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All the ideas for 'Russell's Mathematical Logic', 'Introduction to 'Language Truth and Logic'' and 'Actualism and Possible Worlds'

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23 ideas

2. Reason / D. Definition / 8. Impredicative Definition
10041 Impredicative Definitions refer to the totality to which the object itself belongs [Gödel]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
21716 In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B]
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
10035 Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
10042 Reference to a totality need not refer to a conjunction of all its elements [Gödel]
5. Theory of Logic / K. Features of Logics / 8. Enumerability
10038 A logical system needs a syntactical survey of all possible expressions [Gödel]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
10046 The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
10039 Some arithmetical problems require assumptions which transcend arithmetic [Gödel]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
10043 Mathematical objects are as essential as physical objects are for perception [Gödel]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
10045 Impredicative definitions are admitted into ordinary mathematics [Gödel]
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]
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]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / c. Empirical foundations
5163 Basic propositions refer to a single experience, are incorrigible, and conclusively verifiable [Ayer]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / c. Knowing other minds
5167 The argument from analogy fails, so the best account of other minds is behaviouristic [Ayer]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
5164 A statement is meaningful if observation statements can be deduced from it [Ayer]
5165 Directly verifiable statements must entail at least one new observation statement [Ayer]
5166 The principle of verification is not an empirical hypothesis, but a definition [Ayer]
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
5162 Sentences only express propositions if they are meaningful; otherwise they are 'statements' [Ayer]
14663 Are propositions and states of affairs two separate things, or only one? I incline to say one [Plantinga]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / i. Prescriptivism
5168 Moral approval and disapproval concerns classes of actions, rather than particular actions [Ayer]