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| 8732 | 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. |
| 13426 | Formalists neglect content, but the logicists have focused on generalizations, and neglected form [Ramsey] |
| Full Idea: The formalists neglected the content altogether and made mathematics meaningless, but the logicians neglected the form and made mathematics consist of any true generalisations; only by taking account of both sides can we obtain an adequate theory. | |
| From: Frank P. Ramsey (The Foundations of Mathematics [1925], §1) | |
| A reaction: He says mathematics is 'tautological generalizations'. It is a criticism of modern structuralism that it overemphasises form, and fails to pay attention to the meaning of the concepts which stand at the 'nodes' of the structure. |
| 13425 | Formalism is hopeless, because it focuses on propositions and ignores concepts [Ramsey] |
| Full Idea: The hopelessly inadequate formalist theory is, to some extent, the result of considering only the propositions of mathematics and neglecting the analysis of its concepts. | |
| From: Frank P. Ramsey (The Foundations of Mathematics [1925], §1) | |
| A reaction: You'll have to read Ramsey to see how this thought pans out, but it at least gives a pointer to how to go about addressing the question. |