MWPMW 20 will meet on the University of Notre Dame campus Saturday, November 9th and Sunday, November 10th, 2019.
Stay tuned to these pages for further information.
Marc Lange (U of Pittsburgh)
• “Inference to the Best Explanation as a Form of Non-Deductive Reasoning in Mathematics”
I will argue that mathematical conjectures are sometimes confirmed by mathematical (rather than scientific) evidence by way of an "inference to the best explanation" (IBE). To talk about IBE in mathematics, I will first have to clarify what IBE is and what E in mathematics can sometimes be. For good measure, I will argue that IBE in mathematics can be understood in terms that a Bayesian can countenance.
Rebecca Morris (Stanford University)
• "Intellectual generosity and diversity in mathematics"
William Thurston was described by his fellow mathematicians as an intellectually generous person. But what does it mean to say Thurston was intellectually generous? And what benefits are associated with this virtue? To answer the first question, I will argue that Thurston's intellectual generosity is captured by Roberts and Wood's (2007) analysis. To answer the second question, I will argue that intellectual generosity promotes the development of research communities that are diverse in terms of the mathematical backgrounds of their members. Then I will show that such diversity promotes, and is sometimes required for, mathematical breakthroughs.
R. Roberts and W. J. Wood, Intellectual Virtues: An Essay in Regulative Epistemology, Oxford, 2007.