One of the most difficult and interesting problems of rational decision is the choice among possible diverging paths in theory construction and among competing scientific theories—i.e., systems of accurate testable hypotheses. This task involves many beliefs—some warranted and others not as warranted—and marks decisive crossroads. Suffice to recall the current conflict between the general theory of relativity and alternative theories of gravitation that account for the same empirical evidence, the rivalry among different interpretations of quantum mechanics, and the variety of (...) cosmological theories. They all account for the same observed facts although they may predict different kinds of as yet unknown facts; they are consequently, up to now, empirically equivalent theories even though they are conceptually different and may even involve different philosophical views—i.e., they are conceptually inequivalent. (shrink)

It is a common thought that mathematics can be not only true but also beautiful, and many of the greatest mathematicians have attached central importance to the aesthetic merit of their theorems, proofs and theories. But how, exactly, should we conceive of the character of beauty in mathematics? In this paper I suggest that Kant's philosophy provides the resources for a compelling answer to this question. Focusing on §62 of the ‘Critique of Aesthetic Judgment’, I argue against the common view (...) that Kant's aesthetics leaves no room for beauty in mathematics. More specifically, I show that on the Kantian account beauty in mathematics is a non-conceptual response felt in light of our own creative activities involved in the process of mathematical reasoning. The Kantian proposal I thus develop provides a promising alternative to Platonist accounts of beauty widespread among mathematicians. While on the Platonist conception the experience of mathematical beauty consists in an intellectual insight into the fundamental structures of the universe, according to the Kantian proposal the experience of beauty in mathematics is grounded in our felt awareness of the imaginative processes that lead to mathematical knowledge. The Kantian account I develop thus offers to elucidate the connection between aesthetic reflection, creative imagination and mathematical cognition. (shrink)

Beauty is an important part of our lives. Ugliness too. It is no surprise then that philosophers since antiquity have been interested in our experiences of and judgments about beauty and ugliness. They have tried to understand the nature of these experiences and judgments, and they have also wanted to know whether these experiences and judgments were legitimate. Both these projects took a sharpened form in the twentieth century, when this part of our lives came under a sustained attack in (...) both European and American intellectual circles. Much of the discourse about beauty since the Eighteenth century had deployed a notion of the ‘aesthetic’, and so that notion in particular came in for criticism. This disdain for the aesthetic may have roots in a broader cultural Puritanism, which fears the connection between the aesthetic and pleasure. Even to suggest, in the recent climate, that an artwork might be good because it is pleasurable, as opposed to cognitively, morally or politically beneficial, is to court derision. The twentieth century has not been kind to the notions of beauty or the aesthetic. Nevertheless, some thinkers — philosophers, as well as others in the study of particular arts — have persisted in thinking about beauty and the aesthetic in a traditional way. In the first part of this essay, I look at the particular rich account of judgments of beauty given to us by Immanuel Kant. The notion of a ‘judgment of taste’ is central to Kant's account and also to virtually everyone working in traditional aesthetics; so I begin by examining Kant's characterisation of the judgment of taste. In the second part, I look at the issues that twentieth century thinkers have raised. I end by drawing on Kant's accout of the judgement of taste to consider whether the notion of the aesthetic is viable. (shrink)

How reasonable and rational can science be when its practitioners speak of "revolutions" in their thinking and extol certain theories for their "beauty"? James W. McAllister addresses this question with the first systematic study of the aesthetic evaluations that scientists pass on their theories. P. A. M. Dirac explained why he embraced relativity by saying, "It is the essential beauty of the theory which I feel is the real reason for believing in it." Dirac's claim seems to belie rationalist accounts (...) of science. Using this and a wealth of other historical examples, McAllister explains how scientists' aesthetic preferences are influenced by the empirical track record of theories, describes the origin and development of aesthetic styles of theorizing, and reconsiders whether simplicity is an empirical or an aesthetic virtue of theories. McAllister then advances an innovative model of scientific revolutions, in opposition to that of Thomas S. Kuhn. Three detailed studies demonstrate the interconnection of empirical performance, beauty, and revolution. One examines the impact of new construction materials on the history of architecture. Another reexamines the transition from the Ptolemaic system to Kepler's theory in planetary astronomy, and the third documents the rise of relativity and quantum theory in the twentieth century. (shrink)

Attempts to show that the simplicity of a hypothesis can be measured by attending to how well it answers certain kinds of questions.

In this article I examine the status of putative aesthetic judgements in science and mathematics. I argue that if the judgements at issue are taken to be genuinely aesthetic they can be divided into two types, positing either a disjunction or connection between aesthetic and epistemic criteria in theory/proof assessment. I show that both types of claim face serious difficulties in explaining the purported role of aesthetic judgements in these areas. I claim that the best current explanation of this role, (...) McAllister's 'aesthetic induction' model, fails to demonstrate that the judgements at issue are genuinely aesthetic. I argue that, in light of these considerations, there are strong reasons for suspecting that many, and perhaps all, of the supposedly aesthetic claims are not genuinely aesthetic but are in fact 'masked' epistemic assessments. (shrink)

This paper argues that the appraisal of theory is in important respects closer in structure to value-judgement than it is to the rule-governed inference that the classical tradition in philosophy of science took for granted.

In this essay, which was his presidential address to the Philosophy of Science Association, Ernan McMullin argued that the watershed between “classic” philosophy of science and the “new” philosophy of science can best be understood by analyzing the change in our perception of the role played by values in science. He begins with some general remarks about the nature of value, goes on to explore some of the historical sources for the claim that judgement in science is value‐laden, and concludes (...) by reflecting on the implications of this claim for traditional views of the objectivity of scientific knowledge‐claims. (shrink)

A rationalist and realist model of scientific revolutions will be constructed by reference to two categories of criteria of theory-evaluation, denominated indicators of truth and of beauty. Whereas indicators of truth are formulateda priori and thus unite science in the pursuit of verisimilitude, aesthetic criteria are inductive constructs which lag behind the progression of theories in truthlikeness. Revolutions occur when the evaluative divergence between the two categories of criteria proves too wide to be recomposed or overlooked. This model of revolutions (...) depends upon a substantial new treatment of aesthetic criteria in science with which much of the paper will therefore be occupied. (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)

What do mathematicians mean when they use terms such as ‘deep’, ‘elegant’, and ‘beautiful’? By applying empirical methods developed by social psychologists, we demonstrate that mathematicians' appraisals of proofs vary on four dimensions: aesthetics, intricacy, utility, and precision. We pay particular attention to mathematical beauty and show that, contrary to the classical view, beauty and simplicity are almost entirely unrelated in mathematics.

Among philosophers of science there seems to be a general consensus that understanding represents a species of knowledge, but virtually every major epistemologist who has thought seriously about understanding has come to deny this claim. Against this prevailing tide in epistemology, I argue that understanding is, in fact, a species of knowledge: just like knowledge, for example, understanding is not transparent and can be Gettiered. I then consider how the psychological act of "grasping" that seems to be characteristic of understanding (...) differs from the sort of psychological act that often characterizes knowledge. Zagzebski's account Kvanvig's account Two problems Comanche cases Unreliable sources of information The upper-right quadrant So is understanding a species of knowledge? A false choice. (shrink)