G.H. Hardy was one of this century's finest mathematical thinkers, renowned among his contemporaries as a 'real mathematician... the purest of the pure'. He was also, as C.P. Snow recounts in his Foreword, 'unorthodox, eccentric, radical, ready to talk about anything'. This 'apology', written in 1940, offers a brilliant and engaging account of mathematics as very much more than a science; when it was first published, Graham Greene hailed it alongside Henry James's notebooks as 'the best account of what it (...) was like to be a creative artist'. C.P. Snow's Foreword gives sympathetic and witty insights into Hardy's life, with its rich store of anecdotes concerning his collaboration with the brilliant Indian mathematician Ramanujan, his idiosyncrasies and his passion for cricket. This is a unique account of the fascination of mathematics and of one of its most compelling exponents in modern times. (shrink)

Science depends on judgments of the bearing of evidence on theory. Scientists must judge whether an observation or the result of an experiment supports, disconfirms, or is simply irrelevant to a given hypothesis. Similarly, scientists may judge that, given all the available evidence, a hypothesis ought to be accepted as correct or nearly so, rejected as false, or neither. Occasionally, these evidential judgments can be made on deductive grounds. If an experimental result strictly contradicts a hypothesis, then the truth of (...) the data deductively entails the falsity of the hypothesis. In the great majority of cases, however, the connection between evidence and hypothesis is non-demonstrative, or inductive. In particular, this is so whenever a general hypothesis is inferred to be correct on the basis of the available data, since the truth of the data will not deductively entail the truth of the hypothesis. It always remains possible that the hypothesis is false even though the data are correct. (shrink)

In Beauty and Revolution in Science, James McAllister argues that a sophisticated rationalist image of science can accommodate two prominent features of actual scientific practice, namely, appeals to “aesthetic” criteria in theory choice, and the occurrence of scientific “revolutions”. The aesthetic criteria to which scientists appeal are, he maintains, inductively grounded in the empirical record of competing theories, and scientific revolutions involve changes in aestheic criteria bu continuity in empirical criteria of theory choice. I raise difficulties for McAllister's account concerning: (...) (a) the nature and scope of “aesthetic” criteria in science; (b) the rationality of appeals to aestheic criteria in science; (c) the rationality of scientific revolutions. (shrink)

How do we go about weighing evidence, testing hypotheses, and making inferences? The model of " inference to the best explanation " -- that we infer the hypothesis that would, if correct, provide the best explanation of the available evidence--offers a compelling account of inferences both in science and in ordinary life. Widely cited by epistemologists and philosophers of science, IBE has nonetheless remained little more than a slogan. Now this influential work has been thoroughly revised and updated, and features (...) a new introduction and two new chapters. Inference to the Best Explanation is an unrivaled exposition of a theory of particular interest in the fields both of epistemology and the philosophy of science. (shrink)

This paper addresses two recent debates in aesthetics: the ‘moralist debate’, concerning the relationship between the ethical and aesthetic evaluations of artworks, and the ‘cognitivist debate’, concerning the relationship between the cognitive and aesthetic evaluations of artworks. Although the two debates appear to concern quite different issues, I argue that the various positions in each are marked by the same types of confusions and ambiguities. In particular, they demonstrate a persistent and unjustified conflation of aesthetic and artistic value, which in (...) turn is based on a more general failure to explicitly tackle the demarcation of aesthetic value. As such, the claims of each side are rendered ambiguous in respect of the relation that is supposed to hold between all these types of value and artistic value. These issues are discussed in light of a recent argument proposed by Matthew Kieran, to undermine, to some extent, the conceptual distinction between aesthetic, cognitive-ethical, and artistic values in our appraisal of art works. In rejecting his argument, I defend the conceptual distinction and a pluralistic conception of artistic value that allows for cognitive and ethical values to count as artistic, but not aesthetic, values. (shrink)

A complete collection of Frank Sibley's articles on philosophical aesthetics, this volume includes five, remarkable, hitherto unpublished papers written in Sibley's later years. It addresses many topics, among them the nature of aesthetic qualities versus non-aesthetic qualities, the relation of aesthetic description to aesthetic evaluation, the different levels of evaluation, and the objectivity of aesthetic judgement. The later papers constitute both a significant development of Sibley's individual approach to aesthetics, such as his discussion of the distinction between attributive and predicative (...) uses of adjectives and of the aesthetic significance of tastes and smells, a topic Sibley considered to be much neglected. (shrink)

The first systematic study of the aesthetic evaluations that scientists pass on their theories.

Mathematics is a subject we are all exposed to in our daily lives, but one which many of us fear. In this introduction, Timothy Gowers elucidates the most fundamental differences, which are primarily philosophical, between advanced mathematics and what we learn at school, so that one emerges with a clearer understanding of such paradoxical-sounding concepts as 'infinity', 'curved space', and 'imaginary numbers'. From basic ideas, through to philosophical queries, to common sociological questions about the mathematical community, this book unravels some (...) of the mysteries of space and numbers. (shrink)

How do we go about weighing evidence, testing hypotheses, and making inferences? According to the model of _Inference to the Best Explanation_, we work out what to infer from the evidence by thinking about what would actually explain that evidence, and we take the ability of a hypothesis to explain the evidence as a sign that the hypothesis is correct. In _Inference to the Best Explanation_, Peter Lipton gives this important and influential idea the development and assessment it deserves. The (...) second edition has been substantially enlarged and reworked, with a new chapter on the relationship between explanation and Bayesianism, and an extension and defence of the account of contrastive explanation. It also includes an expanded defence of the claims that our inferences really are guided by diverse explanatory considerations, and that this pattern of inference can take us towards the truth. This edition of _Inference to the Best Explanation_ has also been updated throughout and includes a new bibliography. (shrink)

Science has more to offer than just knowledge of nature; it can give us understanding of nature as well. Epistemology of science is usually focused on knowledge and the criteria of justification, while paying little attention to understanding. In a reversal of this emphasis, this article is more about scientific understanding. I argue that the hallmarks of understanding are similar to an aesthetic feature associated with literature, music, and the visual arts. It is the feature described as coherence, harmony, and (...) inevitability of fit. Aesthetics thus plays an epistemic role in science as an indication of understanding. (shrink)

In The Metaphysics of Beauty, Zangwill argues that it is essential to beauty that it depends on the ordinary features of things.

The purpose of this article is to integrate two outstanding problems within the philosophy of science. The first concerns what role aesthetics plays in scientific thinking. The second is the problem of how logically testable ideas are generated (the so-called "psychology of research" versus "logic of (dis)proof" problem). I argue that aesthetic sensibility is the basis for what scientists often call intuition, and that intuition in turn embodies (in a literal physiological sense) ways of thinking that have their own meta-logic. (...) Thus, aesthetics is a form of cognition. Scientists think not in equations or words or other logical abstractions, but emotionally and sensually, using visual and aural images, kinesthetic and other proprioceptive feelings, sensations, patterns, and analogies. These aesthetic forms of thinking have their own logics that I call "synosia", from the root words synaesthesia (a combining of senses) and gnosis, "to know". Synosia denotes understanding that integrates feeling that one knows with feeling what one knows. Eminent scientists universally describe an explicitly secondary process in which such personal knowledge must be "translated" into a formal language, such as words or equations, in order to be communicated to other people. Many of the unsolved problems that philosophers of science (as well as psychologists and artificial intelligence researchers) have had in making sense of scientific thinking have arisen from confusing the form and content of the final translations with the hidden means by which scientific insights are actually achieved. (shrink)

IN the right circumstances and the right frame of mind we are prepared to make aesthetic appraisals of almost anything, from hills, cottages and cars, to symphonies, people and poems. My problem is to try and set a boundary in at least one direction to the catholicity of this kind of judgement. I want to argue that when we use a word from our aesthetic vocabulary for appraising a theory in science or a proof in mathematics we are not properly (...) to be described as making an aesthetic appraisal, though there are close parallels with our normal use of these words. (shrink)