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Aspects of Vagueness and Some Epistemological Problems Related to their Formalization

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Aspects of Vagueness

Part of the book series: Theory and Decision Library ((TDLU,volume 39))

Abstract

Vagueness, Approximation, Error, Imprecision, Accuracy etc. all share the same “family resemblance”. The discussion in this paper will mainly concern vagueness although sometimes one or another of the other notions will show up.

The topic of vagueness is a very difficult one… it is,…, evident that we have an intuitive sympathy with Frege’s view that a vague expression is one which is, to that extent, defective in sense: any account of vagueness which failed at least to explain this intuitive feeling would be inadequate. At the same time we have also a contrary intuition, that vagueness is an indispensable feature of our language, that we could not operate with language as we do unless many of its expressions displayed this feature: and it is equally a requirement on any satisfactory account of vagueness that it should at least explain our having this intuition also.

Michael DUMMETT

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References

  • Dummett, M.: 1975, ‘Wang’s paradox’, Synthese 30, 301–324, reprinted as chapter 15 of his Truth and Other Enigmas Harvard University Press, Cambridge, Mass. 1978.

    Article  Google Scholar 

  • Gaines, B.R.: 1976, ‘Foundations of Fuzzy Reasoning’ International Journal of Man-Machine Studies, 8, 623–668.

    Article  Google Scholar 

  • Giles, R.: 1976, ‘Lukasiewicz Logic and Fuzzy Set Theory’ International Journal of Man-Machine Studies 8, 313–327.

    Article  Google Scholar 

  • Goguen, J.A.: 1974, ‘Concept Representation in Natural and Artificial Languages’, International Journal of Man-Machine Studies 6, 513–561.

    Article  Google Scholar 

  • Gottwald, S.: 1983, ‘Fuzzy Set Theory, Some Aspects of the Early Development’ (this volume)

    Google Scholar 

  • Katz, M.: 1981, ‘Two Systems of Multi-valued Logic for Science’ Proc. XI Symposium on Multiple-Valued Logics, Oklahoma City, 175–182.

    Google Scholar 

  • Katz, M.: 1982, ‘Real-valued Models with Metric Equality and Uniformly Continuous Predicates’, Journal of Symbolic Logic 47, 772–792.

    Article  Google Scholar 

  • Ludwig, G.: 1981, ‘Imprecision in Physics’ in A. Hartkämper and H. J. Schmidt (eds.), Structure and Approximation in Physical Theories, Plenum Press, New York pp. 7–19.

    Google Scholar 

  • Miller, D.: 1983, ‘Impartial Truth’ (this volume)

    Google Scholar 

  • Parikh, R.: 1977, ‘The Problem of Vague Predicates’ (preprint) Boston University.

    Google Scholar 

  • Parrat, L.G.: 1961, Probability and Experimental Errors in Science, J. Wiley and Sons, New York.

    Google Scholar 

  • Pavelka, J.: 1979, ‘On Fuzzy Logic’, Zeitschrift für Math. Logik und Grundlagen der Math 25, 45–52, 119–134, 447–464.

    Article  Google Scholar 

  • Pultr, A.: 1983, ‘Fuzziness and Fuzzy Equality’ (this volume)

    Google Scholar 

  • Russell, B.: 1923, ‘Vagueness’, Australian Journal of Philosophy, 1, 84–92.

    Article  Google Scholar 

  • Scott, D.: 1976, ‘Does Many-valued Logic has any use?’ in S. Körner (ed.). Philosophy of Logic, Basil Blackwell Oxford pp. 64–74.

    Google Scholar 

  • Skala, H. J.: 1982, ‘Modelling Vagueness’ in M.M. Gupta and E. Sanchez, Fuzzy Information and Decision Processes North-Holland PubL Co., Amsterdam pp. 101–109.

    Google Scholar 

  • Sochor, A.: 1983, ‘The Alternative Set Theory and Its Approach to Cantor’s Set Theory’ (this volume)

    Google Scholar 

  • Synge, J.L.: 1965, Relativity, the Special theory, North- Holland Publ. Co., Amsterdam.

    Google Scholar 

  • von Neumann, J.: 1956, ‘Probabilistic logics and the Synthesis of Reliable Organisms from Unreliable Components’ in C.E. Shannon and J. McCarthy (eds.), Automata Studies, Princeton University Press pp. 43–98.

    Google Scholar 

  • Vopěnka, P.: 1979, Mathematics in the Alternative Set Theory Teubner Verlagsgesellschaft, Leipzig.

    Google Scholar 

  • Wright, C.: 1975, ‘On the coherence of vague predicates’, Synthese 30, 325–365.

    Article  Google Scholar 

  • Zadeh, L.A.: 1975. ‘The Concept of a Linguistic variable and its Application to Approximate Reasoning’, Information Sciences 8, 199–249, 301–357; 9, 43–80.

    Article  Google Scholar 

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© 1984 D. Reidel Publishing Company

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Termini, S. (1984). Aspects of Vagueness and Some Epistemological Problems Related to their Formalization. In: Skala, H.J., Termini, S., Trillas, E. (eds) Aspects of Vagueness. Theory and Decision Library, vol 39. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6309-2_11

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  • DOI: https://doi.org/10.1007/978-94-009-6309-2_11

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-009-6311-5

  • Online ISBN: 978-94-009-6309-2

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