Combining Texts

All the ideas for 'Isagoge ('Introduction')', 'Mathematics without Numbers' and 'Fallibilism'

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7 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]
8. Modes of Existence / D. Universals / 1. Universals
Are genera and species real or conceptual? bodies or incorporeal? in sensibles or separate from them? [Porphyry]
11. Knowledge Aims / B. Certain Knowledge / 3. Fallibilism
We can't normally say that we know something 'but it might be false' [Dougherty]
Fallibilism is consistent with dogmatism or scepticism, and is not alternative to them [Dougherty]
It is best to see the fallibility in the reasons, rather than in the agents or the knowledge [Dougherty]