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All the ideas for 'A Puzzle Concerning Matter and Form', 'A Mathematical Introduction to Logic (2nd)' and 'On Concept and Object'

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40 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 / F. Set Theory ST / 2. Mechanics of Set Theory / a. Symbols of ST
9703 'dom R' indicates the 'domain' of objects having a relation [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]
9710 We write F:A→B to indicate that A maps into B (the output of F on A is in B) [Enderton]
9707 'F(x)' is the unique value which F assumes for a value of x [Enderton]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
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]
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]
9702 A 'domain' of a relation is the set of members of ordered pairs in the relation [Enderton]
9701 A 'relation' is a set of ordered pairs [Enderton]
9706 A 'function' is a relation in which each object is related to just one other object [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]
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
9715 An 'equivalence relation' is a reflexive, symmetric and transitive binary relation [Enderton]
9716 We 'partition' a set into distinct subsets, according to each relation on its objects [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 / E. Structures of Logic / 1. Logical Form
4975 A thought can be split in many ways, so that different parts appear as subject or predicate [Frege]
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]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
9949 There is the concept, the object falling under it, and the extension (a set, which is also an object) [Frege, by George/Velleman]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
18995 Frege mistakenly takes existence to be a property of concepts, instead of being about things [Frege, by Yablo]
8. Modes of Existence / B. Properties / 10. Properties as Predicates
10317 It is unclear whether Frege included qualities among his abstract objects [Frege, by Hale]
8. Modes of Existence / C. Powers and Dispositions / 4. Powers as Essence
16755 The possible Aristotelian view that forms are real and active principles is clearly wrong [Fine,K, by Pasnau]
9. Objects / A. Existence of Objects / 3. Objects in Thought
10535 Frege's 'objects' are both the referents of proper names, and what predicates are true or false of [Frege, by Dummett]
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]
18. Thought / D. Concepts / 3. Ontology of Concepts / c. Fregean concepts
9839 Frege equated the concepts under which an object falls with its properties [Frege, by Dummett]
18. Thought / D. Concepts / 5. Concepts and Language / b. Concepts are linguistic
4973 As I understand it, a concept is the meaning of a grammatical predicate [Frege]
19. Language / A. Nature of Meaning / 2. Meaning as Mental
9167 Frege felt that meanings must be public, so they are abstractions rather than mental entities [Frege, by Putnam]
19. Language / D. Propositions / 2. Abstract Propositions / a. Propositions as sense
4974 For all the multiplicity of languages, mankind has a common stock of thoughts [Frege]