Combining Texts

All the ideas for 'Intensional Logic', 'Proper Names' and 'Elements of Set Theory'

expand these ideas     |    start again     |     specify just one area for these texts

20 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 / 2. Mechanics of Set Theory / b. Terminology of ST
13201 ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton]
13204 The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton]
13206 A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
13200 Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton]
13199 The empty set may look pointless, but many sets can be constructed from it [Enderton]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
13203 The singleton is defined using the pairing axiom (as {x,x}) [Enderton]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
13202 Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
13205 We can only define functions if Choice tells us which items are involved [Enderton]
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 / 1. Naming / b. Names as descriptive
7746 We don't normally think of names as having senses (e.g. we don't give definitions of them) [Searle]
7747 How can a proper name be correlated with its object if it hasn't got a sense? [Searle]
7748 'Aristotle' means more than just 'an object that was christened "Aristotle"' [Searle]
7749 Reference for proper names presupposes a set of uniquely referring descriptions [Searle]
7750 Proper names are logically connected with their characteristics, in a loose way [Searle]
5. Theory of Logic / F. Referring in Logic / 3. Property (λ-) Abstraction
11028 λ-abstraction disambiguates the scope of modal operators [Fitting]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
15377 Definite descriptions pick out different objects in different possible worlds [Fitting]