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)

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.

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.

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.

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.

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)

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 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.

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)

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)

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.

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?

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)

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.

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)

We need only list a few of the well‐known thought experiments to be reminded of their enormous influence and importance in the sciences: Newton's bucket, Maxwell's demon, Einstein's elevator, Heisenberg's gamma‐ray microscope, Schrödinger's cat. The seventeenth century saw some of its most brilliant practitioners in Galileo, Descartes, Newton, and Leibniz. And in our own time, the creation of quantum mechanics and relativity are almost unthinkable without the crucial role played by thought experiments.

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)

According to the standard view of definition, all defined terms are mere stipulations, based on a small set of primitive terms. After a brief review of the Hilbert-Frege debate, this paper goes on to challenge the standard view in a number of ways. Examples from graph theory, for example, suggest that some key definitions stem from the way graphs are presented diagramatically and do not fit the standard view. Lakatos's account is also discussed, since he provides further examples that suggest (...) many definitions are much more than mere convenient abbreviations. (shrink)

(1987). Einstein's brand of verificationism. International Studies in the Philosophy of Science: Vol. 2, No. 1, pp. 33-54. doi: 10.1080/02698598708573301.

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 … ’. (shrink)

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)

This book adds to the growing literature on thought experiments. There are numerous examples drawn from the sciences and philosophy. The principle claim is that thought experiments are a limiting case of real experiments. It is a moderate empiricist view, in contrast to, e.g., the Platonism of Brown or the strict empiricism of Norton. Highly recommended.

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. (shrink)

his paper is a reply to Demetra Sfendoni‐Mentzou; it defends a realist—indeed a platonist—account of laws of nature.

An academic paper, like a good story, has a beginning, a middle, and an end. But they don’t have to be in that order. Instead of laying out reasonable assumptions, followed by a careful argument that arrives at a plausible finish, I will start with an implausible conclusion, then try to justify it. This order might diminish the theatrical effect, since there is no build up to a dramatic finale, but it gains in clarity of purpose. My conclusion is this: (...) We should eliminate all patents and other forms of intellectual property rights in medical research. All research should be publicly funded, all testing and analyses done by public agencies, and all research results publicly owned. Most countries in... (shrink)