Combining Texts

All the ideas for 'Leibniz', 'On the Source of Necessity' and 'First-order Logic, 2nd-order, Completeness'

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14 ideas

4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / g. System S4

15102

S4 says there must be some necessary truths (the actual ones, of which there is at least one) [Cameron]

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]

9. Objects / F. Identity among Objects / 7. Indiscernible Objects

7566	The Identity of Indiscernibles is really the same as the verification principle [Jolley]

10. Modality / C. Sources of Modality / 1. Sources of Necessity

15103

Blackburn fails to show that the necessary cannot be grounded in the contingent [Cameron]

27. Natural Reality / D. Time / 1. Nature of Time / f. Eternalism

15104

The 'moving spotlight' theory makes one time privileged, while all times are on a par ontologically [Cameron]