Combining Texts

All the ideas for 'Philosophical Explanations', 'Elements of Intuitionism (2nd ed)' and 'On the Introduction of Transfinite Numbers'

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8 ideas

4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic

18832

Mathematical statements and entities that result from an infinite process must lack a truth-value [Dummett]

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]

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]

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]

18180

Von Neumann numbers are preferred, because they continue into the transfinite [Maddy on Neumann]

15925

Each Von Neumann ordinal number is the set of its predecessors [Neumann, by Lavine]

11. Knowledge Aims / A. Knowledge / 4. Belief / c. Aim of beliefs

3570	Maybe knowledge is belief which 'tracks' the truth [Nozick, by Williams,M]

13. Knowledge Criteria / C. External Justification / 4. Tracking the Facts

2748	A true belief isn't knowledge if it would be believed even if false. It should 'track the truth' [Nozick, by Dancy,J]