Combining Texts

All the ideas for 'Stipulation, Meaning and Apriority', 'On the Introduction of Transfinite Numbers' and 'Letters to Samuel Masson'

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13 ideas

2. Reason / D. Definition / 13. Against Definition
9331 How do we determine which of the sentences containing a term comprise its definition? [Horwich]
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 / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
13190 I don't admit infinite numbers, and consider infinitesimals to be useful fictions [Leibniz]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / g. Von Neumann numbers
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]
18179 For Von Neumann the successor of n is n U {n} (rather than {n}) [Neumann, by Maddy]
12. Knowledge Sources / A. A Priori Knowledge / 1. Nature of the A Priori
9333 A priori belief is not necessarily a priori justification, or a priori knowledge [Horwich]
12. Knowledge Sources / A. A Priori Knowledge / 6. A Priori from Reason
9342 Understanding needs a priori commitment [Horwich]
12. Knowledge Sources / A. A Priori Knowledge / 8. A Priori as Analytic
9332 Meaning is generated by a priori commitment to truth, not the other way around [Horwich]
12. Knowledge Sources / A. A Priori Knowledge / 9. A Priori from Concepts
9341 Meanings and concepts cannot give a priori knowledge, because they may be unacceptable [Horwich]
9334 If we stipulate the meaning of 'number' to make Hume's Principle true, we first need Hume's Principle [Horwich]
12. Knowledge Sources / A. A Priori Knowledge / 10. A Priori as Subjective
9339 A priori knowledge (e.g. classical logic) may derive from the innate structure of our minds [Horwich]