Combining Texts

All the ideas for 'On the Elements of Being: I', 'First-order Logic, 2nd-order, Completeness' and 'Vagueness'

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16 ideas

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

10757

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

10751

Second-order logic needs the sets, and its consequence has epistemological problems [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 / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives

21597

Logical connectives have the highest precision, yet are infected by the vagueness of true and false [Russell, by Williamson]

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]

7. Existence / D. Theories of Reality / 10. Vagueness / d. Vagueness as linguistic

9051	Since natural language is not precise it cannot be in the province of logic [Russell, by Keefe/Smith]

9054	Vagueness is only a characteristic of representations, such as language [Russell]

8. Modes of Existence / B. Properties / 13. Tropes / a. Nature of tropes

8508	A 'trope' is an abstract particular, the occurrence of an essence [Williams,DC]

8509	A world is completely constituted by its tropes and their connections [Williams,DC]

8510	'Socrates is wise' means a concurrence sum contains a member of a similarity set [Williams,DC]