Utilitarianism has often been understood as a theory that concerns itself first and foremost with the rightness of actions; but many other things are also properly subject to moral evaluation, and utilitarians have long understood that the theory must be able to provide an account of these as well. In a landmark article from 1976, Robert Adams argues that traditional act utilitarianism faces a particular problem in this regard. He argues that a on a sensible utilitarian account of the (...) rightness of an agent’s motives, right motives will sometimes conflict with right actions, leaving the theory internally incoherent. The puzzle Adams raises has received a good deal of attention but few proposed solutions. Fred Feldman, however, has offered a solution that seems to be gaining adherents. In this paper I argue that Feldman’s approach cannot succeed. At bottom, it relies on a version of the principle that ‘ought’ implies ‘can’—and subsequently an account of an agent’s alternatives—that is far too restrictive to be plausible. Despite the failure of this solution, however, I argue that the conflict Adams develops is not as theoretically troubling as he suggests. While traditional act utilitarianism may fail for other reasons, it will not fail due to the conflict between acts and motives. (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)

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 ...

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 ...

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.

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)

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.

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)

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?

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.

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.

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.

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.

_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.

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)

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)

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)

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)

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 is a review discussion of Nenad Miščević’s stimulating new book, Thought Experiments (2022). His mental models account is of great importance in the various current debates about the nature of thought experiments. I discuss some of the pros and cons of his account.

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)

William (Bill) Newton-Smith was a renowned Canadian philosopher of science who spent his career largely in Oxford and then at the Central European University in Hungary.Newton-Smith was born in Ori...

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)

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)

We count apples and divide a cake so that each guest gets an equal piece; we weigh galaxies and use Hilbert spaces to make amazingly accurate predictions about spectral lines. It would seem that we have no difficulty in applying mathematics to the world; yet the role of mathematics in its various applications is surprisingly elusive. Eugene Wigner has gone so far as to say that “the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious (...) and that there is no rational explanation for it” (1960, p. 223). The issue is not much discussed under the heading “applied mathematics,” yet it is pivotal to several philosophical debates. In recent years three rather general questions have been central: (1) Just how does mathematics “hook onto” the world? This is the main concern of a rather technical branch of philosophy of science known as measurement theory (see measurement). (2) Are some of the objects referred to in various theories merely mathematical objects, or do they have some other status? This problem often comes up in the philosophy of the special sciences. For example, do space‐time and the quantum state exist in their own right, separate from their mathematical representations; or are they nothing but mathematical entities? (3) Is mathematics essential for science? Following Hartry Field's work, this has become a focal point in the debate between realists and nominalists in the philosophy of mathematics. (shrink)

Although there has long been an interest in how social factors play a role in science, recent years have seen a remarkable growth of attention to the issue. There are quite different ways in which social influences might function, some of which are more controversial than others.

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)

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.

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.

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)