Combining Texts

All the ideas for 'Defending the Axioms', 'Completeness of Axioms of Logic' and 'Introduction to 'Evidentialism''

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10 ideas

4. Formal Logic / C. Predicate Calculus PC / 3. Completeness of PC
17751 Gödel proved the completeness of first order predicate logic in 1930 [Gödel, by Walicki]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
17610 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
17620 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
17605 Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy]
17625 If two mathematical themes coincide, that suggest a single deep truth [Maddy]
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 / 4. Mathematical Empiricism / c. Against mathematical empiricism
17614 The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy]
13. Knowledge Criteria / B. Internal Justification / 3. Evidentialism / b. Evidentialism
19518 Evidentialism says justifications supervene on the available evidence [Conee/Feldman]
20. Action / C. Motives for Action / 3. Acting on Reason / c. Reasons as causes
19519 Rational decisions are either taken to be based on evidence, or to be explained causally [Conee/Feldman]