Combining Texts

All the ideas for 'Exigency to Exist in Essences', 'Believing the Axioms I' and 'Reference and Definite Descriptions'

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22 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
13011 New axioms are being sought, to determine the size of the continuum [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
13014 Extensional sets are clearer, simpler, unique and expressive [Maddy]
13013 The Axiom of Extensionality seems to be analytic [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
13021 The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy]
13022 Infinite sets are essential for giving an account of the real numbers [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
13023 The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
13024 Efforts to prove the Axiom of Choice have failed [Maddy]
13025 Modern views say the Choice set exists, even if it can't be constructed [Maddy]
13026 A large array of theorems depend on the Axiom of Choice [Maddy]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
13019 The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
13018 Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / a. Descriptions
7760 Russell only uses descriptions attributively, and Strawson only referentially [Donnellan, by Lycan]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
5811 A definite description can have a non-referential use [Donnellan]
5812 Definite descriptions are 'attributive' if they say something about x, and 'referential' if they pick x out [Donnellan]
5814 'The x is F' only presumes that x exists; it does not actually entail the existence [Donnellan]
7. Existence / A. Nature of Existence / 5. Reason for Existence
19400 Possibles demand existence, so as many of them as possible must actually exist [Leibniz]
19401 God's sufficient reason for choosing reality is in the fitness or perfection of possibilities [Leibniz]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
19402 The actual universe is the richest composite of what is possible [Leibniz]
19. Language / B. Reference / 4. Descriptive Reference / b. Reference by description
10435 A definite description 'the F' is referential if the speaker could thereby be referring to something not-F [Donnellan, by Sainsbury]
10451 Donnellan is unclear whether the referential-attributive distinction is semantic or pragmatic [Bach on Donnellan]
5813 A description can successfully refer, even if its application to the subject is not believed [Donnellan]
19. Language / B. Reference / 5. Speaker's Reference
5815 Whether a definite description is referential or attributive depends on the speaker's intention [Donnellan]