The General Character of Mathematical Logic, Part 1
The General Character of Mathematical Logic, Part 1
Sku: 10100A0E050
Archival Number: CD/mp3 101
Author: Lonergan, B.
Language(s): English
Decade: 1950
Description:
CD/mp3 101, part 1 of lecture 1 on mathematical logic 1957. Corresponds to CWL 18, pp. 3-20. Sponsor: William Spreitzer. The question will be, What about it? What is there in mathematical logic for us? What are we to guard against? The first half of this first lecture will provide a descriptive approach, the second half (CD/mp3 102) an analytic approach. As contrasted with traditional logic, mathematical logic studies entire deductive systems or Logical Formalizations (LFs). A deductive system consists of axioms, rules of derivation, and conclusions. What are the properties of such a system? Three kinds of questions are asked: questions of coherence, questions of completeness, and the decision question, namely, can all the problems that arise in the system be solved mechanically? Lonergan discusses the reasons given for the close link between the investigation of deductive systems and mathematics, and then the fact that the investigation is both symbolic and technical. Mathematical logic is contrasted with the casual insights that occur in Euclid's Elements. Lonergan contrasts mathematical logic with scholastic procedures: the symbolic technique cannot draw distinctions without starting all over; there is a debate among symbolic logicians regarding the principle of excluded middle; Scholastic philosophy includes structural distinctions that apply to every concept; and Scholastics employ analogous terms. The final point in the general description has to do with the reliance of mathematical logic on paradoxes that it cannot deal with in the same way that Scholastic philosophy would.