LaTeX for Logicians

It's been up for a while now, but better late than never: Peter Smith (Cambridge) has set up a very handy page of links to LaTeX class files, style files, and instructions, especially for logicians. It includes, for instance, links to Josh Parson's style file for setting formulas in Frege's Begriffsschrift notation. Also, Peter's own … Continue reading LaTeX for Logicians

Blog Rules

Brian Weatherson has started a discussion about rules as to what it is ok to write about in philosophy blogs. This was taken up by Lindsay Beyerstein and Gustavo Llarull. In the comments at TAR, I suggested that it's doubtful that new rules are needed. Blogging is a relatively new phenomenon, but academic discussion (in … Continue reading Blog Rules

Free-variable Tableaux

Wolfgang Schwartz asks here if there is a "canonical" way to build free-variable tableaux which are guaranteed to close if the original formula is valid. It seems to me that this must be the case, since free-variable tableaux are a complete proof method. But maybe I don't understand the question.The point of free-variable tableaux is … Continue reading Free-variable Tableaux

Great Moments in Logic

Greg Restall has a nice page of short descriptions of some important logicians' work. Kinda like my Who are Boole, Fitch, and Tarski page, only more in-depth.

Characterization of the axiomatizable prenex fragments of first-order Gödel logics

In: 33rd International Symposium on Multiple-valued Logic. Proceedings. Tokyo, May 16-19, 2003 (IEEE Computer Society Press, 2003) 175-180 (with Matthias Baaz and Norbert Preining)

Abstract: The prenex fragments of first-order infinite-valued Gödel logics are classified. It is shown that the prenex Gödel logics characterized by finite and by uncountable subsets of [0, 1] are axiomatizable, and that the prenex fragments of all countably infinite Gödel logics are not axiomatizable.

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Hilbert’s Finitism: Historical, Philosophical, and Metamathematical Perspectives

Source

Dissertation, University of California, Berkeley, Spring 2001

Abstract

In the 1920s, David Hilbert proposed a research program with the aim of providing mathematics with a secure foundation. This was to be accomplished by first formalizing logic and mathematics in their entirety, and then showing—using only so-called finitistic principles—that these formalizations are free of contradictions.