Combining Texts

All the ideas for 'Counterpart theory and Quant. Modal Logic', 'A Mathematical Introduction to Logic (2nd)' and 'Modal Logic within Counterfactual Logic'

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43 ideas

4. Formal Logic / B. Propositional Logic PL / 3. Truth Tables
9724 Until the 1960s the only semantics was truth-tables [Enderton]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
14626 In S5 matters of possibility and necessity are non-contingent [Williamson]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / a. Symbols of ST
9707 'F(x)' is the unique value which F assumes for a value of x [Enderton]
9705 'fld R' indicates the 'field' of all objects in the relation [Enderton]
9704 'ran R' indicates the 'range' of objects being related to [Enderton]
9703 'dom R' indicates the 'domain' of objects having a relation [Enderton]
9710 We write F:A→B to indicate that A maps into B (the output of F on A is in B) [Enderton]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
9699 The 'powerset' of a set is all the subsets of a given set [Enderton]
9700 Two sets are 'disjoint' iff their intersection is empty [Enderton]
9712 A relation is 'symmetric' on a set if every ordered pair has the relation in both directions [Enderton]
9713 A relation is 'transitive' if it can be carried over from two ordered pairs to a third [Enderton]
9701 A 'relation' is a set of ordered pairs [Enderton]
9702 A 'domain' of a relation is the set of members of ordered pairs in the relation [Enderton]
9708 A function 'maps A into B' if the relating things are set A, and the things related to are all in B [Enderton]
9709 A function 'maps A onto B' if the relating things are set A, and the things related to are set B [Enderton]
9711 A relation is 'reflexive' on a set if every member bears the relation to itself [Enderton]
9706 A 'function' is a relation in which each object is related to just one other object [Enderton]
9714 A relation satisfies 'trichotomy' if all pairs are either relations, or contain identical objects [Enderton]
9717 A set is 'dominated' by another if a one-to-one function maps the first set into a subset of the second [Enderton]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / e. Equivalence classes
9716 We 'partition' a set into distinct subsets, according to each relation on its objects [Enderton]
9715 An 'equivalence relation' is a reflexive, symmetric and transitive binary relation [Enderton]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
9722 Inference not from content, but from the fact that it was said, is 'conversational implicature' [Enderton]
5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
9718 Validity is either semantic (what preserves truth), or proof-theoretic (following procedures) [Enderton]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
9721 A logical truth or tautology is a logical consequence of the empty set [Enderton]
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
9994 A truth assignment to the components of a wff 'satisfy' it if the wff is then True [Enderton]
5. Theory of Logic / K. Features of Logics / 3. Soundness
9719 A proof theory is 'sound' if its valid inferences entail semantic validity [Enderton]
5. Theory of Logic / K. Features of Logics / 4. Completeness
9720 A proof theory is 'complete' if semantically valid inferences entail proof-theoretic validity [Enderton]
5. Theory of Logic / K. Features of Logics / 6. Compactness
9995 Proof in finite subsets is sufficient for proof in an infinite set [Enderton]
5. Theory of Logic / K. Features of Logics / 7. Decidability
9996 Expressions are 'decidable' if inclusion in them (or not) can be proved [Enderton]
5. Theory of Logic / K. Features of Logics / 8. Enumerability
9997 For a reasonable language, the set of valid wff's can always be enumerated [Enderton]
9. Objects / D. Essence of Objects / 1. Essences of Objects
11976 Aristotelian essentialism says essences are not relative to specification [Lewis]
10. Modality / A. Necessity / 1. Types of Modality
14625 Necessity is counterfactually implied by its negation; possibility does not counterfactually imply its negation [Williamson]
10. Modality / A. Necessity / 7. Natural Necessity
11978 Causal necessities hold in all worlds compatible with the laws of nature [Lewis]
10. Modality / B. Possibility / 8. Conditionals / a. Conditionals
14623 Strict conditionals imply counterfactual conditionals: □(A⊃B)⊃(A□→B) [Williamson]
10. Modality / B. Possibility / 8. Conditionals / f. Pragmatics of conditionals
9723 Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton]
10. Modality / B. Possibility / 9. Counterfactuals
14624 Counterfactual conditionals transmit possibility: (A□→B)⊃(◊A⊃◊B) [Williamson]
10. Modality / C. Sources of Modality / 1. Sources of Necessity
14531 Rather than define counterfactuals using necessity, maybe necessity is a special case of counterfactuals [Williamson, by Hale/Hoffmann,A]
10. Modality / E. Possible worlds / 3. Transworld Objects / b. Rigid designation
11979 It doesn't take the whole of a possible Humphrey to win the election [Lewis]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
16994 Counterpart theory is bizarre, as no one cares what happens to a mere counterpart [Kripke on Lewis]
11974 Counterparts are not the original thing, but resemble it more than other things do [Lewis]
11975 If the closest resembler to you is in fact quite unlike you, then you have no counterpart [Lewis]
11977 Essential attributes are those shared with all the counterparts [Lewis]
15. Nature of Minds / C. Capacities of Minds / 2. Imagination
14628 Imagination is important, in evaluating possibility and necessity, via counterfactuals [Williamson]