Combining Texts

All the ideas for 'Phenomenal and Perceptual Concepts', 'Papancasudani' and 'On the Introduction of Transfinite Numbers'

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7 ideas

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
18. Thought / B. Mechanics of Thought / 5. Mental Files
16369 There is a single file per object, memorised, reactivated, consolidated and expanded [Papineau, by Recanati]
     Full Idea: For Papineau there is just one file, which is initialised on the first encounter with the object, stored in memory, reactivated on further encounters, and consolidated with familiarity. Accumulation of information shows it is the same file.
     From: report of David Papineau (Phenomenal and Perceptual Concepts [2006]) by François Recanati - Mental Files 7.2
     A reaction: Recanati attempts to refute this view, defending a more complex taxonomy of files. I'm sympathetic to Papineau, as distinct shift in file type doesn't sound very plausible. Simplicity suggests Papineau as a better starting-point.
25. Social Practice / F. Life Issues / 1. Causing Death
7907 Human killing is worse if the victim is virtuous [Buddhaghosa]
     Full Idea: In the case of humans killing is the more blameworthy the more virtuous the victim is.
     From: Buddhaghosa (Papancasudani [c.400], 9.7-10)
     A reaction: This sentiment has almost become a taboo in western society, and yet it is present all the time. The greatest outcry is about murders of really good citizens. Occasionally the murder of a villain causes little regret.