Combining Philosophers

Ideas for Rescher,N/Oppenheim,P, Leon Horsten and Adolph Rami

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8 ideas

5. Theory of Logic / A. Overview of Logic / 6. Classical Logic

15326

Doubt is thrown on classical logic by the way it so easily produces the liar paradox [Horsten]

5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens

15341

Deduction Theorem: ψ only derivable from φ iff φ→ψ are axioms [Horsten]

5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic

15328

A theory is 'non-conservative' if it facilitates new mathematical proofs [Horsten]

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

15349

It is easier to imagine truth-value gaps (for the Liar, say) than for truth-value gluts (both T and F) [Horsten]

5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction

15366

Satisfaction is a primitive notion, and very liable to semantical paradoxes [Horsten]

5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms

10884

A theory is 'categorical' if it has just one model up to isomorphism [Horsten]

5. Theory of Logic / K. Features of Logics / 5. Incompleteness

15353

The first incompleteness theorem means that consistency does not entail soundness [Horsten]

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

15355

Strengthened Liar: 'this sentence is not true in any context' - in no context can this be evaluated [Horsten]