Combining Texts

All the ideas for 'Defending the Axioms', 'Why Constitution is not Identity' and 'Abstract of 'The Fourfold Root''

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19 ideas

2. Reason / B. Laws of Thought / 2. Sufficient Reason
4187 'There is nothing without a reason why it should be rather than not be' (a generalisation of 'Why?') [Schopenhauer]
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]
9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
16078 Clay is intrinsically and atomically the same as statue (and that lacks 'modal properties') [Rudder Baker]
16077 The clay is not a statue - it borrows that property from the statue it constitutes [Rudder Baker]
9. Objects / B. Unity of Objects / 3. Unity Problems / d. Coincident objects
16080 Is it possible for two things that are identical to become two separate things? [Rudder Baker]
9. Objects / C. Structure of Objects / 6. Constitution of an Object
16076 Constitution is not identity, as consideration of essential predicates shows [Rudder Baker]
16081 The constitution view gives a unified account of the relation of persons/bodies, statues/bronze etc [Rudder Baker]
16082 Statues essentially have relational properties lacked by lumps [Rudder Baker]
10. Modality / C. Sources of Modality / 1. Sources of Necessity
4192 All necessity arises from causation, which is conditioned; there is no absolute or unconditioned necessity [Schopenhauer]
11. Knowledge Aims / A. Knowledge / 2. Understanding
4190 All understanding is an immediate apprehension of the causal relation [Schopenhauer]
16. Persons / C. Self-Awareness / 2. Knowing the Self
4191 What we know in ourselves is not a knower but a will [Schopenhauer]
16. Persons / D. Continuity of the Self / 3. Reference of 'I'
21368 The knot of the world is the use of 'I' to refer to both willing and knowing [Schopenhauer]
27. Natural Reality / D. Time / 1. Nature of Time / b. Relative time
4189 Time may be defined as the possibility of mutually exclusive conditions of the same thing [Schopenhauer]