Combining Philosophers

All the ideas for Eubulides, Goodman,N/Quine,W and Marcus Rossberg

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14 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 / 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]

5. Theory of Logic / L. Paradox / 1. Paradox

6007	If you know your father, but don't recognise your father veiled, you know and don't know the same person [Eubulides, by Dancy,R]

5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox

6006	If you say truly that you are lying, you are lying [Eubulides, by Dancy,R]

5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / b. The Heap paradox ('Sorites')

6008	Removing one grain doesn't destroy a heap, so a heap can't be destroyed [Eubulides, by Dancy,R]

8. Modes of Existence / E. Nominalism / 1. Nominalism / c. Nominalism about abstracta

17619

We renounce all abstract entities [Goodman/Quine]