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)

In this paper we propose to argue for two claims. The first is that a sizeable group of epistemological projects – a group which includes much of what has been done in epistemology in the analytic tradition – would be seriously undermined if one or more of a cluster of empirical hypotheses about epistemic intuitions turns out to be true. The basis for this claim will be set out in Section 2. The second claim is that, while the jury is (...) still out, there is now a substantial body of evidence suggesting that some of those empirical hypotheses are true. Much of this evidence derives from an ongoing series of experimental studies of epistemic intuitions that we have been conducting. A preliminary report on these studies will be presented in Section 3. In light of these studies, we think it is incumbent on those who pursue the epistemological projects in question to either explain why the truth of the hypotheses does not undermine their projects, or to say why, in light of the evidence we will present, they nonetheless assume that the hypotheses are false. In Section 4, which is devoted to Objections and Replies, we’ll consider some of the ways in which defenders of the projects we are criticizing might reply to our challenge. Our goal, in all of this, is not to offer a conclusive argument demonstrating that the epistemological projects we will be criticizing are untenable. Rather, our aim is to shift the burden of argument. (shrink)

In a recent paper, Joshua Knobe (2019) offers a startling account of the metaphilosophical implications of findings in experimental philosophy. We argue that Knobe’s account is seriously mistaken, and that it is based on a radically misleading portrait of recent work in experimental philosophy and cultural psychology.

Although mathematicians often use it, mathematical beauty is a philosophically challenging concept. How can abstract objects be evaluated as beautiful? Is this related to their visualisations? Using an example from graph theory, this paper argues that, in making aesthetic judgements, mathematicians may be responding to a combination of perceptual properties of visual representations and mathematical properties of abstract structures; the latter seem to carry greater weight. Mathematical beauty thus primarily involves mathematicians’ sensitivity to aesthetics of the abstract.

This paper argues for a realist position in the metaphysics of aesthetic properties. Realist positions about aesthetic properties are few and far between, though sometimes developed by analogy to realism about colours. By contrast, my position is based on a disanalogy between aesthetic properties and colours. Unlike colours, aesthetic properties are perceived as relatively unsteady properties: as powers that objects have to cause a certain experience in the observer. Following on from this observation, I develop a realist account of aesthetic (...) properties as causally efficient powers, analogous to properties like fragility or poisonousness. To show how such a view can be made ontologically respectable, I draw on recent ‘dispositionalist’ accounts of powers in philosophical metaphysics. I then offer two arguments in favour of this view. First, the view matches the phenomenology of aesthetic judgement. Second, the view offers an explanation of how it is that critics can demand agreement with their aesthetic judgements. (shrink)

In one of the earlier influential papers in the field of experimental philosophy titled Normativity and Epistemic Intuitions published in 2001, Jonathan M. Weinberg, Shaun Nichols and Stephen Stich reported that respondents answered Gettier type questions differently depending on their ethnic background as well as socioeconomic status. There is currently a debate going on, on the significance of the results of Weinberg et al. (2001) and its implications for philosophical methodology in general and epistemology in specific. Despite the debates, however, (...) to our knowledge, there has not been a replication attempt of the experiments of the original paper. We collected data from four different sources (two on-line and two in-person) to replicate the experiments. Despite several different data sets and in various cases larger sample sizes and hence greater power to detect differences, we failed to detect significant differences between the above-mentioned ethnic and socioeconomic groups. Our results suggest that epistemic intuitions are more robust across ethnic and socioeconomic groups than Weinberg et al. (2001) indicates. Given our data, we believe that the notion of differences in epistemic intuitions among different ethnic and socioeconomic groups that follows from Weinberg et al. (2001) needs to be corrected. (shrink)

It has been observed that whereas painters and musicians are likely to be embarrassed by references to the beauty in their work, mathematicians instead like to engage in discussions of the beauty of mathematics. Professional artists are more likely to stress the technical rather than the aesthetic aspects of their work. Mathematicians, instead, are fond of passing judgment on the beauty of their favored pieces of mathematics. Even a cursory observation shows that the characteristics of mathematical beauty are at variance (...) with those of artistic beauty. For example, courses in art appreciation are fairly common; it is however unthinkable to find any mathematical beauty appreciation courses taught anywhere. The purpose of the present paper is to try to uncover the sense of the term beauty as it is currently used by mathematicians. (shrink)

The literature on mathematical explanation contains numerous examples of explanatory, and not so explanatory proofs. In this paper we report results of an empirical study aimed at investigating mathematicians’ notion of explanatoriness, and its relationship to accounts of mathematical explanation. Using a Comparative Judgement approach, we asked 38 mathematicians to assess the explanatory value of several proofs of the same proposition. We found an extremely high level of agreement among mathematicians, and some inconsistencies between their assessments and claims in the (...) literature regarding the explanatoriness of certain types of proofs. (shrink)

Theories of reference have been central to analytic philosophy, and two views, the descriptivist view of reference and the causal-historical view of reference, have dominated the field. In this research tradition, theories of reference are assessed by consulting one’s intuitions about the reference of terms in hypothetical situations. However, recent work in cultural psychology (e.g., Nisbett et al. 2001) has shown systematic cognitive differences between East Asians and Westerners, and some work indicates that this extends to intuitions about philosophical cases (...) (Weinberg et al. 2001). In light of these findings on cultural differences, two experiments were conducted which explored intuitions about reference in Westerners and East Asians. Both experiments indicate that, for certain central cases, Westerners are more likely than East Asians to report intuitions that are consistent with the causal-historical view. These results constitute prima facie evidence that semantic intuitions vary from culture to culture, and the paper argues that this fact raises questions about the nature of the philosophical enterprise of developing a theory of reference. (shrink)

In this article, we present evidence that in four different cultural groups that speak quite different languages there are cases of justified true beliefs that are not judged to be cases of knowledge. We hypothesize that this intuitive judgment, which we call “the Gettier intuition,” may be a reflection of an underlying innate and universal core folk epistemology, and we highlight the philosophical significance of its universality.

In an article in Cognition, Machery, Mallon, Nichols, and Stich [Machery et al., 2004] present data which purports to show that “East Asian” native Cantonese speakers tend to have descriptivist intuitions about the referents of proper names, while “Western” native English speakers tend to have causal-historical intuitions about proper names. Machery et al take this finding to support the view that some intuitions, the universality of which they claim is central to philosophical theories, vary according to cultural background. Machery et (...) al hypothesize that the differences in intuitions about reference stem from general psychological differences between Eastern and Western subjects. Machery et al conclude from their findings that the philosophical methodology of consulting intuitions about hypothetical cases is flawed vis ` a vis the goal of determining truths about some philosophical domains. To quote Machery et al, “our data indicate that philosophers must radically revise their methodology” because “the intuitions philosophers pronounce from their armchairs are likely to be a product of their own culture and their academic training” ( [Machery et al., 2004] pp.B9). “The evidence suggests that it is wrong for philosophers to assume a priori the universality of their own semantic intuitions” ( [Machery et al., 2004] pp. B8). In the following study, I present data incompatible with Machery et al’s results. Native Cantonese-speaking immigrants from a Cantonese diaspora 1 in Southern California do not have descriptivist intuitions about the referents of proper names when presented with a Cantonese story and Cantonese questions about reference and truth-value. This data raises questions about the quality of Machery et al’s study and the conclusions they draw from it. (shrink)

Within the existing metaphilosophical literature on experimental philosophy, a great deal of attention has been devoted to the claim that there are large differences in philosophical intuitions between people of different demographic groups. Some philosophers argue that this claim has important metaphilosophical implications; others argue that it does not. However, the actual empirical work within experimental philosophy seems to point to a very different sort of metaphilosophical question. Specifically, what the actual empirical work suggests is that intuitions are surprisingly robust (...) across demographic groups. Prior to empirical study, it seemed plausible that unexpected patterns of intuition found in one demographic group would not emerge in other demographic groups. Yet, again and again, empirical work obtains the opposite result: that unexpected patterns found in one demographic group actually emerge also in other demographic groups. I cite 30 studies that find this sort of robustness. I then argue that to the extent that metaphilosophical work is to engage with the actual findings from experimental philosophy, it needs to explore the implications of the surprising robustness of philosophical intuitions across demographic differences. (shrink)

Claims about people's intuitions have long played an important role in philosophical debates. The new field of experimental philosophy seeks to subject such claims to rigorous tests using the traditional methods of cognitive science – systematic experimentation and statistical analysis. Work in experimental philosophy thus far has investigated people's intuitions in philosophy of language, philosophy of mind, epistemology, and ethics. Although it is now generally agreed that experimental philosophers have made surprising discoveries about people's intuitions in each of these areas, (...) considerable disagreement remains about the philosophical significance of the key findings. Some have argued that work in experimental philosophy should be assessed by asking whether it can contribute to the kind of inquiry that is normally pursued within analytic philosophy, while others suggest that work in experimental philosophy is best understood as a contribution to a more traditional sort of philosophical inquiry that long predates the birth of analytic philosophy. (shrink)

The present volume provides an introduction to the major themes of work in experimental philosophy, bringing together some of the most influential articles in ...

Experimental philosophy is a new interdisciplinary field that uses methods normally associated with psychology to investigate questions normally associated with philosophy. The present review focuses on research in experimental philosophy on four central questions. First, why is it that people's moral judgments appear to influence their intuitions about seemingly nonmoral questions? Second, do people think that moral questions have objective answers, or do they see morality as fundamentally relative? Third, do people believe in free will, and do they see free (...) will as compatible with determinism? Fourth, how do people determine whether an entity is conscious? (shrink)

In “Normativity and Epistemic Intuitions”, Weinberg, Nichols and Stich famously argue from empirical data that East Asians and Westerners have different intuitions about Gettier -style cases. We attempted to replicate their study about the Car case, but failed to detect a cross - cultural difference. Our study used the same methods and case taken verbatim, but sampled an East Asian population 2.5 times greater than NEI’s 23 participants. We found no evidence supporting the existence of cross - cultural difference about (...) the intuition concerning the Gettier car case. Taken together with the failures of both of the existing replication studies, our results provide strong evidence that the purported cross - cultural difference in Gettier intuitions does not exist. (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.

Editorial: Folk Epistemology. The Cognitive Bases of Epistemic Evaluation Content Type Journal Article Pages 477-482 DOI 10.1007/s13164-010-0046-8 Authors Christophe Heintz, Department of Cognitive Science, Central European University, Budapest, Hungary Dario Taraborelli, Centre for Research in Social Simulation, Department of Sociology, University of Surrey, Guildford, UK Journal Review of Philosophy and Psychology Online ISSN 1878-5166 Print ISSN 1878-5158 Journal Volume Volume 1 Journal Issue Volume 1, Number 4.

We challenge an argument that aims to support Aesthetic Realism by claiming, first, that common sense is realist about aesthetic judgments because it considers that aesthetic judgments can be right or wrong, and, second, that becauseAesthetic Realism comes from and accounts for “folk aesthetics,” it is the best aesthetic theory available.We empirically evaluate this argument by probing whether ordinary people with no training whatsoever in the subtle debates of aesthetic philosophy consider their aesthetic judgments as right or wrong. Having shown (...) that the results do not support the main premise of the argument, we discuss the consequences for Aesthetic Realism and address possible objections to our study. (shrink)

We challenge an argument that aims to support Aesthetic Realism by claiming, first, that common sense is realist about aesthetic judgments because it considers that aesthetic judgments can be right or wrong, and, second, that becauseAesthetic Realism comes from and accounts for “folk aesthetics,” it is the best aesthetic theory available.We empirically evaluate this argument by probing whether ordinary people with no training whatsoever in the subtle debates of aesthetic philosophy consider their aesthetic judgments as right or wrong. Having shown (...) that the results do not support the main premise of the argument, we discuss the consequences for Aesthetic Realism and address possible objections to our study. (shrink)

The book addresses for the first time the dynamics associated with the modernization of mathematics in China from the nineteenth to the mid-twentieth century from a transcultural global historical perspective. Rather than depict the transformations of mathematical knowledge in terms of a process of westernization, the book analyzes the complex interactions between different scientific communities and the ways in which the past, modernity, language, and mathematics were negotiated in a global context. In each chapter, Andrea Bréard provides vivid portraits of (...) a series of go-betweens based on a vast array of translated primary sources hitherto unavailable to a non-Chinese readership. They not only illustrate how Chinese scholars mediated between new mathematical objects and discursive modes, but also how they instrumentalized their autochthonous scientific roots in specific political and intellectual contexts. While sometimes technical in style, the book addresses all readers who are interested in the global and cultural history of science and the complexities involved in the making of universal mathematics. “While the pursuit of modernity is in the title, entanglement is of as much interest. Using the famous ‘Nine Chapters’ as a framework, Bréard considers a wide range of that entanglement from divination to data management. Bréard’s analysis and thought-provoking insights show once again how much we can learn when two cultures intersect. A fascinating read!”. (shrink)

We investigated whether mathematicians typically agree about the qualities of mathematical proofs. Between-mathematician consensus in proof appraisals is an implicit assumption of many arguments made by philosophers of mathematics, but to our knowledge the issue has not previously been empirically investigated. We asked a group of mathematicians to assess a specific proof on four dimensions, using the framework identified by Inglis and Aberdein (2015). We found widespread disagreement between our participants about the aesthetics, intricacy, precision and utility of the proof, (...) suggesting that a priori assumptions about the consistency of mathematical proof appraisals are unreasonable. (shrink)

Many of the methods commonly used to research mathematical practice, such as analyses of historical episodes or individual cases, are particularly well-suited to generating causal hypotheses, but less well-suited to testing causal hypotheses. In this paper we reflect on the contribution that the so-called hypothetico-deductive method, with a particular focus on experimental studies, can make to our understanding of mathematical practice. By way of illustration, we report an experiment that investigated how mathematicians attribute aesthetic properties to mathematical proofs. We demonstrate (...) that perceptions of the aesthetic properties of mathematical proofs are, in some cases at least, subject to social influence. Specifically, we show that mathematicians’ aesthetic judgements tend to conform to the judgements made by others. Pedagogical implications are discussed. (shrink)

Normative questions – particularly questions about what we should believe and how we should behave – have always been high on the agenda for philosophers, and over the centuries there has been no shortage of answers proposed. But this abundance of answers raises yet another fundamental philosophical question: How should we evaluate the proposed answers; how can we determine whether an answer to a normative question is a good one? The best known and most widely used method for evaluating answers (...) to normative questions can be traced all the way back to Plato. Recently, however, cognitive scientists interested in cross cultural differences have reported findings that pose a serious challenge to this venerable philosophical method. Indeed, in light of these new findings some philosophers – I am one of them – have come to think that after 2400 years it may be time for philosophy to stop relying on Plato’s method. In the pages that follow I’ll sketch the path that led me to this conclusion. (shrink)