Combining Texts

Ideas for 'Logical Pluralism', 'Reply to Second Objections' and 'First-order Logic, 2nd-order, Completeness'

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19 ideas

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic

13235

Logic studies consequence; logical truths are consequences of everything, or nothing [Beall/Restall]

13238

Syllogisms are only logic when they use variables, and not concrete terms [Beall/Restall]

5. Theory of Logic / A. Overview of Logic / 2. History of Logic

13234

The view of logic as knowing a body of truths looks out-of-date [Beall/Restall]

5. Theory of Logic / A. Overview of Logic / 4. Pure Logic

13232

Logic studies arguments, not formal languages; this involves interpretations [Beall/Restall]

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 / A. Overview of Logic / 8. Logic of Mathematics

13241

The model theory of classical predicate logic is mathematics [Beall/Restall]

5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence

13253

There are several different consequence relations [Beall/Restall]

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 / B. Logical Consequence / 4. Semantic Consequence |=

13240

A sentence follows from others if they always model it [Beall/Restall]

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 / I. Semantics of Logic / 3. Logical Truth

13236

Logical truth is much more important if mathematics rests on it, as logicism claims [Beall/Restall]

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 / 6. Paradoxes in Language / d. The Preface paradox

13237

Preface Paradox affirms and denies the conjunction of propositions in the book [Beall/Restall]