Philosophers have rightly condemned lookism—that is, discrimination in favor of attractive people or against unattractive people—in education, the justice system, the workplace and elsewhere. Surprisingly, however, the almost universal preference for attractive romantic and sexual partners has rarely received serious ethical scrutiny. On its face, it’s unclear whether this is a form of discrimination we should reject or tolerate. I consider arguments for both views. On the one hand, a strong case can be made that preferring attractive partners is bad. (...) The idea is that choosing partners based on looks seems essentially similar to other objectionable forms of discrimination. (In particular, the preference for attractive partners is arguably both unfair and harmful to a significant degree.) One can try to resist this conclusion in several ways. I consider three possible replies. The first has to do with the possibility of controlling our partner preferences. The second pertains to attractiveness and “good genes”. The last attempts to link certain aspects of attractiveness to a prospective partner’s personality and values. I argue that the first two replies fail conclusively, while the third only amounts to a limited defense of a particular kind of attractiveness preference. So the idea that we should often avoid preferring attractive partners is compelling. (shrink)
Mathematicians distinguish between proofs that explain their results and those that merely prove. This paper explores the nature of explanatory proofs, their role in mathematical practice, and some of the reasons why philosophers should care about them. Among the questions addressed are the following: what kinds of proofs are generally explanatory (or not)? What makes a proof explanatory? Do all mathematical explanations involve proof in an essential way? Are there really such things as explanatory proofs, and if so, how do (...) they relate to the sorts of explanation encountered in philosophy of science and metaphysics? (shrink)
Models are indispensable tools of scientific inquiry, and one of their main uses is to improve our understanding of the phenomena they represent. How do models accomplish this? And what does this tell us about the nature of understanding? While much recent work has aimed at answering these questions, philosophers' focus has been squarely on models in empirical science. I aim to show that pure mathematics also deserves a seat at the table. I begin by presenting two cases: Cramér’s random (...) model of the prime numbers and the function field model of the integers. These cases show that mathematicians, like empirical scientists, rely on unrealistic models to gain understanding of complex phenomena. They also have important implications for some much-discussed theses about scientific understanding. First, modeling practices in mathematics confirm that one can gain understanding without obtaining an explanation. Second, these cases undermine the popular thesis that unrealistic models confer understanding by imparting counterfactual knowledge. (shrink)
A proof P of a theorem T is transferable when a typical expert can become convinced of T solely on the basis of their prior knowledge and the information contained in P. Easwaran has argued that transferability is a constraint on acceptable proof. Meanwhile, a proof P is fixable when it’s possible for other experts to correct any mistakes P contains without having to develop significant new mathematics. Habgood-Coote and Tanswell have observed that some acceptable proofs are both fixable and (...) in need of fixing, in the sense that they contain nontrivial mistakes. The claim that acceptable proofs must be transferable seems quite plausible. The claim that some acceptable proofs need fixing seems plausible too. Unfortunately, these attractive suggestions stand in tension with one another. I argue that the transferability requirement is the problem. Acceptable proofs need only satisfy a weaker requirement I call “corrigibility”. I explain why, despite appearances, the corrigibility standard is preferable to stricter alternatives. (shrink)
Bill D'Alessandro talks to Kenny Easwaran about fractal music, Zoom conferences, being a good referee, teaching in math and philosophy, the rationalist community and its relationship to academia, decision-theoretic pluralism, and the city of Manhattan, Kansas.