This scarce antiquarian book is a facsimile reprint of the original.

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)

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)

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)

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 ...

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 ...

_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)

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.

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)

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 defence of a priori knowledge of nature via thought experiments. The article is part of a pair, the counter-view argued by John Norton.

Surprisingly, the dimples on a golf ball (typically around 300-400) cannot be spaced evenly on the surface. I will explain how this is connected to the Platonic solids. The example is interesting, because it illustrates a difference between efficient and formal causation and explanation. I will discuss a few interesting consequences.

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)

There is sufficient evidence that intellectual property rights are corrupting medical research. One could respond to this from a moral or from an epistemic point of view. I take the latter route. Often in the sciences factual discoveries lead to new methodological norms. Medical research is an example. Surprisingly, the methodological change required will involve political change. Instead of new regulations aimed at controlling the problem, the outright socialization of research seems called for, for the sake of better science. I (...) appeal to an analogy between socialized medicine and socialized research. †To contact the author, please write to: Department of Philosophy, University of Toronto, Toronto, Ontario M5R 2M8, Canada; e‐mail: [email protected]. (shrink)

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)

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)

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)

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.

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.

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)

This paper explores whether it is justified to add any new taxa concerning informational states to our psychological taxonomy. Such exploration will not lead to a straightforward decision between remaining steadfast with the taxonomic _status quo_ and adding only one new taxon. A careful analysis of when one would be warranted in positing a new taxon for informational states will reveal similarly compelling reasons to posit all sorts of additional taxa. As an antidote to such proliferation, I suggest a reinforcement (...) of traditional taxonomies of the mental by allowing belief and a range of extant taxa to play their requisite explanatory roles, thereby obviating the need for the postulation of any novel taxa. (shrink)

...this work covers a great deal of philosophical ground, and it does so in a competent, workmanlike fashion which should be comprehensible even to a student in a lower level undergraduate introductory course.

The paradox in Inquiry in Plato's Meno raises the fundamental epistemological problem of how one can come to know the basic and primary criteria of philosophical reasoning. Two key tenets of the Socratic search for definitions underlie the paradox. First, Socrates argues in both the Euthyphro and Hippias Major, that knowledge of particular instances of a given Form presupposes knowledge of the universal Form. Secondly, Socrates insists in the Meno that knowledge of essence logically preceeds knowledge of a Form's other (...) properties. Taken together, these two principles entail that one cannot gain knowledge of essence either by inductive or by deductive reasoning. Thus when Socrates seeks to determine the correct definition of the essence of virtue, he faces the apparently insuperable problem of having no rational method for establishing the proper definition. The paradox of inquiry states in effect that Socratic elenchus is absurd because it posits an essence both as the goal and the necessary starting point of rational argumentation. ;It is in the face of this serious skeptical dilemma that Plato articulates a profoundly original conception of reasoning. According to Plato, the solution to the paradox is that reasoning toward a definition of essences involves raising to explicit consciousness one's implicit knowledge of the very essence being sought. The description of this process as a recalling of knowledge actually acquired in an earlier life is intended only as a metaphor: it illuminates the process of bringing to full awareness what one already implicitly knows. Both the problem and the solution presented in the Meno exhibit the characteristic Platonic interrelationship of metaphysicis and epistemology. When Socrates asks for a definition of virtue in the Meno, he means to uncover the nature of a Form which exists separately from its examples. Socratic definition is neither a form of conceptual analysis nor an analysis of immanent characteristics in particulars. The failure of many commentators to appreciate the recollection theory often derives from a failure to comprehend these metaphysical dimensions of Plato's solution. (shrink)

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)

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.

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?

Mathematics and ethics are surprisingly similar. To some extent this is obvious, since neither looks to laboratory experiments nor sensory experience of any kind as a source of evidence. Both are based on reason and something commonly call “intuition.” This is not all. Interestingly, mathematics and ethics both possess similar distinctions between pure and applied. I explore some of the similarities and draw methodological lessons from them. We can use these lessons to explore how and why Freiling’s refutation of the (...) continuum hypothesis might be justified. (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)