Mathematical Logic and Scholasticism, part 2
Sku: 11000A0E050
Archival Number: CD/mp3 110
Author: Lonergan, B.
Language(s): English,
Decade: 1950

CD/mp3 110, part 2 of lecture 5 on mathematical logic 1957. Corresponds to CWL 18, pp. 128-38 and 347-77. Scholastic manuals of philosophy are not axiomatic structures proceeding from a closely defined set of premises and consisting in nothing but a series of deductions from those premises. Scholasticism is a dynamic procedure in which you deduce, but where the deductions come from elements that de facto are true, and in a manner such that it is developing. Still, the question arises, Should we try for such an axiomatic structure? Our philosophy as philosophy of science cannot be a monolith but must be an open structure that determines the shapes of things in which the sciences can develop and allows them freedom to develop within those shapes. Could a philosophy so conceived be presented in an axiomatic structure? It is not impossible, but it would not be very useful. The real problems in philosophy are in getting people to the starting point, opening up their minds and bringing them to fundamental truths on which the system would rest. The problem is a transformation of the subject. Does mathematical logic eliminate existence? The answer depends on what is meant by 'existence.' If existence is what you know when you answer yes to the question, Is it? then if a mathematical-logical system has any reference to anything beyond itself, it is affirming existence in the sense of 'it is true that.' Does it eliminate substance? The notion of substance is not fundamental in mathematical logic, as it is in Aristotelian logic. And if one's notion of science depends exclusively on Aristotle, one does not appreciate the significance of relational structures. Still, there cannot be an explanatory science that does not invoke a notion of substance. It is required to go from description to explanation, to bring explanations into closer harmony with what is described, to correct descriptions as science develops, and so on. But 'substance' is an extremely ambiguous term. 'Substance' is the concrete unity-identity-whole that is grasped by intelligence in a spatiotemporal multiplicity of phenomena. It is not what you see or feel but what you understand in what you see and feel. Again, we are talking about a problem of the development of the subject. Questions began with the notion of substance but quickly moved to vertical finality, the natural desire to know God by God's essence, and related issues.


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