Abstract
This paper just contains some reflections on the well known classical ’Sorites Paradox’, under which it appears that some imprecise linguistic terms cannot have a crisp extension, that there is no any subset containing the elements in the universe verifying the term. Such reflections are conducted from a typically layperson’s point of view that heaps are not definable by means of the number of grains of sand they have, but mainly by its three-dimensional shape. Representing imprecise terms P by means of fuzzy sets, or contextual membership functions, it is shown that the Black’s separation point is sometimes uniquely determinable, and that it always exists a crisp subset whose elements are ’more’ P than either not P, or an opposite of P. Additionally, some considerations on the case of heaps once compared with the shape of either a pyramid, or a circular cone, are done.
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References
Black, M.: Reasoning with Loose Concepts. Dialogue 2, 1–12 (1963)
Masquelet, A.C.: Le Raisonnement Médical. PUF, Paris (2006) (in French)
Sorensen, R.A.: Vagueness and Contradiction. Clarendon Press, Oxford (2001)
Trillas, E.: On Negation Functions in Fuzzy Set Theory. In: Barro, S., Bugarin, A., Sobrino, A. (eds.) Advances of Fuzzy Logic, pp. 31–43. Universidad de Santiago de Compostela (1998)
Trillas, E.: Conjectures in De Morgan Algebras and with Fuzzy Sets. Submitted to NAFIPS 2012 (2012)
García-Honrado, I., Trillas, E.: On an Attempt to Formalize Guessing. In: Seising, R., Sanz González, V. (eds.) Soft Computing in Humanities and Social Sciences. STUDFUZZ, vol. 273, pp. 243–264. Springer, Heidelberg (2012)
Trillas, E., Guadarrama, S.: Fuzzy Representations Need a Careful Design. International Journal of General Systems 39(3), 329–346 (2010)
Trillas, E., Urtubey, L.A.: Towards the Dissolution of the Sorites Paradox. Applied Soft Computing 11(2), 1506–1510 (2011)
Williamson, T.: Vagueness. Routledge, London (1994)
Zadeh, L.A.: From Computing with Numbers to Computing with Words. IEEE Transactions on Circuits and Systems 46(1), 105–119 (1999)
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Trillas, E., Garcìa-Honrado, I. (2013). A Layperson Reflection on Sorites. In: Seising, R., Tabacchi, M. (eds) Fuzziness and Medicine: Philosophical Reflections and Application Systems in Health Care. Studies in Fuzziness and Soft Computing, vol 302. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36527-0_15
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DOI: https://doi.org/10.1007/978-3-642-36527-0_15
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