An Issue with the Concept of Entailment
Mathematics Letters
Volume 2, Issue 4, August 2016, Pages: 28-31
Received: Sep. 4, 2016; Accepted: Oct. 12, 2016; Published: Oct. 21, 2016
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Marcia R. Pinheiro, Department of Mathematics and Philosophy, IICSE University, Wilmington, USA
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Entailment is an interesting sigmatoid: It should mean one thing, but it means another, just for starters. When used in Mathematics, it is usually with the sense of saying that something is definitely true. That would be the use in Classical Logic then. When used in Logic, it became something else. Now it was about how the logical system, which can be any nonclassical one, could be making a proposition become true or false. The major issue we found in 2000, when learning from the own nonclassicists what they do, was that they talk about Nonclassical Logic, therefore a way of thinking that is not Cartesian, yet they stick to the notion of entailment we use in Mathematics, and therefore to the Classical Logic ways. We here discuss exactly this.
Logical System, Logic, Nonclassical, Classical, Entailment, Implication
To cite this article
Marcia R. Pinheiro, An Issue with the Concept of Entailment, Mathematics Letters. Vol. 2, No. 4, 2016, pp. 28-31. doi: 10.11648/
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Pinheiro, M. R. (2016). Completeness. IOSR - Jornal of Mathematics, 12(5), 34–37. Retrieved from
Johnstone, P. T. (1987). Notes on Logic and Set Theory. Cambridge University Press. Retrieved from A&hl=en&sa=X&ved=0ahUKEwj1vsrXsfDOAhXG7hoKHSguAsw4KBDoAQgaMAA#v=onepage&q=logical entailment tautology&f=false
Rouse, M. (2016). Fuzzy Logic. Retrieved September 27, 2016, from
Priest, G. (2001). An Introduction to Non-Classical Logic. Cambridge University Press.
Mares, E. (1998). Relevance Logic. Retrieved October 15, 2016, from
Harper, D. (2001). Entail. Retrieved September 3, 2016, from
Allan, K. (2010). Concise Encyclopedia of Semantics. Elsevier. Retrieved from not entail example logic&f=false
Stanford Logic Group. (2016). Logical Properties and Relationships. Retrieved September 3, 2016, from
Hajek, P. (2002). Fuzzy Logic. Retrieved September 4, 2016, from
Introduction to Logic. (2004). Retrieved September 4, 2016, from
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