Single Idea 15341

[catalogued under 5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens]

Full Idea

The Deduction Theorem says ψ is derivable in classical predicate logic from ψ iff the sentence φ→ψ is a theorem of classical logic. Hence inferring φ to ψ is truth-preserving iff the axiom scheme φ→ψ is provable.

Gist of Idea

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

Source

Leon Horsten (The Tarskian Turn [2011], 02.2)

Book Reference

Horsten,Leon: 'The Tarskian Turn' [MIT 2011], p.18


A Reaction

Horsten offers this to show that the Tarski bi-conditionals can themselves be justified, and not just the rule of inference involved. Apparently you can only derive something if you first announce that you have the ability to derive it. Odd.