Mathematics Letters

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An Issue with the Concept of Entailment

Received: 04 September 2016    Accepted: 12 October 2016    Published: 21 October 2016
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Abstract

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.

DOI 10.11648/j.ml.20160204.11
Published in Mathematics Letters (Volume 2, Issue 4, August 2016)
Page(s) 28-31
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Logical System, Logic, Nonclassical, Classical, Entailment, Implication

References
[1] Pinheiro, M. R. (2016). Completeness. IOSR - Jornal of Mathematics, 12(5), 34–37. Retrieved from https://www.researchgate.net/publication/307122839_Completeness
[2] 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
[3] Rouse, M. (2016). Fuzzy Logic. Retrieved September 27, 2016, from http://whatis.techtarget.com/definition/fuzzy-logic
[4] Priest, G. (2001). An Introduction to Non-Classical Logic. Cambridge University Press.
[5] Mares, E. (1998). Relevance Logic. Retrieved October 15, 2016, from http://plato.stanford.edu/entries/logic-relevance/
[6] Harper, D. (2001). Entail. Retrieved September 3, 2016, from http://www.etymonline.com/index.php?search=Entailment
[7] 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
[8] Stanford Logic Group. (2016). Logical Properties and Relationships. Retrieved September 3, 2016, from http://logic.stanford.edu/intrologic/notes/chapter_03.html
[9] Hajek, P. (2002). Fuzzy Logic. Retrieved September 4, 2016, from http://plato.stanford.edu/entries/logic-fuzzy/
[10] Introduction to Logic. (2004). Retrieved September 4, 2016, from http://philosophy.lander.edu/logic/conditional.html
Author Information
  • Department of Mathematics and Philosophy, IICSE University, Wilmington, USA

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    Marcia R. Pinheiro. (2016). An Issue with the Concept of Entailment. Mathematics Letters, 2(4), 28-31. https://doi.org/10.11648/j.ml.20160204.11

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  • @article{10.11648/j.ml.20160204.11,
      author = {Marcia R. Pinheiro},
      title = {An Issue with the Concept of Entailment},
      journal = {Mathematics Letters},
      volume = {2},
      number = {4},
      pages = {28-31},
      doi = {10.11648/j.ml.20160204.11},
      url = {https://doi.org/10.11648/j.ml.20160204.11},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ml.20160204.11},
      abstract = {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.},
     year = {2016}
    }
    

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