Combining Texts

All the ideas for 'Defending the Axioms', 'Predest.,God's foreknowledge and contingents' and 'Varieties of Causation'

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12 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]
7. Existence / E. Categories / 5. Category Anti-Realism
Our words and concepts don't always correspond to what is out there [William of Ockham]
9. Objects / D. Essence of Objects / 12. Essential Parts
Mereological essentialism says an entity must have exactly those parts [Sosa]
26. Natural Theory / C. Causation / 9. General Causation / b. Nomological causation
What law would explain causation in the case of causing a table to come into existence? [Sosa]
26. Natural Theory / C. Causation / 9. General Causation / d. Causal necessity
The necessitated is not always a result or consequence of the necessitator [Sosa]
Where is the necessary causation in the three people being tall making everybody tall? [Sosa]