Combining Texts

All the ideas for 'works', 'Grundlagen (Foundations of Theory of Manifolds)' and 'Henry V'

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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
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
13007 Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz]
     Full Idea: Archimedes gave a sort of definition of 'straight line' when he said it is the shortest line between two points.
     From: report of Archimedes (fragments/reports [c.240 BCE]) by Gottfried Leibniz - New Essays on Human Understanding 4.13
     A reaction: Commentators observe that this reduces the purity of the original Euclidean axioms, because it involves distance and measurement, which are absent from the purest geometry.
25. Social Practice / E. Policies / 1. War / b. Justice in war
23565 Our obedience to the king erases any crimes we commit for him [Shakespeare]
     Full Idea: We know enough if we know we are the king's men. Our obedience to the king wipes the crime of it out of us.
     From: William Shakespeare (Henry V [1599]), quoted by Michael Walzer - Just and Unjust Wars 03
     A reaction: He is referring to the slaughter of the French servants behind the lines at Agincourt. A classic expression of 'I was just obeying orders', which was rejected at Nurnberg in 1946. Depends on the seriousness of the crime.