Mathematical Logic and Scholasticism, part 1
Sku: 10900A0E050
Archival Number: CD/mp3 109
Author: Lonergan, B.
Language(s): English
Decade: 1950
Description:
CD/mp3 109, part 1 of lecture 5 on mathematical logic 1957. Corresponds to CWL 18, pp. 115-28. Mathematical logic introduces a new factor in the problem of method. Of itself, the symbolic technique is philosophically indifferent, but the unawareness of presuppositions leads to real problems. In particular, mathematical logic tends to be exploited in an empiricist-pragmatic direction. From a practical point of view, to continue to treat logic as philosophically indifferent is a sound procedure, but theoretically it is essential to get straight the issue of foundations. Good judgment is needed regarding the fundamental terms that one links together to supply oneself with first principles in philosophy, and especially with regard to the notion of being. We are not in the cultural position that Aquinas was in, where metaphysics could be the starting point in these endeavors. Psychology and epistemology should be expressed first in a way that does not presuppose metaphysics. The foundations of logic are the same as the foundations of the epistemological problem, of metaphysics, of ethics. Those foundations lie in the concrete individual, not in propositions. It would be difficult to work out foundations of logic if one begins with metaphysics. Next, there is the issue of whether Scholastic thought is to be cast in the form of an axiomatic system. Is it to begin with a set of principles and premises and say nothing that cannot be deduced with strict rigor from those? In general, Scholastic thought does not proceed in this manner. But there is a tendency to a deductivism in some Scholastic schools, a position that is easier to substantiate from Scotus than from Aquinas. The key issue is to distinguish nonempirical, empirical, and comprehensive types of inquiry. Nonempirical types are found in mathematics, empirical in natural science, comprehensive in philosophy and theology. In the nonempirical, there is little or no appeal to concrete matters of fact. Thus mathematics is deductive. But it is also constructive, and that is what makes possible rigorous deduction. That possibility of deduction exists only to some extent in empirical inquiry, where there is first the movement from data to principles before there is a deductive movement from the principles back to the data. Thus science is deductive to the extent that it is constructive, that is, in the second movement. Even then, neither in mathematics nor in science is there a single axiomatic system. As for the logical structure of the comprehensive types of inquiry, the fixity of philosophy is that of an invariant form in which the sciences are not only included but are free to develop. In general, the Scholastic procedure is not a deductive procedure from a limited, sharply defined set of premises. The Scholastic uses the spontaneous dynamism of the human mind. Its conceptions are open to development, further distinctions, and so on.