The Development and Limits of Mathematical Logic, part 2
The Development and Limits of Mathematical Logic, part 2
Sku: 10400A0E050
Archival Number: CD/mp3 104
Author: Lonergan, B.
Language(s): English
Decade: 1950
Description:
CD/mp3 104, part 2 of lecture 2 on mathematical logic 1957. Corresponds to CWL 18, pp. 56-67 and 330-33. The deductivist preconception regarding knowledge will derive a set of propositions into primitive and derived, where the derivation occurs in accord with certain rules. Hilbert's proposal was found subject to a set of limitations. Godelian limitations Lonergan identifies with that of inverse insight. The history of mathematics and science has been a discovery that not everything is to be understood, and this discovery always opens up new fields. Lonergan discusses several ways of transcending or getting beyond Godelian limitations: merely avoiding them, using indefinitely large stratifications, giving different meanings to 'enumerable,' as well as the work of Leon Henkin and Hao Wong. The latter is particularly interesting to Lonergan, with his notion of an indefinite series of systems. In the question-and-answer session Lonergan explained what is meant by a functional calculus of the first order, said more about Godelian limitations, and showed how concepts arise within a heuristic structure.