Combining Texts

All the ideas for 'Defending the Axioms', 'Introductions to Utilitarianism and its Critics' and 'Why Constitution is not Identity'

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19 ideas

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]
9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
Clay is intrinsically and atomically the same as statue (and that lacks 'modal properties') [Rudder Baker]
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
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
Statues essentially have relational properties lacked by lumps [Rudder Baker]
Constitution is not identity, as consideration of essential predicates shows [Rudder Baker]
The constitution view gives a unified account of the relation of persons/bodies, statues/bronze etc [Rudder Baker]
22. Metaethics / C. The Good / 1. Goodness / g. Consequentialism
You can't separate acts from the people performing them [Glover]
22. Metaethics / C. The Good / 1. Goodness / h. Good as benefit
Aggression in defence may be beneficial but morally corrupting [Glover]
23. Ethics / D. Deontological Ethics / 1. Deontology
Duty prohibits some acts, whatever their consequences [Glover]
23. Ethics / E. Utilitarianism / 1. Utilitarianism
Satisfaction of desires is not at all the same as achieving happiness [Glover, by PG]
23. Ethics / E. Utilitarianism / 5. Rule Utilitarianism
Rule-utilitarianism is either act-utilitarianism, or not really utilitarian [Glover]
24. Political Theory / A. Basis of a State / 2. Population / a. Human population
How can utilitarianism decide the ideal population size? [Glover]