Combining Texts

All the ideas for '', 'What are Sets and What are they For?' and 'Significance of the Kripkean Nec A Posteriori'

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20 ideas

1. Philosophy / C. History of Philosophy / 5. Modern Philosophy / c. Modern philosophy mid-period
13966 Analytic philosophy loved the necessary a priori analytic, linguistic modality, and rigour [Soames]
1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis
13974 If philosophy is analysis of meaning, available to all competent speakers, what's left for philosophers? [Soames]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
14239 The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley]
14240 The empty set is something, not nothing! [Oliver/Smiley]
14241 We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley]
14242 Maybe we can treat the empty set symbol as just meaning an empty term [Oliver/Smiley]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
14243 The unit set may be needed to express intersections that leave a single member [Oliver/Smiley]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
11211 If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
11210 Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt]
11212 The sense of a connective comes from primitively obvious rules of inference [Rumfitt]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
14234 If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley]
14237 We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
14245 Logical truths are true no matter what exists - but predicate calculus insists that something exists [Oliver/Smiley]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
14246 If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
14247 Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / a. Essence as necessary properties
13969 Kripkean essential properties and relations are necessary, in all genuinely possible worlds [Soames]
10. Modality / C. Sources of Modality / 3. Necessity by Convention
13973 A key achievement of Kripke is showing that important modalities are not linguistic in source [Soames]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
13968 Kripkean possible worlds are abstract maximal states in which the real world could have been [Soames]
19. Language / C. Assigning Meanings / 10. Two-Dimensional Semantics
13972 Two-dimensionalism reinstates descriptivism, and reconnects necessity and apriority to analyticity [Soames]
19. Language / F. Communication / 3. Denial
11214 We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt]