0616631 - FLÚ 2025 RIV SE eng J - Journal Article
Pezlar, Ivo
Absurdity as the impossible command in natural deduction.
Theoria-A Swedish Journal of Philosophy. Roč. 91, č. 1 (2025), s. 25-44. ISSN 0040-5825. E-ISSN 1755-2567
Grant - others:AV ČR(CZ) LQ300092101
Program: Prémie Lumina quaeruntur
Institutional support: RVO:67985955
Keywords : absurdity * falsity * natural deduction * proof theory * speech acts
OECD category: Philosophy, History and Philosophy of science and technology
Method of publishing: Limited access
Result website:
https://doi.org/10.1111/theo.12567DOI: https://doi.org/10.1111/theo.12567

In this paper, we propose a new approach to absurdity in the context of natural deduction for intuitionistic and classical logic. It combines the aspects of both the logical approach, which treats absurdity as a propositional constant, and the structural approach, which treats absurdity as a structural punctuation mark signalling the dead end of derivations. In particular, we will treat absurdity as an impossible command, that is, a speech act composed of an imperative force indicator, and the false propositional constant, that is, a proposition that cannot be true by definition. In return, we obtain a framework that constitutes a middle ground between the logical and structural approaches. For example, it allows us to consider the ex falso quodlibet rule as a kind of structural rule, specifically, a semi-structural rule, and at the same time also maintain that negation can be reduced to implication of absurdity, specifically, to its propositional content.
Permanent Link: https://hdl.handle.net/11104/0363664