Combining Texts

All the ideas for 'Philosophical Explanations', 'Wang's Paradox' and 'Structuralism Reconsidered'

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5 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / d. Natural numbers
Numbers are identified by their main properties and relations, involving the successor function [MacBride]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
For mathematical objects to be positions, positions themselves must exist first [MacBride]
7. Existence / D. Theories of Reality / 10. Vagueness / b. Vagueness of reality
To say reality itself is vague is not properly intelligible [Dummett]
11. Knowledge Aims / A. Knowledge / 4. Belief / c. Aim of beliefs
Maybe knowledge is belief which 'tracks' the truth [Nozick, by Williams,M]
13. Knowledge Criteria / C. External Justification / 4. Tracking the Facts
A true belief isn't knowledge if it would be believed even if false. It should 'track the truth' [Nozick, by Dancy,J]