Combining Texts

All the ideas for 'Vagaries of Definition', 'Contributions of Philosophy (On Appropriation)' and 'Defending the Axioms'

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11 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / b. Philosophy as transcendent
15586 When philosophy makes itself intelligible, it commits suicide [Heidegger]
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]
8203 All the arithmetical entities can be reduced to classes of integers, and hence to sets [Quine]
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]
19. Language / A. Nature of Meaning / 10. Denial of Meanings
8202 Meaning is essence divorced from things and wedded to words [Quine]
19. Language / E. Analyticity / 4. Analytic/Synthetic Critique
8201 The distinction between meaning and further information is as vague as the essence/accident distinction [Quine]