Combining Texts

All the ideas for 'Defending the Axioms', 'Critique of the Gotha Program' and 'The Language of Morals'

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14 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 / C. Structure of Existence / 5. Supervenience / c. Significance of supervenience
The goodness of a picture supervenes on the picture; duplicates must be equally good [Hare]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / i. Prescriptivism
In primary evaluative words like 'ought' prescription is constant but description can vary [Hare, by Hooker,B]
24. Political Theory / C. Ruling a State / 4. Changing the State / c. Revolution
In moving from capitalism to communism a revolutionary dictatorship of the proletariat is needed [Marx]
24. Political Theory / D. Ideologies / 9. Communism
People who only have their labour power are the slaves of those permitting them to work [Marx]
From each according to his ability, to each according to his need [Marx]
Freedom is making the state subordinate to its society [Marx]
25. Social Practice / A. Freedoms / 2. Freedom of belief
Bourgeois 'freedom of conscience' just tolerates all sorts of religious intolerance [Marx]