Combining Texts

All the ideas for 'Defending the Axioms', 'Universals and Particulars' and 'Preface to Great Instauration (Renewal)'

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11 ideas

1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy
6602 Philosophy is like a statue which is worshipped but never advances [Bacon]
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]
8. Modes of Existence / D. Universals / 6. Platonic Forms / c. Self-predication
4442 Most thinkers now reject self-predication (whiteness is NOT white) so there is no Third Man problem [Armstrong]
12. Knowledge Sources / B. Perception / 1. Perception
16724 The senses deceive, but also show their own errors [Bacon]
14. Science / A. Basis of Science / 3. Experiment
6603 Nature is revealed when we put it under pressure rather than observe it [Bacon]