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All the ideas for 'Many, but almost one', 'Intro to Naming,Necessity and Natural Kinds' and 'Introduction to the Theory of Logic'

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26 ideas

2. Reason / D. Definition / 1. Definitions
5831 The new view is that "water" is a name, and has no definition [Schwartz,SP]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
10888 Sets can be defined by 'enumeration', or by 'abstraction' (based on a property) [Zalabardo]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
10889 The 'Cartesian Product' of two sets relates them by pairing every element with every element [Zalabardo]
10890 A 'partial ordering' is reflexive, antisymmetric and transitive [Zalabardo]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
10886 Determinacy: an object is either in a set, or it isn't [Zalabardo]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / l. Axiom of Specification
10887 Specification: Determinate totals of objects always make a set [Zalabardo]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
10897 A first-order 'sentence' is a formula with no free variables [Zalabardo]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
10893 Γ |= φ for sentences if φ is true when all of Γ is true [Zalabardo]
10899 Γ |= φ if φ is true when all of Γ is true, for all structures and interpretations [Zalabardo]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / b. Basic connectives
10896 Propositional logic just needs ¬, and one of ∧, ∨ and → [Zalabardo]
5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
5829 We refer to Thales successfully by name, even if all descriptions of him are false [Schwartz,SP]
5830 The traditional theory of names says some of the descriptions must be correct [Schwartz,SP]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
10898 The semantics shows how truth values depend on instantiations of properties and relations [Zalabardo]
10902 We can do semantics by looking at given propositions, or by building new ones [Zalabardo]
5. Theory of Logic / I. Semantics of Logic / 2. Formal Truth
10892 We make a truth assignment to T and F, which may be true and false, but merely differ from one another [Zalabardo]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
10895 'Logically true' (|= φ) is true for every truth-assignment [Zalabardo]
10900 Logically true sentences are true in all structures [Zalabardo]
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
10901 Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true [Zalabardo]
10894 A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true [Zalabardo]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10903 A structure models a sentence if it is true in the model, and a set of sentences if they are all true in the model [Zalabardo]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
10891 If a set is defined by induction, then proof by induction can be applied to it [Zalabardo]
7. Existence / D. Theories of Reality / 10. Vagueness / d. Vagueness as linguistic
15538 Semantic indecision explains vagueness (if we have precisifications to be undecided about) [Lewis]
9. Objects / B. Unity of Objects / 3. Unity Problems / b. Cat and its tail
15537 If cats are vague, we deny that the many cats are one, or deny that the one cat is many [Lewis]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
15536 We have one cloud, but many possible boundaries and aggregates for it [Lewis]
18. Thought / C. Content / 8. Intension
5826 The intension of "lemon" is the conjunction of properties associated with it [Schwartz,SP]
19. Language / F. Communication / 6. Interpreting Language / c. Principle of charity
15539 Basic to pragmatics is taking a message in a way that makes sense of it [Lewis]