Combining Texts

All the ideas for 'reports', 'First-order Logic, 2nd-order, Completeness' and 'Many, but almost one'

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15 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 / 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

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]

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]

25. Social Practice / D. Justice / 3. Punishment / c. Deterrence of crime

1743	The greatest deterrence for injustice is if uninjured parties feel as much indignation as those who are injured [Solon, by Diog. Laertius]