Combining Texts

Ideas for 'Defending the Axioms', 'Mathematical Truth' and 'Against Structural Universals'

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6 ideas

6. Mathematics / A. Nature of Mathematics / 1. Mathematics

9935	Mathematical truth is always compromising between ordinary language and sensible epistemology [Benacerraf]

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis

17615

Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy]

6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory

17618

Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy]

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism

17927

Realists have semantics without epistemology, anti-realists epistemology but bad semantics [Benacerraf, by Colyvan]

9936	The platonist view of mathematics doesn't fit our epistemology very well [Benacerraf]

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism

17614

The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy]