4 ideas
| 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. |
| 17697 | The existence of an arbitrarily large number refutes the idea that numbers come from experience [Hilbert] |
| Full Idea: The standpoint of pure experience seems to me to be refuted by the objection that the existence, possible or actual, of an arbitrarily large number can never be derived through experience, that is, through experiment. | |
| From: David Hilbert (On the Foundations of Logic and Arithmetic [1904], p.130) | |
| A reaction: Alternatively, empiricism refutes infinite numbers! No modern mathematician will accept that, but you wonder in what sense the proposed entities qualify as 'numbers'. |
| 17698 | Logic already contains some arithmetic, so the two must be developed together [Hilbert] |
| Full Idea: In the traditional exposition of the laws of logic certain fundamental arithmetic notions are already used, for example in the notion of set, and to some extent also of number. Thus we turn in a circle, and a partly simultaneous development is required. | |
| From: David Hilbert (On the Foundations of Logic and Arithmetic [1904], p.131) | |
| A reaction: If the Axiom of Infinity is meant, it may be possible to purge the arithmetic from the logic. Then the challenge to derive arithmetic from it becomes rather tougher. |
| 21799 | We just use the word 'faculty' when we don't know the psychological cause [Galen] |
| Full Idea: So long as we are ignorant of the true essence of the cause which is operating, we call it a 'faculty'. | |
| From: Galen (On the Natural Faculties [c.170], I.iv), quoted by Dominik Perler - Intro to The Faculties: a History 2 | |
| A reaction: This is probably the view of most modern neuroscientists. I want to defend the idea that we need the concept of a faculty in philosophy, even if the psychologists and neuroscientists say it is too vague for their purposes. |