Combining Texts

All the ideas for 'The Basing Relation', 'Mathematics and the Metaphysicians' and 'Mathematics: Form and Function'

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7 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
18189 ZFC could contain a contradiction, and it can never prove its own consistency [MacLane]
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / a. Achilles paradox
7557 To solve Zeno's paradox, reject the axiom that the whole has more terms than the parts [Russell]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
10059 In mathematic we are ignorant of both subject-matter and truth [Russell]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / b. Mark of the infinite
7556 A collection is infinite if you can remove some terms without diminishing its number [Russell]
11. Knowledge Aims / A. Knowledge / 4. Belief / a. Beliefs
19696 There are reasons 'for which' a belief is held, reasons 'why' it is believed, and reasons 'to' believe it [Neta]
19697 The basing relation of a reason to a belief should both support and explain the belief [Neta]
12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence
7554 Self-evidence is often a mere will-o'-the-wisp [Russell]