Combining Texts

All the ideas for 'Defending the Axioms', 'Survival and Identity, with postscript' and 'The Statesman'

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


17 ideas

1. Philosophy / F. Analytic Philosophy / 2. Analysis by Division
Whenever you perceive a community of things, you should also hunt out differences in the group [Plato]
2. Reason / D. Definition / 2. Aims of Definition
To reveal a nature, divide down, and strip away what it has in common with other things [Plato]
No one wants to define 'weaving' just for the sake of weaving [Plato]
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 / A. Necessity / 4. De re / De dicto modality
De re modal predicates are ambiguous [Lewis, by Rudder Baker]
12. Knowledge Sources / A. A Priori Knowledge / 3. Innate Knowledge / b. Recollection doctrine
The soul gets its goodness from god, and its evil from previous existence. [Plato]
19. Language / F. Communication / 1. Rhetoric
The question of whether or not to persuade comes before the science of persuasion [Plato]
21. Aesthetics / A. Aesthetic Experience / 5. Natural Beauty
Non-physical beauty can only be shown clearly by speech [Plato]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / f. The Mean
The arts produce good and beautiful things by preserving the mean [Plato]
24. Political Theory / D. Ideologies / 5. Democracy / a. Nature of democracy
Democracy is the worst of good constitutions, but the best of bad constitutions [Plato, by Aristotle]
28. God / A. Divine Nature / 2. Divine Nature
Only divine things can always stay the same, and bodies are not like that [Plato]