Combining Philosophers

All the ideas for David Fair, Hermann Weyl and Steven Weinberg

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5 ideas

2. Reason / D. Definition / 1. Definitions
Definition just needs negation, known variables, conjunction, disjunction, substitution and quantification [Weyl, by Lavine]
     Full Idea: For mathematics, Weyl arrived (by 1917) at a satisfactory list of definition principles: negation, identification of variables, conjunction, disjunction, substitution of constants, and existential quantification over the domain.
     From: report of Hermann Weyl (works [1917]) by Shaughan Lavine - Understanding the Infinite V.3
     A reaction: Lavine summarises this as 'first-order logic with parameters'.
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
It is spooky the way mathematics anticipates physics [Weinberg]
     Full Idea: It is positively spooky how the physicist finds the mathematician has been there before him or her.
     From: Steven Weinberg (Lecture on Applicability of Mathematics [1986], p.725), quoted by Stewart Shapiro - Thinking About Mathematics 2.3
     A reaction: This suggests that mathematics might be the study of possibilities or hypotheticals, like mental rehearsals for physics. See Hellman's modal structuralism. Maybe mathematicians are reading the mind of God, but I doubt that.
26. Natural Theory / C. Causation / 4. Naturalised causation
Science has shown that causal relations are just transfers of energy or momentum [Fair, by Sosa/Tooley]
     Full Idea: Basic causal relations can, as a consequence of our scientific knowledge, be identified with certain physicalistic [sic] relations between objects that can be characterized in terms of transference of either energy or momentum between objects.
     From: report of David Fair (Causation and the Flow of Energy [1979]) by E Sosa / M Tooley - Introduction to 'Causation' §1
     A reaction: Presumably a transfer of momentum is a transfer of energy. If only anyone had the foggiest idea what energy actually is, we'd be doing well. What is energy made of? 'No identity without substance', I say. I like Fair's idea.
Fair shifted his view to talk of counterfactuals about energy flow [Fair, by Schaffer,J]
     Full Idea: Fair, who originated the energy flow view of causation, moved to a view that understands connection in terms of counterfactuals about energy flow.
     From: report of David Fair (Causation and the Flow of Energy [1979]) by Jonathan Schaffer - The Metaphysics of Causation 2.1.2
     A reaction: David Fair was a pupil of David Lewis, the king of the counterfactual view. To me that sounds like a disappointing move, but it is hard to think that a mere flow of energy through space would amount to causation. Cause must work back from an effect.
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / e. Anti scientific essentialism
The limit of science is isomorphism of theories, with essences a matter of indifference [Weyl]
     Full Idea: A science can determine its domain of investigation up to an isomorphic mapping. It remains quite indifferent as to the 'essence' of its objects. The idea of isomorphism demarcates the self-evident boundary of cognition.
     From: Hermann Weyl (Phil of Mathematics and Natural Science [1949], 25-7), quoted by Stewart Shapiro - Philosophy of Mathematics
     A reaction: Shapiro quotes this in support of his structuralism, but it is a striking expression of the idea that if there are such things as essences, they are beyond science. I take Weyl to be wrong. Best explanation reaches out beyond models to essences.