Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'Elements of Set Theory' and 'Intro to 'Philosophy of Logic''

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15 ideas

4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / a. Systems of modal logic
Modal logic is multiple systems, shown in the variety of accessibility relations between worlds [Jacquette]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton]
The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton]
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
Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton]
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
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
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
We can only define functions if Choice tells us which items are involved [Enderton]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
The two main views in philosophy of logic are extensionalism and intensionalism [Jacquette]
5. Theory of Logic / I. Semantics of Logic / 5. Extensionalism
Extensionalists say that quantifiers presuppose the existence of their objects [Jacquette]
5. Theory of Logic / I. Semantics of Logic / 6. Intensionalism
Intensionalists say meaning is determined by the possession of properties [Jacquette]
19. Language / C. Assigning Meanings / 7. Extensional Semantics
Extensionalist semantics forbids reference to nonexistent objects [Jacquette]
Extensionalist semantics is circular, as we must know the extension before assessing 'Fa' [Jacquette]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]