Ideas from 'The Foundations of Mathematics' by Frank P. Ramsey [1925], by Theme Structure

[found in 'Philosophical Papers' by Ramsey,Frank (ed/tr Mellor,D.H.) [CUP 1990,0-521-37621-1]].

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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V

13430

Infinity: there is an infinity of distinguishable individuals

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility

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Reducibility: to every non-elementary function there is an equivalent elementary function

5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic

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Either 'a = b' vacuously names the same thing, or absurdly names different things

5. Theory of Logic / L. Paradox / 1. Paradox

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Contradictions are either purely logical or mathematical, or they involved thought and language

6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique

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Formalists neglect content, but the logicists have focused on generalizations, and neglected form

6. Mathematics / C. Sources of Mathematics / 7. Formalism

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Formalism is hopeless, because it focuses on propositions and ignores concepts

11. Knowledge Aims / A. Knowledge / 4. Belief / d. Cause of beliefs

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I just confront the evidence, and let it act on me

13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge

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A belief is knowledge if it is true, certain and obtained by a reliable process