Combining Texts

All the ideas for 'General Draft', 'Defending the Axioms' and 'The Power of Words'

expand these ideas     |    start again     |     specify just one area for these texts


12 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
Philosophy is homesickness - the urge to be at home everywhere [Novalis]
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 / C. Capacities of Minds / 6. Idealisation
Desire for perfection is an illness, if it turns against what is imperfect [Novalis]
24. Political Theory / D. Ideologies / 3. Conservatism
National leaders want to preserve necessary order - but always the existing order [Weil]
24. Political Theory / D. Ideologies / 14. Nationalism
National prestige consists of behaving as if you could beat the others in a war [Weil]
25. Social Practice / E. Policies / 1. War / a. Just wars
Modern wars are fought in the name of empty words which are given capital letters [Weil]