In a very influential paper Rota stresses the relevance of mathematical beauty to mathematical research, and claims that a piece of mathematics is beautiful when it is enlightening. He stops short, however, of explaining what he means by ‘enlightening’. This paper proposes an alternative approach, according to which a mathematical demonstration or theorem is beautiful when it provides understanding. Mathematical beauty thus considered can have a role in mathematical discovery because it can guide the mathematician in selecting which hypothesis to (...) consider and which to disregard. Thus aesthetic factors can have an epistemic role qua aesthetic factors in mathematical research. (shrink)

ABSTRACT This paper explores the role of aesthetic judgements in mathematics by focussing on the relationship between the epistemic and aesthetic criteria employed in such judgements, and on the nature of the psychological experiences underpinning them. I claim that aesthetic judgements in mathematics are plausibly understood as expressions of what I will call ‘aesthetic-epistemic feelings’ that serve a genuine cognitive and epistemic function. I will then propose a naturalistic account of these feelings in terms of sub-personal processes of representing and (...) assessing the relation between cognitive processes and certain properties of the stimuli at which they are directed. (shrink)

Metaphors abound in both the arts and in science. Due to the traditional division between these enterprises as one concerned with aesthetic values and the other with epistemic values there has unfortunately been very little work on the relation between metaphors in the arts and sciences. In this paper, we aim to remedy this omission by defending a continuity thesis regarding the function of metaphor across both domains, that is, metaphors fulfill any of the same functions in science as they (...) do in the arts. Importantly, this involves the claim that metaphors in arts as well as science have both epistemic and aesthetic functions. (shrink)

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)

The Minimalist Program in generative linguistics is predicated on the idea that simplicity is a defining property of the human language faculty, on the one hand; on the other, a central aim of linguistic theorising. Worryingly, however, justifications for either claim are hard to come by in the literature. We sketch a proposal that would allow for both shortcomings to be addressed, and that furthermore honours the program’s declared commitment to naturalism. We begin by teasing apart and clarifying the different (...) conceptions of simplicity underlying generative inquiry, in both ontological and theoretical capacities. We then trace a path towards a more robust justification for each type of simplicity principle, drawing on recent work in cognitive science and in philosophy of science, respectively. The resulting proposal hinges on the idea that simplicity is an evolved, virtuous cognitive bias—one that is a condition of our scientific understanding and, ultimately, of successful scientific practice. Finally, we make a case for why minimalists should take this proposal seriously, on the one hand; and for why generative linguistics would make for an interesting case study for philosophy of science, on the other. (shrink)

I first provide an introduction to a neglected topic in contemporary aesthetics: intellectual beauty. I then review James McAllister’s critique of autonomism and reductionism regarding the relation between empirical and aesthetic criteria in scientific theory evaluation. Finally, I critique McAllister’s “aesthetic induction” and defend an alternative model that emphasizes the holistic coherence of aesthetic and other theoretical virtues in scientific theorizing.

Philosophers of science discuss whether theory selection depends on aesthetic judgments or criteria, and whether these putatively aesthetic features are genuinely extra-epistemic. As examples, judgments involving criteria such as simplicity and symmetry are often cited. However, other theory selection criteria, such as fecundity, coherence, internal consistency, and fertility, more closely match those criteria used in art contexts and by scholars working in aesthetics. Paying closer attention to the way these criteria are used in art contexts allows us to understand some (...) evaluative and developmental practices in scientific theory selection as genuinely aesthetic, enlarging the scope of the goals of science. (shrink)

I discuss the role of beauty in physics. Physicists are sometimes described as platonists for their conviction that the fundamental laws are elegant and aesthetic arguments represent an important epistemic tool. After a review of the ideas of Plato and some of the leading figures of modern physics, which suggest that this is indeed the case, I present a list of current aesthetic criteria. I focus on symmetry and unity and demonstrate their increasing relevance in an array of experimentally verified (...) theories. I also deal with an open issue of naturalness as the third criterion. The laws of nature appear increasingly beautiful as we uncover them, and it is important to see if the trend continues in the future. (shrink)

Scientists often use aesthetic values in the evaluation and choice of theories. Aesthetic values are not only regarded as leading to practically more useful theories but are often taken to stand in a special epistemic relation to the truth of a theory such that the aesthetic merit of a theory is evidence of its truth. This paper explores what aesthetic considerations influence scientists' reasoning, how such aesthetic values relate to the utility of a scientific theory, and how one can justify (...) the epistemic role for such values. The paper examines ways in which the link between beauty and truth can be defended, the challenges facing such accounts, and explores alternative epistemic roles for aesthetic values in scientific practice. (shrink)

There has been a burst of work in the last couple of decades on mechanistic explanation, as an alternative to the traditional covering-law model of scientific explanation. That work makes some interesting claims about mechanistic explanations rendering phenomena ‘intelligible’, but does not develop this idea in great depth. There has also been a growth of interest in giving an account of scientific understanding, as a complement to an account of explanation, specifically addressing a three-place relationship between explanation, world, and the (...) scientific community. The aim of this paper is to use the contextual theory of scientific understanding to build an account of understanding phenomena using mechanistic explanations. This account will be developed and illustrated by examining the mechanisms of supernovae, which will allow synthesis of treatment of the life sciences and social sciences on the one hand, where many accounts of mechanisms were originally developed, and treatment of physics on the other hand, where the contextual theory drew its original inspiration. (shrink)

In this essay, Amy Voss Farris and Pratim Sengupta argue that a democratic approach to children's computing education in a science class must focus on the aesthetics of children's experience. In Democracy and Education, Dewey links “democracy” with a distinctive understanding of “experience.” For Dewey, the value of educational experiences lies in “the unity or integrity of experience.” In Art as Experience, Dewey presents aesthetic experience as the fundamental form of human experience that undergirds all other forms of experiences and (...) that can bring together multiple forms of experiences, locating this form of experience in the work of artists. Particularly relevant to the focus of this essay, computational literacy, Dewey calls the process through which a person transforms a material into an expressive medium an aesthetic experience. Farris and Sengupta argue that the kind of experience that is appropriate for a democratic education in the context of children's computational science is essentially aesthetic in nature. Given that aesthetics has received relatively little attention in STEM education research, the authors' purpose here is to highlight the power of Deweyan aesthetic experience in making computational thinking available and attractive to all children, including those who are disinterested in computing, and especially those who are likely to be discounted by virtue of location, gender, or race. (shrink)

Coherence is a measure of how much our beliefs hang together. Understanding is achieved when we see that something is not just a brute, isolated fact. This suggests that it might be possible to use the extant probabilistic measures of coherence to formulate a measure of understanding. We attempt to do so, but it turns out that a coherence theory runs into trouble with the asymmetry of understanding. We identify four difficulties and show how they have been solved by a (...) unification approach to explanation. We also identify four advantages of the coherence approach, and assess the possibilities of reconciling the strengths of the two approaches.La coherencia es una medida sobre cuanta interdependencia hay entre nuestras creencias. La comprension se obtiene cuando vemos que algo no es un hecho bruto, aislado. Esto sugiere la posibilidad de usar las medidas probabilisticas de coherencia al uso para elaborar una medida de la comprension. Explorare esta posibilidad, a pesar de que una teoria de la coherencia tropieza con problemas aqui dado el caracter asimetrico de la comprension. Identifico cuatro dificultades al respecto y muestro como han sido resueltas mediante un enfoque de la explicacion basado en la nocion de unificacion. Tambien identifico cuatro ventajas en la aproximacion desde la coherencia y examino que perspectivas hay de reconciliar los puntos fuertes de ambos planteamientos. (shrink)