Combining Texts

All the ideas for 'fragments/reports', 'Truth by Convention' and 'On the Introduction of Transfinite Numbers'

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16 ideas

1. Philosophy / F. Analytic Philosophy / 6. Logical Analysis
If if time is money then if time is not money then time is money then if if if time is not money... [Quine]
2. Reason / D. Definition / 7. Contextual Definition
Definition by words is determinate but relative; fixing contexts could make it absolute [Quine]
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
Quine quickly dismisses If-thenism [Quine, by Musgrave]
5. Theory of Logic / C. Ontology of Logic / 4. Logic by Convention
Logic needs general conventions, but that needs logic to apply them to individual cases [Quine, by Rey]
Claims that logic and mathematics are conventional are either empty, uninteresting, or false [Quine]
Logic isn't conventional, because logic is needed to infer logic from conventions [Quine]
If a convention cannot be communicated until after its adoption, what is its role? [Quine]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
If analytic geometry identifies figures with arithmetical relations, logicism can include geometry [Quine]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
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
A von Neumann ordinal is a transitive set with transitive elements [Neumann, by Badiou]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
There are four different possible conventional accounts of geometry [Quine]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / g. Von Neumann numbers
For Von Neumann the successor of n is n U {n} (rather than {n}) [Neumann, by Maddy]
Von Neumann numbers are preferred, because they continue into the transfinite [Maddy on Neumann]
Each Von Neumann ordinal number is the set of its predecessors [Neumann, by Lavine]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
If mathematics follows from definitions, then it is conventional, and part of logic [Quine]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
The cardinal virtues are theoretical (based on knowledge), and others are 'non-theoretical' [Hecato, by Dorandi]