QUOD LIBET DEFINITION LICENSE

QUOD LIBET DEFINITION LICENSE

Such a license isnotspecific to any logical constants, but amounts to ablanket policy. It simply isthe structural rule that tells us that any sentence whatsoever follows from a con-tradiction. Its roleis best accounted for by according it the status of astructural rule. But on the view I am proposingno such constant is needed becauseEFQis not an operational rule at all. Of course this means thatEFQis left withouta logical constant which it serves to eliminate. 'I submit that these difficulties can be overcome simply by treating⊥as a punc-tuation marker, as Tennant suggests. In particular, he says that Ex Falso is unacceptable for the reason that it asserts something about the consequences of something impossible (van Heijenoort 1967: 421).' Kolmogorov said that, just like PEM, Ex Falso “has no intuitive foundation” (van Heijenoort 1967: 419). 461).Īccording to here: 'Kolmogorov’s criterion whether to keep an axiom was whether a proposition has an “intuitive foundation” or “possesses intuitive obviousness” (van Heijenoort 1967: 421, 422). I contend that both of these approaches are mistaken.' ref.Įx Falso has an ‘anomalous position inside the scheme of introduction/elimination rules’, tarnishing the neat symmetry of the intuitionistic system' (Weir 1986, p. Others, including Dummett, present ⊥ as an elimination rule for ¬ (e.g. EFQ is then understood as the elimination rule for ⊥. 38), one ‘for which there is no canonical proof’ (Prawitz1977, p. He treats ⊥ as a ‘0-place sentential operation’ (Prawitz 1978, p. Gentzen groups the ex falso rule alongside the other operational rules(1969, p. ' There is surprisingly little agreement about the exact status of EFQ in the literature. This does not exclude that I would like axioms and rules to be intuitively acceptable (to me). But also see the references to intuitionism in the answers.Įdit: as pointed out below, it may have been a distraction for me to raise 'intuitionism' in the original question, although Ex Falso arises in classical and intuitionistic logic. The closest justification I see, based on the current answers, is that Ex Falso encodes a (metalogical) desire that the proof system be consistent.

Is the principle of explosion really basic/intuitive and why? But my only intuition for ex falso quodlibet in natural deduction is not immediate but comes from its proof, which rests on disjunctive syllogism (which apparently holds in classical propositional logic and intuitionistic logic). My understanding of inference rules is that they should be intuitively acceptable (like axioms).

Quod libet definition