Combining Philosophers

Ideas for Stilpo, Vann McGee and John Mayberry

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15 ideas

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

17786

The mainstream of modern logic sees it as a branch of mathematics [Mayberry]

5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic

17788

First-order logic only has its main theorems because it is so weak [Mayberry]

5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic

17791

Only second-order logic can capture mathematical structure up to isomorphism [Mayberry]

5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence

18755

Validity is explained as truth in all models, because that relies on the logical terms [McGee]

5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives

18751

Natural language includes connectives like 'because' which are not truth-functional [McGee]

5. Theory of Logic / G. Quantification / 2. Domain of Quantification

17787

Big logic has one fixed domain, but standard logic has a domain for each interpretation [Mayberry]

5. Theory of Logic / G. Quantification / 5. Second-Order Quantification

18761

Second-order variables need to range over more than collections of first-order objects [McGee]

5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic

18753

An ontologically secure semantics for predicate calculus relies on sets [McGee]

5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth

18754

Logically valid sentences are analytic truths which are just true because of their logical words [McGee]

5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems

17790

No Löwenheim-Skolem logic can axiomatise real analysis [Mayberry]

5. Theory of Logic / K. Features of Logics / 1. Axiomatisation

17779

'Classificatory' axioms aim at revealing similarity in morphology of structures [Mayberry]

17778

Axiomatiation relies on isomorphic structures being essentially the same [Mayberry]

17780

'Eliminatory' axioms get rid of traditional ideal and abstract objects [Mayberry]

5. Theory of Logic / K. Features of Logics / 3. Soundness

18757

Soundness theorems are uninformative, because they rely on soundness in their proofs [McGee]

5. Theory of Logic / K. Features of Logics / 6. Compactness

17789

No logic which can axiomatise arithmetic can be compact or complete [Mayberry]