Combining Texts

All the ideas for 'Philosophical Explanations', 'What Numbers Are' and 'Paradox without Self-Reference'

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5 ideas

5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems

17813

Löwenheim-Skolem says any theory with a true interpretation has a model in the natural numbers [White,NP]

5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox

9138	An infinite series of sentences asserting falsehood produces the paradox without self-reference [Yablo, by Sorensen]

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure

17812

Finite cardinalities don't need numbers as objects; numerical quantifiers will do [White,NP]

11. Knowledge Aims / A. Knowledge / 4. Belief / c. Aim of beliefs

3570	Maybe knowledge is belief which 'tracks' the truth [Nozick, by Williams,M]

13. Knowledge Criteria / C. External Justification / 4. Tracking the Facts

2748	A true belief isn't knowledge if it would be believed even if false. It should 'track the truth' [Nozick, by Dancy,J]