Combining Texts

All the ideas for 'Defending the Axioms', 'On Freedom' and 'Upon Nothing: Swansea lecture'

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16 ideas

1. Philosophy / H. Continental Philosophy / 1. Continental Philosophy
Two marxist ideas have dominated in France: base and superstructure, and ideology [Scruton]
1. Philosophy / H. Continental Philosophy / 6. Deconstruction
On the surface of deconstructive writing, technicalities float and then drift away [Scruton]
Deconstruction is the last spasm of romanticism, now become hopeless and destructive [Scruton]
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]
10. Modality / B. Possibility / 5. Contingency
Necessary truths can be analysed into original truths; contingent truths are infinitely analysable [Leibniz]
10. Modality / D. Knowledge of Modality / 2. A Priori Contingent
Only God sees contingent truths a priori [Leibniz]
10. Modality / E. Possible worlds / 3. Transworld Objects / e. Possible Objects
If non-existents are possible, their existence would replace what now exists, which cannot therefore be necessary [Leibniz]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract
The benefits of social freedom outweigh the loneliness, doubt and alienation it brings [Scruton]
24. Political Theory / D. Ideologies / 3. Conservatism
So-called 'liberation' is the enemy of freedom, destroying the very structures that are needed [Scruton]
28. God / A. Divine Nature / 3. Divine Perfections
God does everything in a perfect way, and never acts contrary to reason [Leibniz]