Combining Texts

All the ideas for 'fragments/reports', 'fragments/reports' and 'Defending the Axioms'

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


13 ideas

2. Reason / B. Laws of Thought / 3. Non-Contradiction
Contradiction is impossible [Antisthenes (I), by Aristotle]
2. Reason / D. Definition / 13. Against Definition
Some fools think you cannot define anything, but only say what it is like [Antisthenes (I), by Aristotle]
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]
22. Metaethics / C. The Good / 3. Pleasure / f. Dangers of pleasure
I would rather go mad than experience pleasure [Antisthenes (I)]
23. Ethics / A. Egoism / 1. Ethical Egoism
The greatest good is not the achievement of desire, but to desire what is proper [Menedemus, by Diog. Laertius]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / d. Teaching virtue
Antisthenes said virtue is teachable and permanent, is life's goal, and is like universal wealth [Antisthenes (I), by Long]
28. God / C. Attitudes to God / 2. Pantheism
Antisthenes says there is only one god, which is nature [Antisthenes (I), by Cicero]