Emily Riehl, Justin Clarke-Doane and Simon DeDeo on Meaning and Truth in Mathematics

These talks were given in the same afternoon:

His paper "Hard Proofs and Good Reasons" is here: https://arxiv.org/abs/2410.18994 

30:02 But that “coevolutuon” is what Lakatos wrote about in Proofs and Refutations, isn’t it? And another thing: 27:39 “There’s no causality in mathematics” What about axioms? I mean the fact that some structure is a group causes a whole lot of theorems by Cayley, Sylow and others to hold for that object. Isn’t that the same sort of causality that applies in physics? That this particle of certain size, mass and charge moves in this path in a certain field when propelled in a certain direction at a certain speed from a certain point. There is another theorem of Lagrange that holds for this situation in a very similar way. The only difference is that in physics we don’t always know the precise masses, velocities, positions, fields etc, but under some assumptions we are reasoning the same way, aren’t we? I must have totally missed the point here! 😂 [He is an associate professor in Social and Decision Sciences, so maybe that explains his position?]

See also Doron Zeilberger and Persi Diaconis on Probability and Mathematical Knowledge and Sophie Maclean and Brady Haran on Schur Numbers.

In the following the key phrase is "Domain Specific Foundations". This is where you need to be able to draw distinctions between meaning and truth. 41:18 You can call the denotation of a logical sentence a truth-value, but then you need to draw a distinction between meaning and denotation.

See also Jennifer Nagel on Epistemic Collaboration and Common Knowledge.

Subscribe to Hopkins Natural Philosophy Forum.

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