(McGill University and John Abbott College)
Introduction to the Logic of Circuits
ABSTRACT: This talk will be a tutorial on the categorical proof theory of linear logic, with emphasis on the graphical techniques of the logic of circuits.
(Department of Philosophy, University of Western Australia)
The Epsilon Calculus and Goedel's Theorems
ABSTRACT: It is clear that the Omega Rule gains a different aspect within
the Epsilon Calculus. The generalisation (n)Fn is a logical consequence
of the set X of sentences of the form 'Fm', but it is not normally taken
to be deducible from that set, if X is infinite. With the epsilon
reduction of (n)Fn to Fen-Fn, however, a deduction of the generalisation
is available from a finite subset of X. The point has important applications
in connection with Goedel's Theorems, and elsewhere. For instance
it also corrects Intuitionistic doubts about Indirect Proof, and has significant
consequences for Hilbert's Finitism.