Combining Texts

All the ideas for 'Letters to Antoine Arnauld', 'On the Essence of Truth' and 'On the Introduction of Transfinite Numbers'

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7 ideas

3. Truth / A. Truth Problems / 1. Truth
21953 For Heidegger there is 'ontic' truth or 'uncoveredness', as in "he is a true friend" [Heidegger, by Wrathall]
     Full Idea: We say things like 'he is a true friend'. Heidegger calls this kind of truth 'ontic truth' or the 'uncoveredness' of entities.
     From: report of Martin Heidegger (On the Essence of Truth [1935]) by Mark Wrathall - Heidegger: how to read 7
     A reaction: [In his later essays] The example is very bad for showing a clear alternative meaning of 'true'. I presume it can only be explained in essentialist terms - an entity is 'true' if its appearance and behaviour conforms to its essence.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
13489 Von Neumann treated cardinals as a special sort of ordinal [Neumann, by Hart,WD]
     Full Idea: Von Neumann's decision was to start with the ordinals and to treat cardinals as a special sort of ordinal.
     From: report of John von Neumann (On the Introduction of Transfinite Numbers [1923]) by William D. Hart - The Evolution of Logic 3
     A reaction: [see Hart 73-74 for an explication of this]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
12336 A von Neumann ordinal is a transitive set with transitive elements [Neumann, by Badiou]
     Full Idea: In Von Neumann's definition an ordinal is a transitive set in which all of the elements are transitive.
     From: report of John von Neumann (On the Introduction of Transfinite Numbers [1923]) by Alain Badiou - Briefings on Existence 11
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / g. Von Neumann numbers
18179 For Von Neumann the successor of n is n U {n} (rather than {n}) [Neumann, by Maddy]
     Full Idea: For Von Neumann the successor of n is n U {n} (rather than Zermelo's successor, which is {n}).
     From: report of John von Neumann (On the Introduction of Transfinite Numbers [1923]) by Penelope Maddy - Naturalism in Mathematics I.2 n8
18180 Von Neumann numbers are preferred, because they continue into the transfinite [Maddy on Neumann]
     Full Idea: Von Neumann's version of the natural numbers is in fact preferred because it carries over directly to the transfinite ordinals.
     From: comment on John von Neumann (On the Introduction of Transfinite Numbers [1923]) by Penelope Maddy - Naturalism in Mathematics I.2 n9
15925 Each Von Neumann ordinal number is the set of its predecessors [Neumann, by Lavine]
     Full Idea: Each Von Neumann ordinal number is the set of its predecessors. ...He had shown how to introduce ordinal numbers as sets, making it possible to use them without leaving the domain of sets.
     From: report of John von Neumann (On the Introduction of Transfinite Numbers [1923]) by Shaughan Lavine - Understanding the Infinite V.3
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
21963 It is possible that an omnipotent God might make one and two fail to equal three [Descartes]
     Full Idea: Since every basic truth depends on God's omnipotence, I would not dare to say that God cannot make it....that one and two should not be three.
     From: René Descartes (Letters to Antoine Arnauld [1645]), quoted by A.W. Moore - The Evolution of Modern Metaphysics 01.3
     A reaction: An unusual view. Most people would say that if Descartes can doubt something that simple, he should also doubt his reasons for believing in God's existence.