Situations in which disjunctive syllogism can lead from true premises to a false conclusion
type: Item
instance of: scholarly article
title: Situations in which disjunctive syllogism can lead from true premises to a false conclusion
zbMATH Open document ID: 0910.03003
author: S. V. Bhave
published in: Notre Dame Journal of Formal Logic
publication date: 1998-11-08T00:00:00Z
review text: Relevance logicians have attacked the validity of disjunctive syllogism \((p\vee q, \sim p, \therefore q)\) where the disjunction is merely extensional (i.e. does not support \(\ulcorner\) If it were the case that \(p\), then it would be the case that \(q\urcorner\)). Geach, in his review (Philosophy 52, 495 (1977)) of \textit{A. R. Anderson} and \textit{N. D. Belnap}, Entailment. The logic of relevance and necessity, Vol. 1 (1975; Zbl 0323.02030), pointed out that counterexamples to extensional disjunctive syllogism were not forthcoming. Considering (1) \(\ulcorner p\) is most probably false\(\urcorner\), the author argues that (2) \(\ulcorner p\) is not most probably false\(\urcorner\) is the negation of (1) but not the contradictory of (1), because ``not most probably false'' means the disjunction of all possible truth values of \(p\) with the exception of ``most probably false''. If ``There will be a naval battle tomorrow'' is either most probable, or probable to some degree (other than 0 or 1), then we can use this fact to construct a disjunctive syllogism of the form \(\ulcorner\)(2), (1) or \(q\), so \(q\urcorner\) where \(\ulcorner q\urcorner\) can only be either true or false and is in fact false; this syllogism will have true premises and a false conclusion.
Mathematics Subject Classification ID: 03A05
Mathematics Subject Classification ID: 03B47
zbMATH DE Number: 1192481
zbMATH Keywords: future contingents
zbMATH Keywords: relevance logic
zbMATH Keywords: disjunctive syllogism
reviewed by: Jim Mackenzie
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1305/ndjfl/1039700746
OpenAlex ID: W2012503369
cites work: Q4085699
cites work: Whither relevant arithmetic?
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cites work: Logic on the Australian plan
cites work: Reply to Burgess and to Read
cites work: Q5797033
cites work: Burgess on relevance: A fallacy indeed
DOI: 10.1305/NDJFL/1039700746
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description: scientific article; zbMATH DE number 1192481