Combining Philosophers

All the ideas for H.Putnam/P.Oppenheim, Douglas Edwards and Marcus Rossberg

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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]

8. Modes of Existence / B. Properties / 2. Need for Properties

18430

We accept properties because of type/tokens, reference, and quantification [Edwards]

8. Modes of Existence / B. Properties / 10. Properties as Predicates

18432

Quineans say that predication is primitive and inexplicable [Edwards]

8. Modes of Existence / E. Nominalism / 2. Resemblance Nominalism

18437

Resemblance nominalism requires a second entity to explain 'the rose is crimson' [Edwards]

9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts

18434

That a whole is prior to its parts ('priority monism') is a view gaining in support [Edwards]

14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction

20653

Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson]