Authors
Vasily Olegovich Shangin
Moscow State University
Abstract
ABSTRACTThe paper deals with a problem posed by Mathieu Vidal to provide a formal representation for defective conditional in mathematics Vidal, M. [. The defective conditional in mathematics. Journal of Applied Non-Classical Logics, 24, 169–179]. The key feature of defective conditional is that its truth-value is indeterminate if its antecedent is false. In particular, we are interested in two explanations given by Vidal with the use of trivalent logics. By analysing a simple argument from plane geometry, where defective conditional is in use, he gives two trivalent formal explanations for it. For both explanations, Vidal rigorously shows that trivalent logics cannot adequately represent defective conditional. Preserving Vidal's criteria of defective conditional ad max, we indicate some arguable points in his explanations and present an alternative explanation containing the original conjunction and disjunction in order to show that there are trivalent logics that might be an adequate formal explanation for defective conditional.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
ISBN(s)
DOI 10.1080/11663081.2018.1534488
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 71,410
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

On Notation for Ordinal Numbers.S. C. Kleene - 1938 - Journal of Symbolic Logic 3 (4):150-155.
Natural Deduction for Three-Valued Regular Logics.Yaroslav Petrukhin - 2017 - Logic and Logical Philosophy 26 (2):197–206.

View all 22 references / Add more references

Citations of this work BETA

Add more citations

Similar books and articles

The Defective Conditional in Mathematics.Mathieu Vidal - 2014 - Journal of Applied Non-Classical Logics 24 (1-2):169-179.
Some Remarks on Certain Trivalent Accounts of Presupposition Projection.Benjamin R. George - 2014 - Journal of Applied Non-Classical Logics 24 (1-2):86-117.
What Is the Specificity of Classical Mathematics?Graham Priest - 2017 - Thought: A Journal of Philosophy 6 (2):115-121.

Analytics

Added to PP index
2018-12-06

Total views
12 ( #812,853 of 2,519,810 )

Recent downloads (6 months)
1 ( #406,314 of 2,519,810 )

How can I increase my downloads?

Downloads

My notes