Combining Philosophers

All the ideas for Isaiah, Marcus Rossberg and Stanislaw Lesniewski

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14 ideas

1. Philosophy / D. Nature of Philosophy / 2. Invocation to Philosophy

7493	Let us reason together, saith the Lord [Isaiah]

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 / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects

8249	Class membership is not transitive, unlike being part of a part of the whole [Lesniewski, by George/Van Evra]

27. Natural Reality / E. Cosmology / 1. Cosmology

7608	The world is established, and cannot be moved [Isaiah]

28. God / A. Divine Nature / 1. God

7343	Beside me there is no God [Isaiah]