An Issue with the Concept of Entailment
Volume 2, Issue 4, August 2016, Pages: 28-31
Received: Sep. 4, 2016;
Accepted: Oct. 12, 2016;
Published: Oct. 21, 2016
Views 2506 Downloads 72
Marcia R. Pinheiro, Department of Mathematics and Philosophy, IICSE University, Wilmington, USA
Follow on us
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.
Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Pinheiro, M. R. (2016). Completeness. IOSR - Jornal of Mathematics, 12(5), 34–37. Retrieved from https://www.researchgate.net/publication/307122839_Completeness
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 http://whatis.techtarget.com/definition/fuzzy-logic
Priest, G. (2001). An Introduction to Non-Classical Logic. Cambridge University Press.
Mares, E. (1998). Relevance Logic. Retrieved October 15, 2016, from http://plato.stanford.edu/entries/logic-relevance/
Harper, D. (2001). Entail. Retrieved September 3, 2016, from http://www.etymonline.com/index.php?search=Entailment
Allan, K. (2010). Concise Encyclopedia of Semantics. Elsevier. Retrieved from https://books.google.com.au/books?id=3_1snsgmqU8C&pg=PA561&lpg=PA561&dq=does+not+entail+example+logic&source=bl&ots=jAX-weH0ml&sig=CPfESWbKBv7_sO8ABAz1H5xREDM&hl=en&sa=X&ved=0ahUKEwiX1LSOn_POAhXCE5QKHXf2Afo4ChDoAQgeMAE#v=onepage&q=does not entail example logic&f=false
Stanford Logic Group. (2016). Logical Properties and Relationships. Retrieved September 3, 2016, from http://logic.stanford.edu/intrologic/notes/chapter_03.html
Hajek, P. (2002). Fuzzy Logic. Retrieved September 4, 2016, from http://plato.stanford.edu/entries/logic-fuzzy/
Introduction to Logic. (2004). Retrieved September 4, 2016, from http://philosophy.lander.edu/logic/conditional.html