Combining Texts

All the ideas for 'Defending the Axioms', 'Wittgenstein's 'Tractatus Logico-Philosophicus'' and 'The Anti-Christ'

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20 ideas

1. Philosophy / B. History of Ideas / 2. Ancient Thought
2922 All intelligent Romans were Epicureans [Nietzsche]
3. Truth / A. Truth Problems / 3. Value of Truth
23520 Truth has had to be fought for, and normal life must be sacrificed to achieve it [Nietzsche]
2914 One must never ask whether truth is useful [Nietzsche]
4. Formal Logic / A. Syllogistic Logic / 1. Aristotelian Logic
23505 Aristotelian logic cannot express 'Everyone loves someone' [White,RM]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
17610 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
17620 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
17605 Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy]
17625 If two mathematical themes coincide, that suggest a single deep truth [Maddy]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
17615 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
17618 Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
17614 The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / b. Rational ethics
2921 Philosophy grasps the limits of human reason, and values are beyond it [Nietzsche]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / f. Übermensch
20138 Christianity is at war with the higher type of man, and excommunicates his basic instincts [Nietzsche]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / d. Virtue theory critique
20375 Virtues must be highly personal; if not, it is merely respect for a concept [Nietzsche]
23. Ethics / D. Deontological Ethics / 1. Deontology
2915 Each person should devise his own virtues and categorical imperative [Nietzsche]
28. God / A. Divine Nature / 4. Divine Contradictions
2920 A God who cures us of a head cold at the right moment is a total absurdity [Nietzsche]
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
2917 Christianity is a revolt of things crawling on the ground against elevated things [Nietzsche]
29. Religion / B. Monotheistic Religion / 5. Bible
2918 The story in Genesis is the story of God's fear of science [Nietzsche]
29. Religion / D. Religious Issues / 1. Religious Commitment / e. Fideism
2919 'Faith' means not wanting to know what is true [Nietzsche]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
2916 The great lie of immortality destroys rationality and natural instinct [Nietzsche]