Remarks on the foundations of mathematics

Content provided by Ludwig-Maximilians-Universität München and MCMP Team. All podcast content including episodes, graphics, and podcast descriptions are uploaded and provided directly by Ludwig-Maximilians-Universität München and MCMP Team or their podcast platform partner. If you believe someone is using your copyrighted work without your permission, you can follow the process outlined here https://player.fm/legal.

MCMP – Philosophy of Mathematics «
Remarks on the foundations of mathematics

10+ y ago 1:31:37

MP4

Fetch error

Hmmm there seems to be a problem fetching this series right now. Last successful fetch was on October 13, 2022 23:55 (2y ago)

What now? This series will be checked again in the next day. If you believe it should be working, please verify the publisher's feed link below is valid and includes actual episode links. You can contact support to request the feed be immediately fetched.

Helmut Schwichtenberg (LMU) gives a talk at the MCMP Colloquium (5 December, 2013) titled "Remarks on the foundations of mathematics". Abstract: We consider minimal logic with implication and universal quantification over (typed) object variables. Free type and predicate parameters may occur. For mathematics we need (i) data (the Scott - Ershov partial continuous functionals) and (ii) predicates (defined inductively or coinductively). In this setting we can define (Leibniz) equality, falsity and the missing logical connectives (negation, disjunction, existential quantification, conjunction). Ex-falso-quodlibet can be proved. Using Kreisel's (modified) realizability we can (even practically) extract computational content from proofs, and (internally) prove soundness.

22 episodes

#Germany #LudwigMaximiliansUniversität München Is One #MCMP Team #Philosophy #Logic #Science #Language #Mathematics #Hannes Leitgeb #Stephan Hartmann #Alexander Von Humboldt Foundation #Munich Center For Mathematical Philosophy #MCMP #LMU