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All the ideas for 'Intensional Logic', 'What are Sets and What are they For?' and 'Goodbye Growing Block'

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19 ideas

4. Formal Logic / E. Nonclassical Logics / 8. Intensional Logic
15375 If terms change their designations in different states, they are functions from states to objects [Fitting]
15376 Intensional logic adds a second type of quantification, over intensional objects, or individual concepts [Fitting]
4. Formal Logic / E. Nonclassical Logics / 9. Awareness Logic
15378 Awareness logic adds the restriction of an awareness function to epistemic logic [Fitting]
4. Formal Logic / E. Nonclassical Logics / 10. Justification Logics
15379 Justication logics make explicit the reasons for mathematical truth in proofs [Fitting]
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 / 8. Logic of Mathematics
11026 Classical logic is deliberately extensional, in order to model mathematics [Fitting]
5. Theory of Logic / F. Referring in Logic / 3. Property (λ-) Abstraction
11028 λ-abstraction disambiguates the scope of modal operators [Fitting]
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]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
15377 Definite descriptions pick out different objects in different possible worlds [Fitting]
27. Natural Reality / D. Time / 1. Nature of Time / f. Eternalism
17960 Eternalism says all times are equally real, and future and past objects and properties are real [Merricks]
27. Natural Reality / D. Time / 1. Nature of Time / g. Growing block
17961 Growing block has a subjective present and a growing edge - but these could come apart [Merricks, by PG]