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.

Pat Metheny (Jazz Piano Solos, v. 57)

Another volume of solo piano arrangements, this time of tunes by Pat Metheny (and in some cases Lyle Mays).

Quite a few people of my generation seem to know of Metheny only from the Pat Metheny Group recordings. I happen to think those are amazing, but I know they do not always appeal to jazz purists. But it would be a huge mistake to think Metheny is defined by those recordings. Check out albums like 80/81, Question and Answer, Day Trip, and the recent solo acoustic recordings, such as Moon Dial. Metheny does straight jazz, too. And he writes incredible ballads!

Duke Ellington (Jazz Piano Solos, v. 9)

I am a HUGE Duke Ellington fan. He wrote so much great music, and his band, at its peak, was just incredibly powerful. The great classic is Ellington at Newport, from 1956, which relaunched his career and contains one of the greatest sax solos ever. And there are Jazz Party in Stereo and the great suite Black, Brown and Beige. Not to mention the Concert of Sacred Music, which still blows me away.

I was reading a book about jazz music theory a little while ago. Repeatedly, it would say things like: Jazz musicians didn't relaly start using suspended chords until the 1960s. Except Duke, who was using them in the 30s. He was so far ahead of everyone else that it is ridiculous. 

And if you don't know albums like Money Jungle (with Charles Mingus and Max Roach), then you are in for a real treat: Duke could play 'outside', too. And don't forget the amazing album he made with Coltrane in the early 60s.

This book contains arrangements of some of Duke's music. The links below are to 'official' scores on Musescore, meaning you can't download them without paying, but the complete sheet music is there, and you could play them off a tablet or something. Most helpfully, you can listen to at least some of them (played via MIDI), which is great for getting the rhythms right.

Miles Davis (Jazz Piano Solos, v. 1)

Another post of links to Musescore versions of arrangements of jazz standards. This one is of Miles Davis tunes---mostly ones he wrote, and others he recorded. The difficulty ranges from things I can play (intermediate level) to things it'll be a while until I can play. 

These are 'official' scores, meaning you can't download these 'official' scores without paying (and I've already paid for the books, thank you), but the complete sheet music is there, and you could play them off a tablet or something. Most helpfully, you can listen to them (played via MIDI), which is great for getting the rhythms right.