If you've ever wondered how many words a paper edited in LaTeX really has, here is a nice script that seems to get it right.

Showing posts from February, 2009

The workshop hit off with a tutorial on inaccessible cardinals by Benedikt Löwe (Amsterdam). It was quite entertaining and really informative. The main gist was this. Take the hierarchy of ordinals. Play around with it to get a hierarchy of cardinals. It turns out, all succesor cardinals are regular and there are also non-regular limit cardinals. Now, ZFC cannot prove the existence of regular limit cardinals (also called inaccessible cardinals). Interestingly, however, we can relate the existence of something as weird and prima facie useless as inaccessible cardinals to certain proble…

Arnold Neumaier asked why exactly Lindenbaum is credited with Lindenbaum Theorem, and the answer (given by Panu Raatikainen) is that it was never published by Lindenbaum, but it is credited to Lindenbaum by Tarski in On fundamental concepts of metamathematics (1930), theorem 12 and footnote, p. 34 in the English translation of Logic, Semantics, Metamathematics.

Since I did some Polish logic and still was lame enough not to know this, I'm grateful to Panu for the reference.

Right now, I’m looking at Hempel’s Empiricist Criteria of Cognitive Significance: Problems and Changes. At some point, he mentions Ayer’s revised verifiability requirement and Church’s argument against it, without explaining either of them. Below, a minor addendum which covers these things.

On p. 29 (Martinich pagination) Hempel discusses Ayer’s formulation of the testability criterion. The first formulation from Language, Truth and Logic is pretty much this:

A sentence S has empirical import if from S in conjunction with suitable subsidiary hypotheses it is possible to derive observation sentences which are not derivable from the subsidiary hypotheses alone. Hempel then explains why this criterion is too wide: it allows empirical import to any sentence whatsoever. Take S to …