Combining Texts

All the ideas for 'A Résumé of Metaphysics', 'The Logic of Decision' and 'First-order Logic, 2nd-order, Completeness'

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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]

10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / b. Worlds as fictions

16285

A possible world can be seen as a complete and consistent novel [Jeffrey]

14. Science / C. Induction / 6. Bayes's Theorem

19155

Instead of gambling, Jeffrey made the objects of Bayesian preference to be propositions [Jeffrey, by Davidson]

22. Metaethics / C. The Good / 3. Pleasure / a. Nature of pleasure

5049	Intelligent pleasure is the perception of beauty, order and perfection [Leibniz]

28. God / A. Divine Nature / 3. Divine Perfections

5048	Perfection is simply quantity of reality [Leibniz]

29. Religion / D. Religious Issues / 3. Problem of Evil / b. Human Evil

5050	Evil serves a greater good, and pain is necessary for higher pleasure [Leibniz]