Awodey Explains Significance of Homotopy Type Theory to Philosophy of Mathematics

Steve Awodey (CMU) explains the relevance of the foundational program of homotopy type theory and the univalence axiom to the philosophy of mathematics in a new preprint, "Structuralism, Invariance, and Univalence." Recent advances in foundations of mathematics have led to some developments that are signicant for the philosophy of mathematics, particularly structuralism. Specically, the discovery … Continue reading Awodey Explains Significance of Homotopy Type Theory to Philosophy of Mathematics

Gödel’s Incompleteness Theorems Formally Verified

Going through old emails, I found the following announcement by Larry Paulson, posted to the FOM list by Jeremy Avigad.  Good stuff, including the link to Stanis?aw ?wierczkowski's monograph in Dissertationes Mathematicae where he carries out the proof of the incompleteness theorems in HF, the theory of hereditarily finite sets. This should be of independent … Continue reading Gödel’s Incompleteness Theorems Formally Verified

Ergo, An Open Access Journal of Philosophy

http://quod.lib.umich.edu/e/ergo  Ergo is a general, open access philosophy journal accepting submissions on all philosophical topics and from all philosophical traditions. This includes, among other things: history of philosophy, work in both the analytic and continental traditions, as well as formal and empirically informed philosophy. Ergo uses a triple-anonymous peer review process and aims to return … Continue reading Ergo, An Open Access Journal of Philosophy