Reflection on Set theory: Is the barber example a genuine illustration of Russell's paradox?
DOI:
https://doi.org/10.54097/ehss.v8i.4283Keywords:
Russell’s Paradox; Barber Paradox; Degrees of paradoxicality.Abstract
Since the formulation of Russell’s paradox, many people have created more accessible models while trying to understand and solve the paradox. The Barber paradox is the most famous one, but it is not the case that this paradox was not proposed by Russell. This paper will demonstrate the nature of both paradoxes through truth-functional language and propose possible solutions (theory of types) for Russell’s paradox. The reason why the Barber paradox is a pseudo paradox will also be illustrated with a possible solution. There is a huge difference between the paradoxes due to the fundamental difference in the set, and more reasons will be clarified in the paper.
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References
Quine, W V O. The Ways of Paradox, and Other Essays. New York, NY, USA: Harvard University Press, 1966.
Russell, B. “Letter to Frege,” in Jean van Heijenoort (ed.), From Frege to Gödel, Cambridge, Mass.: Harvard University Press, 1967, 124–125
Russell, B. The Principles of Mathematics. Cambridge, England: Allen & Unwin. 1967.
Church, A. A Formulation of the Simple Theory of Types. The Journal of Symbolic Logic, 1940, 5(2): 56–68.
Russell, B. “Appendix B: The Doctrine of Types,” in Bertrand Russell, The Principles of Mathematics, Cambridge: Cambridge University Press, 1903, 523–528.
Carroll, L., Washburn, M. A Logical Paradox. Source: Mind, New Series, [online] 1984, 3(11): 436-440.
Barendregt, H. Problems in Type Theory. Computational Logic, 1999, 99-111
Raclavsky, J. The Barber Paradox: On its Paradoxicality and its Relationship to Russell’s Paradox. Prolegomena, 2014, 13(2): 269-278.
Moulder, J. “Is Russell’s Paradox Genuine?” Philosophy, 1974, 49(189): 295–302
Quine, W V, Quine, W V O. Confessions of a confirmed extensionalist and other essays. Harvard University Press, 2008.
Raclavský, J. Two standard and two modal squares of opposition, The Square of Opposition: A Cornerstone of Thought. Birkhäuser, Cham, 2017: 119-142.
Frege, G. Begriffsschrift: Eine der arithmetischen nachgebildete Formelsprache des reinen Denkens. Halle a.d.S.: Louis Nebert, 1897.
Kaplan, D. How to Russell a Frege-church. The Journal of Philosophy, 1976, 72(19): 716-729.
Josang, A., Elouedi, Z. Redefining Material Implication in the Framework of Subjective Logic. Research Gate preprint, 2022.
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