Combining Texts

All the ideas for 'Defending the Axioms', 'fragments/reports' and 'Essence and Potentiality'

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22 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]
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / a. Achilles paradox
1507 We don't have time for infinite quantity, but we do for infinite divisibility, because time is also divisible [Aristotle on Zeno of Elea]
5109 The fast runner must always reach the point from which the slower runner started [Zeno of Elea, by Aristotle]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / b. The Heap paradox ('Sorites')
1512 Zeno is wrong that one grain of millet makes a sound; why should one grain achieve what the whole bushel does? [Aristotle on Zeno of Elea]
5. Theory of Logic / L. Paradox / 7. Paradoxes of Time
1508 Zeno's arrow paradox depends on the assumption that time is composed of nows [Aristotle on Zeno of Elea]
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]
8. Modes of Existence / C. Powers and Dispositions / 4. Powers as Essence
17954 Essence is a thing's necessities, but what about its possibilities (which may not be realised)? [Vetter]
9. Objects / D. Essence of Objects / 4. Essence as Definition
17953 Real definition fits abstracta, but not individual concrete objects like Socrates [Vetter]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / a. Essence as necessary properties
17952 Modal accounts make essence less mysterious, by basing them on the clearer necessity [Vetter]
10. Modality / A. Necessity / 5. Metaphysical Necessity
17959 Metaphysical necessity is even more deeply empirical than Kripke has argued [Vetter]
10. Modality / B. Possibility / 1. Possibility
17955 Possible worlds allow us to talk about degrees of possibility [Vetter]
17957 Maybe possibility is constituted by potentiality [Vetter]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / c. Possible but inconceivable
17958 The apparently metaphysically possible may only be epistemically possible [Vetter]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
17956 Closeness of worlds should be determined by the intrinsic nature of relevant objects [Vetter]
26. Natural Theory / A. Speculations on Nature / 1. Nature
454 If there are many things they must have a finite number, but there must be endless things between them [Zeno of Elea]
27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement
455 That which moves, moves neither in the place in which it is, nor in that in which it is not [Zeno of Elea]
27. Natural Reality / C. Space / 5. Relational Space
1511 If everything is in a place, what is the place in? Place doesn't exist [Zeno of Elea, by Simplicius]