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.

A Note on the Strength of Disentangled Truth-Theories

Abstract

So-called `disentangled' truth-theories are supposed to prevent assumptions about the truth of statements in the object-language from inadvertently strengthening the background syntax. In earlier work, I proved some limitative results in an attempt to show that the strategy works, but those results leave several questions unanswered. We address some of them here. We also discuss a subtlety that has so far been overlooked in discussions of these theories.

Find it here: https://philpapers.org/rec/HECANO-6

This is another short paper that is a kind of appendix to an in-progress paper on the question whether there are or could be epistemically potent proofs of consistency. It may be submitted to a journal like Thought or Analysis at some point.

Some Remarks on 'Logical' Reflection

 Abstract:

Cezary Cieśliński has proved a result shows that highlights `logical reflection': The principle that every logically provable sentence is true. He suggests further that this result has a good deal of philosophical significance, specifically for the so-called `conservativeness argument' against deflationism. This note discusses the question to what extent Cieśliński's result generalizes, and just how strong `logical reflection' is, and suggests that the answers to these questions call the philosophical (though not the technical) significance of Cieśliński's result into doubt.  

On my website: http://rkheck.frege.org/pdf/unpublished/CieslinskiNote.pdf

On PhilPapers: https://philpapers.org/rec/HECSRO

This is a short paper, under 4000 words, which I will probably submit to Thought or Analysis. But mostly it's a kind of appendix to an in-progress paper on the question whether there can be a 'cogent' consistency proof. That one will be posted before long.