Combining Texts

All the ideas for 'Actualism and Possible Worlds', 'Letters to Frege' and 'Defending the Axioms'

expand these ideas     |    start again     |     specify just one area for these texts

18 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 / 5. Paradoxes in Set Theory / d. Russell's paradox
13365 Russell's Paradox is a stripped-down version of Cantor's Paradox [Priest,G on Russell]
10711 Russell's paradox means we cannot assume that every property is collectivizing [Potter on Russell]
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 / a. Nature of Being
14664 Necessary beings (numbers, properties, sets, propositions, states of affairs, God) exist in all possible worlds [Plantinga]
8. Modes of Existence / B. Properties / 11. Properties as Sets
9127 Russell refuted Frege's principle that there is a set for each property [Russell, by Sorensen]
9. Objects / D. Essence of Objects / 1. Essences of Objects
14666 Socrates is a contingent being, but his essence is not; without Socrates, his essence is unexemplified [Plantinga]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
14662 Possible worlds clarify possibility, propositions, properties, sets, counterfacts, time, determinism etc. [Plantinga]
10. Modality / E. Possible worlds / 1. Possible Worlds / d. Possible worlds actualism
16472 Plantinga's actualism is nominal, because he fills actuality with possibilia [Stalnaker on Plantinga]
18. Thought / C. Content / 6. Broad Content
7531 We don't assert private thoughts; the objects are part of what we assert [Russell]
19. Language / C. Assigning Meanings / 8. Possible Worlds Semantics
16469 Plantinga has domains of sets of essences, variables denoting essences, and predicates as functions [Plantinga, by Stalnaker]
16470 Plantinga's essences have their own properties - so will have essences, giving a hierarchy [Stalnaker on Plantinga]
19. Language / D. Propositions / 1. Propositions
14663 Are propositions and states of affairs two separate things, or only one? I incline to say one [Plantinga]