Combining Texts

All the ideas for 'The Gettier Problem', 'Anti-Semite and Jew' and 'On the Introduction of Transfinite Numbers'

unexpand these ideas     |    start again     |     specify just one area for these texts

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
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / b. Gettier problem
19699 A Gettier case is a belief which is true, and its fallible justification involves some luck [Hetherington]
     Full Idea: A Gettier case contains a belief which is true and well justified without being knowledge. Its justificatory support is also fallible, ...and there is considerable luck in how the belief combnes being true with being justified.
     From: Stephen Hetherington (The Gettier Problem [2011], 5)
     A reaction: This makes luck the key factor. 'Luck' is a rather vague concept, and so the sort of luck involved must first be spelled out. Or the varieties of luck that can produce this outcome.
23. Ethics / F. Existentialism / 6. Authentic Self
22232 Authenticity is taking responsibility for a situation, with all its risks and emotions [Sartre]
     Full Idea: Authenticity consists in having a true and lucid consciousness of the situation, in assuming the responsibilities and risks that it involves, in accepting it in pride of humiliation, sometimes in horror and hate.
     From: Jean-Paul Sartre (Anti-Semite and Jew [1946], p.90), quoted by Christine Daigle - Jean-Paul Sartre 2.4
     A reaction: [Not sure what 'pride of humiliation' is, so it may be a typo for 'or']