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Remarks on the foundations of mathematics
Remarks on the foundations of mathematics
ratings:
Length:
92 minutes
Released:
Feb 21, 2014
Format:
Podcast episode
Description
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.
Released:
Feb 21, 2014
Format:
Podcast episode
Titles in the series (22)
Haecceities and Mathematical Structuralism: Colloquium Mathematical Philosophy by MCMP – Philosophy of Mathematics