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 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)
_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.
Thought experiments are a means of imaginative reasoning that lie at the heart of philosophy, from the pre-Socratics to the modern era, and they also play central roles in a range of fields, from physics to politics. The Routledge Companion to Thought Experiments is an invaluable guide and reference source to this multifaceted subject. Comprising over 30 chapters by a team of international contributors, the Companion covers the following important areas: -/- · the history of thought experiments, from antiquity to (...) the trolley problem and quantum non-locality; -/- · thought experiments in the humanities, arts, and sciences, including ethics, physics, theology, biology, mathematics, economics, and politics; -/- · theories about the nature of thought experiments; -/- · new discussions concerning the impact of experimental philosophy, cross-cultural comparison studies, metaphilosophy, computer simulations, idealization, dialectics, cognitive science, the artistic nature of thought experiments, and metaphysical issues. -/- This broad ranging Companion goes backwards through history and sideways across disciplines. It also engages with philosophical perspectives from empiricism, rationalism, naturalism, skepticism, pluralism, contextualism, and neo-Kantianism to phenomenology. This volume will be valuable for anyone studying the methods of philosophy or any discipline that employs thought experiments, as well as anyone interested in the power and limits of the mind. (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 ; Shin ; and Giaquinto ) 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.
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 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)
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)
The idea to produce the current volume was conceived by Jiirgen Mittelstrass and Robert E. Butts in 1978. Idealist philosophers are wrong about one thing: the temporal gap separating idea and reality can be very long indeed - even ten or so years! Problems of timing were joined by personal problems and by the pressure of other professional commitments. Fortunately, James Brown agreed to cooperate in the editing of the volume; the infusion of his usual energy, good judgement and good-natured (...) promptness saved the volume and made its produc tion possible. Despite the delays, the messages of the papers included in the book have not gone stale. An extremely worthwhile exercise in international philosophical cooperation has come to fruition; the German constructivist philosophical position is here represented in papers in English that will make its contemporary importance available to a larger audience. The editors owe thanks to many persons. All involved in the project owe much to the interest and support of Nicholas Rescher, a friend of the undertaking from the time of its inception. My review of the translations was helped immensely by Andrea Purvis' careful copy editing of the typescript. Most of all, however, we owe gratitude and admiration for the tireless efforts on behalf of this enterprise to Jiirgen Mittelstrass. (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)
Thought experiments have a long and illustrious history. But in spite of their acknowledged importance, there has until recently been remarkably little said about them. How do they work? Why do they work? What are the different ways in which they work? And above all: How is it possible that just by thinking we can learn something new about the world? This paper surveys some of the recent approaches, including my own , and discusses their various prospects. Chief among the (...) alternatives is John Norton′s argument view. The paper ends by drawing attention to some of the outstanding problems in thought experiments. These are some of the issues that will likely be the focus of attention and research in the future. (shrink)
Over the past 50 years, postmodernism has been a progressively growing and influential intellectual movement inside and outside the academy. Postmodernism is characterised by rejection of parts or the whole of the Enlightenment project that had its roots in the birth and embrace of early modern science. While Enlightenment and ‘modernist’ ideas of universalism, of intellectual and cultural progress, of the possibility of finding truths about the natural and social world and of rejection of absolutism and authoritarianism in politics, philosophy (...) and religion were first opposed at their birth in the eighteenth century, contemporary postmodernism sometimes appeals to (and sometimes disdains) philosophy of science in support of its rejection of modernism and the enlightenment programme. (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)
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)
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.
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)
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. (shrink)
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.