Diversity Reading List

Abstract:

A source of tension between Philosophers of Mathematics and Mathematicians is the fact that each group feels ignored by the other; daily mathematical practice seems barely affected by the questions the Philosophers are considering. In this talk I will describe an issue that does have an impact on mathematical practice, and a philosophical stance on mathematics that is detectable in the work of practising mathematicians. No doubt controversially, I will call this issue ‘morality’, but the term is not of my coining: there are mathematicians across the world who use the word ‘morally’ to great effect in private, and I propose that there should be a public theory of what they mean by this. The issue arises because proofs, despite being revered as the backbone of mathematical truth, often contribute very little to a mathematician’s understanding. ‘Moral’ considerations, however, contribute a great deal. I will first describe what these ‘moral’ considerations might be, and why mathematicians have appropriated the word ‘morality’ for this notion. However, not all mathematicians are concerned with such notions, and I will give a characterisation of ‘moralist’ mathematics and ‘moralist’ mathematicians, and discuss the development of ‘morality’ in individuals and in mathematics as a whole. Finally, I will propose a theory for standardising or universalising a system of mathematical morality, and discuss how this might help in the development of good mathematics.

Abstract: Prominent mathematician William Thurston was praised by other mathematicians for his intellectual generosity. But what does it mean to say Thurston was intellectually generous? And is being intellectually generous beneficial? To answer these questions I turn to virtue epistemology and, in particular, Roberts and Wood's (2007) analysis of intellectual generosity. By appealing to Thurston's own writings and interviewing mathematicians who knew and worked with him, I argue that Roberts and Wood's analysis nicely captures the sense in which he was intellectually generous. I then argue that intellectual generosity is beneficial because it counteracts negative effects of the reward structure of mathematics that can stymie mathematical progress.

Abstract: Why, when asking oneself whether to believe that p, must one immediately recognize that this question is settled by, and only by, answering the question whether p is true? Truth is not an optional end for first-personal doxastic deliberation, providing an instrumental or extrinsic reason that an agent may take or leave at will. Otherwise there would be an inferential step between discovering the truth with respect to p and determining whether to believe that p, involving a bridge premise that it is good (in whichever sense of good one likes, moral, prudential, aesthetic, allthings-considered, etc.) to believe the truth with respect to p. But there is no such gap between the two questions within the first-personal deliberative perspective; the question whether to believe that p seems to collapse into the question whether p is true.

Summary: This paper aims to explore the implication of rejecting Cartesianism for our relationship to the normative realm. It is argued that it implies that this relationship is more fraught than many would like to think. Without privileged access to our own minds, there are no norms that can invariably guide our actions, and no norms that are immune from blameless violation. This will come as bad news to those normative theorists who think that certain central normative notions - e.g. the ethical ought or epistemic justification - should be cashed out in terms of subjects' mental states precisely in order to generate norms that are action-guiding and immune from blameless vi- olation. Meanwhile Anti-Cartesianism might come as good news to those normative theorists who resist cashing out norms in terms of mental states. For Anti-Cartesnianism implies that no norms - however closely tied to the mental - can be perfectly action-guiding or totally immune from blameless violation. More generally, once we have accepted that our relationship to our own minds lacks the perfect intimacy promised by Cartesianism, we are, for better or worse, left with the view that the normative realm is suffused with ignorance and bad luck.

Abstract: Some personal thoughts and opinions on what “good quality mathematics” is and whether one should try to define this term rigorously. As a case study, the story of Szemer´edi’s theorem is presented.

Abstract: In this paper I distinguish three degrees of epistemic egoism, each of which has an ethical analogue, and I argue that all three are incoherent. Since epistemic autonomy is frequently identified with one of these forms of epistemic egoism, it follows that epistemic autonomy as commonly understood is incoherent. I end with a brief discussion of the idea of moral autonomy and suggest that its component of epistemic autonomy in the realm of the moral is problematic.