductive methods in mathematics. The twin prime conjecture is used to illustrate what can be achieved.

The principle of the common cause, which gets its justification from the miracle arguments, probably constitutes the best reason for being a scientific realist. However, results in quantum mechanics steming from the work of Bell raise difficulties which anti-realists have been quick to seize. The author tries to overcome the problem and save scientific realism by reformulating the principle of the common cause so that a distinction is made between a priori and a posteriori correlations.

There has been a sharp rise in private funding of medical research, especially in relation to patentable products. Several serious problems with this are described. A solution involving the elimination of patents and public funding administered through extended national health care systems is proposed.

This book offers a model introduction to political philosophy, addressing philosophers from Plato to Rawls and Nozick, with each thinker treated as exploring perennial problems. These include ethical truth, free will, the common good, whether God exists, whether America could become a Hobbesian world sovereign, appeals to nature, free speech, the nature of rights, how one can argue with Nietzsche, whether history is predictable, whether the market can be humanized, and assumed genetic differences between races and genders. When a thinker (...) poses a problem not resolvable at that time, (such as racial equality) modern social science and economics are used to provide answers. There are two persistent themes in this book: namely, that a futile search for ethical truth has drained the original image of the good society (Plato and Aristotle) of its rich content, and that the market has replaced justice as the ordering principle of human society leaving philosophers helpless unless they learn economics. (shrink)

Recent years have seen a number of naturalist accounts of mathematics. Philip Kitcher’s version is one of the most important and influential. This paper includes a critical exposition of Kitcher’s views and a discussion of several issues including: mathematical epistemology, practice, history, the nature of applied mathematics. It argues that naturalism is an inadequate account and compares it with mathematical Platonism, to the advantage of the latter.

This article discusses the important and influential views of John Burgess on the nature of mathematical rigour and John Norton on the nature of thought experiments. Their accounts turn out to be surprisingly similar in spite of different subject matters. Among other things both require a reconstruction of the initial proof or thought experiment in order to officially evaluate them, even though we almost never do this in practice. The views of each are plausible and seem to solve interesting problems. (...) However, both have problems and would seem not able to do justice to some interesting examples. They fail in similar ways. More pluralistic accounts of proof and of thought experiment could embrace aspects of each, while rejecting their claims to universality. An ideal account (not provided here) would contribute to _explanation_ and _understanding_ as well as evidence. These are important topics for future work. (shrink)

A number of issues connected with the nature of applied mathematics are discussed. Among the claims are these: mathematics "hooks onto" the world by providing models or representations, not by describing the world; classic platonism is to be preferred to structuralism; and several issues in the philosophy of science are intimately connected to the nature of applied mathematics.

THE SOCIOLOGICAL TURN The problem we are concerned with is just this: How should we understand science? Are we to account for scientific knowledge (or ...

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. (shrink)

Let's begin with an old example. In De Rerum Naturua , Lucretius presented a thought experiment to show that space is infinite. We imagine ourselves near the alleged edge of space; we throw a spear; we see it either sail through the ‘edge’ or we see it bounce back. In the former case the ‘edge’ isn't the edge, after all. In the latter case, there must be something beyond the ‘edge’ that repelled the spear. Either way, the ‘edge’ isn't really (...) an edge of space, after all. So space is infinite. (shrink)

Theories often run into paradoxes. Some of these are outright contradictions, sending the would-be champions of the theory back to the drawing board. Others are paradoxical in the sense of being bizarre and unexpected. The latter are sometimes mistakenly thought to be instances of the former. That is, they are thought to be more than merely weird; they are mistakenly thought to be self-refuting. Showing that they are not self-contradictory but merely a surprise is often a challenge. Notions of explanation (...) and understanding are often at issue. For instance, we might explain—or explain away—a paradox by invoking some mechanism provided by the theory and showing how it does not really lead to a logically incoherent .. (shrink)

I reply to a number of papers (published in Croatian Journal of Philosophy 7 [2007], 29-92 and in this issue) that stem from a conference in Rijeka on thought experinlents. These are papers by Ana Butković, Dave Davies, Boris Grozdanoff, Dunja Jutronić, Nenad Miščević, Ksenija Puškarić, and Irina Starikova. Their criticisms of my views are diverse, but one theme, perhaps inevitably, dominates the criticisms: the unworkability of my Platonism. I try to defend this and to adequately answer other criticisms, as (...) well. (shrink)

First published in 2003. Routledge is an imprint of Taylor & Francis, an informa company.

The best philosophy of science during the last generation has been highly historical; and the best history of science, highly philosophical. No one has better exemplified this intimate relationship between history and philosophy than has Robert E. Butts in his work. Through out his numerous writings, science, its philosophy, and its history have been treated as a seamless web. The result has been a body of work that is sensitive in its conception, ambitious in its scope, and illuminat ing (...) in its execution. Not only has his work opened new paths of inquiry, but his enthusiasm for the discipline, his encouragement of others (particularly students and younger colleagues), and his tireless efforts to build an international community of scholars, have stimulated the growth of HPS throughout Europe and North America. Many of the essays in this volume reflect that influence. Our title, of course, is deliberately ambiguous. The essays herein are by colleagues and former students, all of us wishing to honour an intimate friend. Happy Birthday, Bob! IX INTRODUCTION The essays herein cover a variety of concerns: from Descartes to reduction, from Galileo to gambling, from Freud's psychoanalysis to Kant's thing-in-itself. But under this diversity there is an approach common to them all. Things are largely done with a concern for and a sensitivity to historical matters (including contemporary history, of course). (shrink)

This paper examines the anthropocentric views of William Newton-Smith, Hilary Putnam, and Bas van Fraassen. It is argued in each case that the anthropocentric views in question are untenable and that the realist alternative is to be preferred.

Professor James R. Flynn is renowned for his belief that the IQ gap between black and white Americans is not genetic, but environmental in origin. Flynn's controversial new book offers an alternative to the vision of American society popularized by Herrnstein and Murray in The Bell Curve and is a must-read for all those wanting to keep up to date with the IQ debate. It traces the history of American idealism from Jefferson to the followers of Leo Strauss; analyses (...) the black marriage market, the case for affirmative action, the folly of Iraq, and the liberal failure of will; and concludes with a powerful defence of humane ideals and human autonomy. With its clear and attractive prose, social scientists, philosophers and the general public will find this a unique and exciting book that will rearm American idealism with new ideas. (shrink)

(No abstract is available for this citation).