Combining Texts

All the ideas for 'Mathematics without Numbers', 'Contextualism Defended' and 'Idealism: a critical survey'

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8 ideas

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend]
Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara]
Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / b. Pro-coherentism
We can no more expect a precise definition of coherence than we can of the moral ideal [Ewing]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / c. Coherentism critique
If undetailed, 'coherence' is just a vague words that covers all possible arguments [Ewing]
13. Knowledge Criteria / C. External Justification / 6. Contextual Justification / a. Contextualism
Contextualism says sceptical arguments are true, relative to their strict context [Cohen,S]
Knowledge is context-sensitive, because justification is [Cohen,S]
13. Knowledge Criteria / C. External Justification / 6. Contextual Justification / b. Invariantism
There aren't invariant high standards for knowledge, because even those can be raised [Cohen,S]