more from David Bostock

Single Idea 13755

[catalogued under 5. Theory of Logic / H. Proof Systems / 4. Natural Deduction]

Full Idea

Many books take RAA (reductio) and DNE (double neg) as the natural deduction introduction- and elimination-rules for negation, but RAA is not a natural introduction rule. I prefer TND (tertium) and EFQ (ex falso) for ¬-introduction and -elimination.

Gist of Idea

Excluded middle is an introduction rule for negation, and ex falso quodlibet will eliminate it

Source

David Bostock (Intermediate Logic [1997], 6.2)

Book Reference

Bostock,David: 'Intermediate Logic' [OUP 1997], p.251


Related Ideas

Idea 13754 Natural deduction rules for → are the Deduction Theorem (→I) and Modus Ponens (→E) [Bostock]

Idea 9402 RAA: If assuming A will prove B∧¬B, then derive ¬A [Lemmon]

Idea 9396 DN: Given A, we may derive ¬¬A [Lemmon]

Idea 9024 Excluded middle has three different definitions [Quine]

Idea 13353 'Negation' says that Γ,¬φ|= iff Γ|=φ [Bostock]