The Development and Limits of Mathematical Logic, part 1
The Development and Limits of Mathematical Logic, part 1
Sku: 10300A0E050
Archival Number: CD/mp3 103
Author: Lonergan, B.
Language(s): English
Decade: 1950
Description:
CD/mp3 103, part 1 of lecture 2 on mathematical logic 1957. Corresponds to CWL 18, pp. 38-55. The ideal of deducing rigorously deductive systems from minimal suppositions has been formulated as an axiomatic system or logical formalization. Terms and propositions are distinguished into derived and non-derived or primitive. Rules of derivation must be stated explicitly. Mathematical logicians have shown that the ideal works for certain fields. The development of mathematical logic regards where it works and why, and where it does not work and why. There has been a variety of lines of endeavor, some of which are described briefly: axiomatic set theory, Whitehead-Russell, Hilbert, intuitionism, Gonseth, and Bourbaki. The key aspect to the lecture, though, has to do with what Lonergan calls Godelian limitations, a series of theorems setting limitations to the possibility of reaching the ideal of a rigorously deductivist logical-mathematical system.