Combining Texts

All the ideas for 'Defending the Axioms', 'The Nature of Judgement' and 'On the Infinite'

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21 ideas

1. Philosophy / C. History of Philosophy / 5. Modern Philosophy / b. Modern philosophy beginnings
6405 Moore's 'The Nature of Judgement' (1898) marked the rejection (with Russell) of idealism [Moore,GE, by Grayling]
1. Philosophy / F. Analytic Philosophy / 1. Nature of Analysis
7527 Analysis for Moore and Russell is carving up the world, not investigating language [Moore,GE, by Monk]
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 / 1. Mathematics
12456 I aim to establish certainty for mathematical methods [Hilbert]
12461 We believe all mathematical problems are solvable [Hilbert]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
9633 No one shall drive us out of the paradise the Cantor has created for us [Hilbert]
12460 We extend finite statements with ideal ones, in order to preserve our logic [Hilbert]
12462 Only the finite can bring certainty to the infinite [Hilbert]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
12455 The idea of an infinite totality is an illusion [Hilbert]
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 / A. Nature of Mathematics / 5. The Infinite / j. Infinite divisibility
12457 There is no continuum in reality to realise the infinitely small [Hilbert]
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]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
12459 The subject matter of mathematics is immediate and clear concrete symbols [Hilbert]
6. Mathematics / C. Sources of Mathematics / 8. Finitism
18112 Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
9636 My theory aims at the certitude of mathematical methods [Hilbert]
19. Language / D. Propositions / 3. Concrete Propositions
22302 Moor bypassed problems of correspondence by saying true propositions ARE facts [Moore,GE, by Potter]
19. Language / D. Propositions / 5. Unity of Propositions
7526 Hegelians say propositions defy analysis, but Moore says they can be broken down [Moore,GE, by Monk]