The Foundations of Logic, part 1
Sku: 10700A0E050
Archival Number: CD/mp3 107
Author: Lonergan, B.
Language(s): English
Decade: 1950
Description:
CD/mp 3 107, part 1 of lecture 4 on mathematical logic 1957. Corresponds to CWL 18, pp. 87-106. Mathematical logic as a technique admits more in the way of refinement, precision, and capacity to deal with large, complicated questions than does traditional logic. But what is essentially new is the invasion of the field of 'minor logic' by philosophic differences that formerly were considered outside logic. These give rise to differences in the conception and use of logic, and thus to the problem of foundations. There have arisen two philosophic movements in connection with this development of mathematical logic: logical atomism (Russell) and logical positivism (Wittgenstein). In both movements there is a presupposition that a language is equivalent to a logical calculus plus a vocabulary. No questions are to be asked about the logical calculus itself, and this is the point to be challenged. The problem of foundations can be posed (1) as a problem of choice of any given system either absolutely or relatively to a particular task, (2) as the problem of the basis from which larger problems such as transfinite induction for arithmetic are addressed, (3) as a basis for dealing not only with the infinite but also with the finite domain of matters of fact, with the constantly changing background and context to any type of knowledge in the concrete sphere, and (4) as a basis for discussing the fact that developing intelligence and perfectly transparent expression form a dialectical couple. But the fundamental issue is the ambivalence of technique. It offers the alternative of a rational commitment to truth, and on that ground an acceptance with restrictions of the mathematical-logical systems, or a nonrational, pragmatic acquiescence in the fact of talk, where 'It works' replaces the virtually unconditioned. Examples are given of this attitude. Some samples of foundations of logic under the headings of middle term, subject term, and predication. Other samples constitute the substance of the next recording (cd/mp3 108). The answer to the ambivalence of the symbolic techniques is to emphasize these elements in Aristotelian and the Aristotelian tradition that have been eclipsed.