Combining Texts

All the ideas for 'Defending the Axioms', 'Shame and Necessity' and 'Of Human Freedom'

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20 ideas

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]
7. Existence / A. Nature of Existence / 3. Being / c. Becoming
22076 Being is only perceptible to itself as becoming [Schelling]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
22074 We must show that the whole of nature, because it is effective, is grounded in freedom [Schelling]
16. Persons / F. Free Will / 2. Sources of Free Will
22075 Only idealism has given us the genuine concept of freedom [Schelling]
16. Persons / F. Free Will / 5. Against Free Will
2176 There is only a problem of free will if you think the notion of 'voluntary' can be metaphysically deepened [Williams,B]
2181 It is an absurd Kantian idea that at the limit rationality and freedom coincide [Williams,B]
20. Action / B. Preliminaries of Action / 2. Willed Action / d. Weakness of will
4317 We judge weakness of will by an assessment after the event is concluded [Williams,B, by Cottingham]
20. Action / C. Motives for Action / 4. Responsibility for Actions
2174 Responsibility involves cause, intention, state of mind, and response after the event [Williams,B]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / g. Moral responsibility
2178 In bad actions, guilt points towards victims, and shame to the agent [Williams,B]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / a. Nature of virtue
2169 Greek moral progress came when 'virtue' was freed from social status [Williams,B]
23. Ethics / D. Deontological Ethics / 2. Duty
2172 The modern idea of duty is unknown in archaic Greece [Williams,B]
23. Ethics / D. Deontological Ethics / 6. Motivation for Duty
2179 If the moral self is seen as characterless, then other people have a very limited role in our moral lives [Williams,B]
2180 If reason cannot lead people to good, we must hope they have an internal voice [Williams,B]
29. Religion / D. Religious Issues / 3. Problem of Evil / a. Problem of Evil
2175 There is a problem of evil only if you expect the world to be good [Williams,B]