Combining Texts

All the ideas for 'Freedom to Act', 'What Mary Didn't Know' and 'Defending the Axioms'

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11 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy]
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy]
If two mathematical themes coincide, that suggest a single deep truth [Maddy]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
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
Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy]
15. Nature of Minds / B. Features of Minds / 5. Qualia / a. Nature of qualia
I say Mary does not have new knowledge, but knows an old fact in a new way [Perry on Jackson]
Is it unfair that physicalist knowledge can be written down, but dualist knowledge can't be [Perry on Jackson]
Mary knows all the physical facts of seeing red, but experiencing it is new knowledge [Jackson]
20. Action / C. Motives for Action / 3. Acting on Reason / c. Reasons as causes
Deviant causal chain: a reason causes an action, but isn't the reason for which it was performed [Davidson, by Neta]