Combining Texts

All the ideas for 'First-order Logic, 2nd-order, Completeness', 'Aristotle and Descartes on Matter' and 'Letters to Russell'

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14 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined

7085	The main problem of philosophy is what can and cannot be thought and expressed [Wittgenstein, by Grayling]

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]

7. Existence / C. Structure of Existence / 6. Fundamentals / d. Logical atoms

23463

Atomic facts correspond to true elementary propositions [Wittgenstein]

19. Language / D. Propositions / 4. Mental Propositions

23490

A thought is mental constituents that relate to reality as words do [Wittgenstein]

26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / b. Prime matter

19399

Prime matter is nothing when it is at rest [Leibniz]