VISITING SPEAKER:
Hartley
Slater
(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.