Truth, Reflection, and Implicit Commitment

 New paper, forthcoming in a volume on the foundations of mathematics. Abstract:

The 'Implicit Commitment Thesis' (ICT) states that, if you accept a mathematical theory, then you are 'implicitly committed' to its consistency, and perhaps also to various sorts of reflection principles. This is meant to have various consequences, such as that consistency proofs can never be cogent: give us reason to believe that a theory is consisetent. I here consider a sampling of arguments for ICT and argue that they are all wanting. At the end, I suggest that we should, anyway, think of soundness proofs, in particular, not as attempts to justify reflection principles but as attempts to explain why they are true. 

Get it here. 

This is the paper for which the two short notes posted earlier, "A Note on the Strength of Disentangled Truth-Theories" and "Some Remarks on 'Logical' Reflection", are essentially appendices. 

Frege Arithmetic and the Epistemology of 'Everyday' Arithmetic

For the conference in honor of Crispin Wright held in St Andrews recently, I gave a talk that continued a discussion several of us had been having at the UConn conference a couple years ago, celebrating the 40th anniversary of Frege's Conception of Numbers as Objects. The subject of that discussion was whether there's any plausibility to the claim that Frege's Theorem might throw light on the epistemology of ordinary arithmetical knowledge, that is, the arithmetical knowledge of the legendary queer on the Clapham omnibus. I argued in the talk that there might well be such a case to be made. 

I don't know if I'll ever write up this material, so I'm making the slides available on my website.