The aim of this paper is proving that our solution is better than the solution presented by the own Russell and what is today the most accepted solution to the Russell’s Paradox, which is the solution of Zermelo and Frankael. We presented our solution a few years ago, and that is a solution that we believe should be considered to be the actual solution. We decided to do what Dr. Hyde asked us to do in 2000 in terms of The Sorites Paradox and our solution to it, which is studying all objections to all solutions that have been previously presented and then saying why our solution does not suffer from those problems. We then analyze the solution presented by the own Russell back then on top of the most accepted solution, that of Zermelo and Frankael. We do all from the most unbiased perspective as possible. We seem to be able to prove, with solid argumentation, that our solution to the Russell’s Paradox is the best solution so far. The methods we use are: analytical and synthetic studies, application of the results of the synthetic studies, and tests of soundness in reasoning based on the foundations of Logic. Each time something is found to be unsound we direct ourselves to our own solution and assess it in the same way to see if the study of ours also leads to unsoundness. Our results are that our solution is sounder than the solutions presented by Russell, Zermelo, and Frankael. The conclusion is that it is very likely to be the case that we have a final solution.
| Published in | International Journal of Theoretical and Applied Mathematics (Volume 2, Issue 2) |
| DOI | 10.11648/j.ijtam.20160202.22 |
| Page(s) | 110-114 |
| 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), 2016. Published by Science Publishing Group |
Logic, Russell, Paradox, Language, Classical Logic
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| [2] | Aatu. (2003). Russell’s Theory of Types. Retrieved October 14, 2016, from http://planetmath.org/russellstheoryoftypes |
| [3] | Pinheiro, M. R. (2016). The Sorites x Classical Logic. Retrieved October 16, 2016, from https://www.researchgate.net/publication/307936102_The_Sorites_x_Classical_Logic |
| [4] | Pinheiro, M. R. (2016). Possible Worlds x Psychiatry. International Journal of Humanities and Social Science Invention, 5 (10), 68–76. Retrieved from https://www.researchgate.net/publication/308968450_Possible_Worlds_x_Psychiatry |
| [5] | Baldwin, J. T., & Lessmann, O. (2016). What is Russell’s paradox? Retrieved October 14, 2016, from https://www.scientificamerican.com/article/what-is-russells-paradox/ |
| [6] | Klement, K. C. (2016). Russell’s Paradox. Retrieved October 14, 2016, from http://www.iep.utm.edu/par-russ/ |
| [7] | Hallett, M. (2013). Zermelo’s Axiomatization of Set Theory. Retrieved October 14, 2016, from http://plato.stanford.edu/entries/zermelo-set-theory/ |
| [8] | Hart, K. P. (2010). Axioms of Set Theory. Retrieved October 14, 2016, from http://fa.its.tudelft.nl/~hart/37/onderwijs/set_theory/Jech/01-axioms_of_set_theory.pdf |
| [9] | Pinheiro, M. R. (2012). Concerning the Solution to the Russell’s Paradox. E-Logos, 20. Retrieved from http://www.academia.edu/9817490/Solution_to_the_Russells_Paradox |
| [10] | Pinheiro, M. R. (2015). Infinis. Protosociology. Retrieved from https://www.researchgate.net/publication/286930813_Infinis |
| [11] | Bauer, A. (2005). The Law of Excluded Middle. Retrieved October 16, 2016, from http://math.andrej.com/2005/05/13/the-law-of-excluded-middle/ |
APA Style
Marcia R. Pinheiro. (2016). Russell’s Paradox, Our Solution, and the Other Solutions. International Journal of Theoretical and Applied Mathematics, 2(2), 110-114. https://doi.org/10.11648/j.ijtam.20160202.22
ACS Style
Marcia R. Pinheiro. Russell’s Paradox, Our Solution, and the Other Solutions. Int. J. Theor. Appl. Math. 2016, 2(2), 110-114. doi: 10.11648/j.ijtam.20160202.22
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Download@article{10.11648/j.ijtam.20160202.22,
author = {Marcia R. Pinheiro},
title = {Russell’s Paradox, Our Solution, and the Other Solutions},
journal = {International Journal of Theoretical and Applied Mathematics},
volume = {2},
number = {2},
pages = {110-114},
doi = {10.11648/j.ijtam.20160202.22},
url = {https://doi.org/10.11648/j.ijtam.20160202.22},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20160202.22},
abstract = {The aim of this paper is proving that our solution is better than the solution presented by the own Russell and what is today the most accepted solution to the Russell’s Paradox, which is the solution of Zermelo and Frankael. We presented our solution a few years ago, and that is a solution that we believe should be considered to be the actual solution. We decided to do what Dr. Hyde asked us to do in 2000 in terms of The Sorites Paradox and our solution to it, which is studying all objections to all solutions that have been previously presented and then saying why our solution does not suffer from those problems. We then analyze the solution presented by the own Russell back then on top of the most accepted solution, that of Zermelo and Frankael. We do all from the most unbiased perspective as possible. We seem to be able to prove, with solid argumentation, that our solution to the Russell’s Paradox is the best solution so far. The methods we use are: analytical and synthetic studies, application of the results of the synthetic studies, and tests of soundness in reasoning based on the foundations of Logic. Each time something is found to be unsound we direct ourselves to our own solution and assess it in the same way to see if the study of ours also leads to unsoundness. Our results are that our solution is sounder than the solutions presented by Russell, Zermelo, and Frankael. The conclusion is that it is very likely to be the case that we have a final solution.},
year = {2016}
}
TY - JOUR T1 - Russell’s Paradox, Our Solution, and the Other Solutions AU - Marcia R. Pinheiro Y1 - 2016/12/17 PY - 2016 N1 - https://doi.org/10.11648/j.ijtam.20160202.22 DO - 10.11648/j.ijtam.20160202.22 T2 - International Journal of Theoretical and Applied Mathematics JF - International Journal of Theoretical and Applied Mathematics JO - International Journal of Theoretical and Applied Mathematics SP - 110 EP - 114 PB - Science Publishing Group SN - 2575-5080 UR - https://doi.org/10.11648/j.ijtam.20160202.22 AB - The aim of this paper is proving that our solution is better than the solution presented by the own Russell and what is today the most accepted solution to the Russell’s Paradox, which is the solution of Zermelo and Frankael. We presented our solution a few years ago, and that is a solution that we believe should be considered to be the actual solution. We decided to do what Dr. Hyde asked us to do in 2000 in terms of The Sorites Paradox and our solution to it, which is studying all objections to all solutions that have been previously presented and then saying why our solution does not suffer from those problems. We then analyze the solution presented by the own Russell back then on top of the most accepted solution, that of Zermelo and Frankael. We do all from the most unbiased perspective as possible. We seem to be able to prove, with solid argumentation, that our solution to the Russell’s Paradox is the best solution so far. The methods we use are: analytical and synthetic studies, application of the results of the synthetic studies, and tests of soundness in reasoning based on the foundations of Logic. Each time something is found to be unsound we direct ourselves to our own solution and assess it in the same way to see if the study of ours also leads to unsoundness. Our results are that our solution is sounder than the solutions presented by Russell, Zermelo, and Frankael. The conclusion is that it is very likely to be the case that we have a final solution. VL - 2 IS - 2 ER -
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