Combining Texts

All the ideas for 'On Motion', 'The Realm of Matter' and 'Grundlagen (Foundations of Theory of Manifolds)'

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4 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory
15946 Cantor developed sets from a progression into infinity by addition, multiplication and exponentiation [Cantor, by Lavine]
     Full Idea: Cantor's development of set theory began with his discovery of the progression 0, 1, ....∞, ∞+1, ∞+2, ..∞x2, ∞x3, ...∞^2, ..∞^3, ...∞^∞, ...∞^∞^∞.....
     From: report of George Cantor (Grundlagen (Foundations of Theory of Manifolds) [1883]) by Shaughan Lavine - Understanding the Infinite VIII.2
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
15911 Ordinals are generated by endless succession, followed by a limit ordinal [Cantor, by Lavine]
     Full Idea: Ordinal numbers are generated by two principles: each ordinal has an immediate successor, and each unending sequence has an ordinal number as its limit (that is, an ordinal that is next after such a sequence).
     From: report of George Cantor (Grundlagen (Foundations of Theory of Manifolds) [1883]) by Shaughan Lavine - Understanding the Infinite III.4
7. Existence / A. Nature of Existence / 6. Criterion for Existence
18521 The criterion of existence is the possibility of action [Santayana]
     Full Idea: The possibility of action ...is the criterion of existence, and the test of substantiality.
     From: George Santayana (The Realm of Matter [1930], p.107), quoted by John Heil - The Universe as We Find It
     A reaction: I rather like this. I think I would say the power is the criterion of existence.
27. Natural Reality / B. Modern Physics / 1. Relativity / a. Special relativity
12709 Motion is not absolute, but consists in relation [Leibniz]
     Full Idea: In reality motion is not something absolute, but consists in relation.
     From: Gottfried Leibniz (On Motion [1677], A6.4.1968), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 3
     A reaction: It is often thought that motion being relative was invented by Einstein, but Leibniz wholeheartedly embraced 'Galilean relativity', and refused to even consider any absolute concept of motion. Acceleration is a bit trickier than velocity.