What Absurdity Is Not in Natural Deduction: Structural Approach and the Empty Set.
In this paper, I argue that on a structural view of absurdity within natural deduction frameworks for both classical and intuitionistic logic, absurdity cannot be identified with the empty set; that is, with something that contains nothing. Instead, absurdity should be seen as representing nothing;...
| Publicado en: | Topoi: An International Review of Philosophy Vol. 45; no. 2; pp. 627 - 642 |
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| Formato: | Artículo |
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Springer Nature
May2026
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| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=194359003&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 194359003 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 01677411 NM2 jtl: Topoi: An International Review of Philosophy issn: 01677411 maglogo: N pubinfo: dt: May2026 vid: 45 iid: 2 pid: 237 pub: Springer Nature artinfo: ui: 194359003 10.1007/s11245-025-10205-4 ppf: 627 ppct: 15 formats: fmt: – @attributes: type: T – @attributes: type: P size: 420KB tig: atl: What Absurdity Is Not in Natural Deduction: Structural Approach and the Empty Set. aug: au: Pezlar, Ivo affil: https://ror.org/053avzc18 Institute of Philosophy, Czech Academy of Sciences, Jilska 1, 110 00, Prague, Czech Republic su: Contradiction Proposition (Logic) Nonclassical mathematical logic Intuitionistic mathematics Mathematical logic Logic sug: subj: Contradiction Proposition (Logic) Nonclassical mathematical logic Intuitionistic mathematics Mathematical logic Logic keyword: Absurdity Ex falso quodlibet Falsity Natural deduction Proof-theoretic semantics ab: In this paper, I argue that on a structural view of absurdity within natural deduction frameworks for both classical and intuitionistic logic, absurdity cannot be identified with the empty set; that is, with something that contains nothing. Instead, absurdity should be seen as representing nothing; that is, as the empty space below the inference line, as Neil Tennant originally suggested. However, diverging from Tennant's view that absurdity should be purely a structural notion, I consider an approach that incorporates both structural and logical features. Specifically, this version of absurdity cannot be embedded into other propositions (just like absurdity in the structural approach) yet it is not merely a punctuation mark in the metalanguage but a proper part of the object language of the logic (just like absurdity in the logical approach). This will allow us to show that accepting the structural approach does not require adopting inferences with no conclusion, as was previously thought. Formally, I treat absurdity as a limit case of a signed proposition and, informally, it may be interpreted as a degenerate form of denial that lacks any propositional content. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Topoi: An International Review of Philosophy is a copyright of Springer, 2026. All Rights Reserved. item: Topoi: An International Review of Philosophy holder: Springer Nature dt: @attributes: year: 2026 holdings: @attributes: islocal: N |
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