Combining Texts

All the ideas for 'Defending the Axioms', 'Letter to G.H. Schaller' and 'De Re and De Dicto'

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16 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 / F. Referring in Logic / 1. Naming / a. Names
14650 Maybe proper names involve essentialism [Plantinga]
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 / 3. Nature of Numbers / g. Real numbers
14648 Could I name all of the real numbers in one fell swoop? Call them all 'Charley'? [Plantinga]
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 / A. Existence of Objects / 5. Individuation / d. Individuation by haecceity
14647 Surely self-identity is essential to Socrates? [Plantinga]
9. Objects / D. Essence of Objects / 9. Essence and Properties
14646 An object has a property essentially if it couldn't conceivably have lacked it [Plantinga]
10. Modality / A. Necessity / 4. De re / De dicto modality
14649 Can we find an appropriate 'de dicto' paraphrase for any 'de re' proposition? [Plantinga]
14642 Expressing modality about a statement is 'de dicto'; expressing it of property-possession is 'de re' [Plantinga]
14643 'De dicto' true and 'de re' false is possible, and so is 'de dicto' false and 'de re' true [Plantinga]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
14651 What Socrates could have been, and could have become, are different? [Plantinga]
16. Persons / F. Free Will / 5. Against Free Will
4871 A thing is free if it acts only by the necessity of its own nature [Spinoza]