The goal of this paper is to connect Rota's discussion of the Husserlian notion of Fundierung with Rota's project of giving combinatorics a foundation in his 1964 paper ‘On the foundations of combinatorial theory I’. Section 2 gives the basic tenets of this seminal paper. Sections 3 and 4 spell out the connections made there between Rota's philosophical writings and his mathematical achievements. Section 5 shows how these two developments fit into Rota's analysis of the place of combinatorics in mathematics.

Mathematics is becoming increasingly specialized, divided into a vast and growing number of subfields. While this division of cognitive labor has important benefits, it also has a significant drawb...

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. (shrink)

Abstract In the new millennium there have been important empirical developments in the philosophy of mathematics. One of these is the so-called “Empirical Philosophy of Mathematics”(EPM) of Buldt, Löwe, Müller and Müller-Hill, which aims to complement the methodology of the philosophy of mathematics with empirical work. Among other things, this includes surveys of mathematicians, which EPM believes to give philosophically important results. In this paper I take a critical look at the sociological part of EPM as a case study of (...) ... (shrink)