Combining Philosophers

All the ideas for Oliver,A/Smiley,T, Rayo,A/Uzquiasno,G and John Etchemendy

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20 ideas

3. Truth / F. Semantic Truth / 1. Tarski's Truth / c. Meta-language for truth
19323 'Snow is white' depends on meaning; whether snow is white depends on snow [Etchemendy]
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
19137 We can get a substantive account of Tarski's truth by adding primitive 'true' to the object language [Etchemendy]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
13451 The two best understood conceptions of set are the Iterative and the Limitation of Size [Rayo/Uzquiano]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
14240 The empty set is something, not nothing! [Oliver/Smiley]
14239 The empty set is usually derived from Separation, but it also seems to need Infinity [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]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / m. Axiom of Separation
13452 Some set theories give up Separation in exchange for a universal set [Rayo/Uzquiano]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
14180 Etchemendy says fix the situation and vary the interpretation, or fix interpretations with varying situations [Etchemendy, by Read]
14181 Validity is where either the situation or the interpretation blocks true premises and false conclusion [Etchemendy, by Read]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
13449 We could have unrestricted quantification without having an all-inclusive domain [Rayo/Uzquiano]
13450 Absolute generality is impossible, if there are indefinitely extensible concepts like sets and ordinals [Rayo/Uzquiano]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
13453 Perhaps second-order quantifications cover concepts of objects, rather than plain objects [Rayo/Uzquiano]
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]
19. Language / F. Communication / 5. Pragmatics / a. Contextual meaning
13448 The domain of an assertion is restricted by context, either semantically or pragmatically [Rayo/Uzquiano]