Mathematicians often conduct aesthetic judgements to evaluate mathematical objects such as equations or proofs. But is there a consensus about which mathematical objects are beautiful? We used a comparative judgement technique to measure aesthetic intuitions among British mathematicians, Chinese mathematicians, and British mathematics undergraduates, with the aim of assessing whether judgements of mathematical beauty are influenced by cultural differences or levels of expertise. We found aesthetic agreement both within and across these demographic groups. We conclude that judgements of mathematical beauty (...) are not strongly influenced by cultural difference, levels of expertise, and types of mathematical objects. Our findings contrast with recent studies that found mathematicians often disagree with each other about mathematical beauty. (shrink)

In recent years a new discussion on the nature of philosophical expertise has emerged: whether philosophers possess a special kind of expertise, what such expertise would entail, how to measure it, and related concerns. The aim of the present article is to clarify certain related points across these debates in the hope of paving a clearer path forward, by addressing the following. (1) The expertise defense, which seems central to many discussions on methodology and expertise, has been misconstrued at times. (...) (2) Questions of expertise and methodology could be separated more clearly. (3) The study of expertise may be important in its own right; however, there may be good reasons to give priority to methodological concerns. (4) Finally, when viewed in light of methodological concerns, a new project emerges when engaging with recent contributions to the expertise debate. The present article attempts a brief outline of this project. (shrink)

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)

Normative theories can be useful in developing descriptive theories, as when normative subjective expected utility theory is used to develop descriptive rational choice theory and behavioral game theory. “Ought” questions are also the essence of theories of moral reasoning, a domain of higher mental processing that could not survive without normative considerations.

A critique of inferences from 'is' to 'ought' plays a central role in Elqayam and Evans' defense of descriptivism. However, the reflective equilibrium strategy described by Goodman and embraced by Rawls, Cohen and many others poses an important challenge to that critique. Dual system theories may help respond to that challenge.

The field of experimental philosophy has received considerable attention, essentially for producing results that seem highly counter-intuitive and at the same time question some of the fundamental methods used in philosophy. A substantial part of this attention has focused on the role of intuitions in philosophical methodology. One of the major contributions of experimental philosophy on this topic has been concrete evidence in support of intuitional diversity; the idea that intuitions vary systematically depending on variables such as ethnicity, socioeconomic background, (...) or gender. Because of the important implications, these findings have been the subject of extensive debate. Despite the seeming significance of the findings and despite all the debates that the experimental philosophy movement has prompted, what has not been examined systematically is the reproducibility of the results. Instead, the reported findings have been simply accepted as established facts. We set out to replicate a wide range of experiments and surprisingly failed to reproduce many of the reported findings, some of which are from the most cited and attention grabbing papers of the field. We draw two conclusions from our findings. The first is that the instability of intuitions has been exaggerated by experimental philosophers. Intuitions appear to be more uniform across different demographic groups. The argument that intuitions need to be discarded because they depend on arbitrary factors such as ethnicity, socioeconomic background, or gender does not seem tenable anymore. The second conclusion is that experimental philosophy needs a better system to ensure the reproducibility of published findings. The current research-publication system of various empirical fields, especially those employing statistical methods, leads to an overproduction of false-positive findings in the published literature. Unless changes are made to the current research-publication system, this overproduction is likely to continue, in experimental philosophy as well as other disciplines. (shrink)