Combining Texts

All the ideas for 'Defending the Axioms', 'On Note L to Bayle's 'Rorarius'' and 'Utopia'

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15 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]
15. Nature of Minds / B. Features of Minds / 2. Unconscious Mind
The soul doesn't understand many of its own actions, if perceptions are confused and desires buried [Leibniz]
17. Mind and Body / A. Mind-Body Dualism / 5. Parallelism
We should say that body is mechanism and soul is immaterial, asserting their independence [Leibniz]
24. Political Theory / D. Ideologies / 3. Conservatism
All modern social systems seem to be conspiracies of the rich [More,T]
24. Political Theory / D. Ideologies / 5. Democracy / d. Representative democracy
If you try to get elected, you should be permanently barred from seeking office [More,T]
25. Social Practice / E. Policies / 1. War / a. Just wars
Only Utopians fail to see glory in warfare [More,T]
25. Social Practice / F. Life Issues / 2. Euthanasia
In Utopia, legal euthanasia is considered honourable [More,T]
26. Natural Theory / A. Speculations on Nature / 4. Mathematical Nature
Minds unconsciously count vibration beats in music, and enjoy it when they coincide [Leibniz]
28. God / C. Attitudes to God / 2. Pantheism
In Utopia, the Supreme Being is identical with Nature [More,T]