Combining Texts

All the ideas for 'Universals and Particulars', 'Mathematics and the Metaphysicians' and 'Hilbert's Programme'

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8 ideas

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 / a. The Infinite
17809 Gödel showed that the syntactic approach to the infinite is of limited value [Kreisel]
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]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
17810 The study of mathematical foundations needs new non-mathematical concepts [Kreisel]
8. Modes of Existence / D. Universals / 6. Platonic Forms / c. Self-predication
4442 Most thinkers now reject self-predication (whiteness is NOT white) so there is no Third Man problem [Armstrong]
12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence
7554 Self-evidence is often a mere will-o'-the-wisp [Russell]
27. Natural Reality / C. Space / 3. Points in Space
17811 The natural conception of points ducks the problem of naming or constructing each point [Kreisel]