Combining Texts

All the ideas for 'Propositions', 'First-order Logic, 2nd-order, Completeness' and 'Introduction to 'Modality''

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16 ideas

5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic

10751

Second-order logic needs the sets, and its consequence has epistemological problems [Rossberg]

10757

Henkin semantics has a second domain of predicates and relations (in upper case) [Rossberg]

10759

There are at least seven possible systems of semantics for second-order logic [Rossberg]

5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence

10753

Logical consequence is intuitively semantic, and captured by model theory [Rossberg]

5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-

10752

Γ |- S says S can be deduced from Γ; Γ |= S says a good model for Γ makes S true [Rossberg]

5. Theory of Logic / E. Structures of Logic / 1. Logical Form

10754

In proof-theory, logical form is shown by the logical constants [Rossberg]

5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive

9455	Maybe proper names have the content of fixing a thing's category [Bealer]

5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions

9454	The four leading theories of definite descriptions are Frege's, Russell's, Evans's, and Prior's [Bealer]

5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models

10756

A model is a domain, and an interpretation assigning objects, predicates, relations etc. [Rossberg]

5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms

10758

If models of a mathematical theory are all isomorphic, it is 'categorical', with essentially one model [Rossberg]

5. Theory of Logic / K. Features of Logics / 4. Completeness

10761

Completeness can always be achieved by cunning model-design [Rossberg]

5. Theory of Logic / K. Features of Logics / 5. Incompleteness

10755

A deductive system is only incomplete with respect to a formal semantics [Rossberg]

10. Modality / A. Necessity / 1. Types of Modality

14528

Maybe modal thought is unavoidable, as a priori recognition of necessary truth-preservation in reasoning [Hale/Hoffmann,A]

19. Language / D. Propositions / 1. Propositions

9453	Sentences saying the same with the same rigid designators may still express different propositions [Bealer]

9452	Propositions might be reduced to functions (worlds to truth values), or ordered sets of properties and relations [Bealer]

19. Language / D. Propositions / 2. Abstract Propositions / a. Propositions as sense

9451	Modal logic and brain science have reaffirmed traditional belief in propositions [Bealer]