Combining Texts

All the ideas for 'Science and Method', 'What Does It All Mean?' and 'Principles of Theoretical Logic'

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3 ideas

4. Formal Logic / C. Predicate Calculus PC / 1. Predicate Calculus PC
17750 The first clear proof of the consistency of the first order predicate logic was in 1928 [Hilbert/Ackermann, by Walicki]
     Full Idea: The first clear proof of the consistency of the first order predicate logic is found in the 1928 book of Hilbert and Ackermann.
     From: report of Hilbert,D/Ackermann,W (Principles of Theoretical Logic [1928]) by Michal Walicki - Introduction to Mathematical Logic History E.2.1
6. Mathematics / A. Nature of Mathematics / 2. Geometry
10245 One geometry cannot be more true than another [Poincaré]
     Full Idea: One geometry cannot be more true than another; it can only be more convenient.
     From: Henri Poincaré (Science and Method [1908], p.65), quoted by Stewart Shapiro - Philosophy of Mathematics
     A reaction: This is the culminating view after new geometries were developed by tinkering with Euclid's parallels postulate.
19. Language / A. Nature of Meaning / 6. Meaning as Use
4001 The meaning of a word contains all its possible uses as well as its actual ones [Nagel]
     Full Idea: The meaning of a word contains all its possible uses, true and false, not only its actual ones.
     From: Thomas Nagel (What Does It All Mean? [1987], Ch.5)
     A reaction: It has always seemed to me that meaning is not use, because you can't use it if it hasn't already got a meaning. What use is a meaningless word?