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Fuzzy Pictures as Philosophical Problem and Scientific Practice pp 187–191Cite as

Pictorial Vagueness as Scientific Practice: Picture-Making and the Mathematical Practice of Fuzzy Categorization

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Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 348))

Abstract

Vagueness is practice and is in mathematical practice too. In this chapter I take stock of assumptions and conclusions I have presented in previous chapters and I examine them further. To place fuzziness at the center of a philosophical account of vagueness is to place more than subjective uncertainty or an objective property in an alternative to epistemic accounts; it is to place also an objective activity and a practice of mathematics and of human and machine categorization. Fuzziness represents them and its empirical and technical applications aim to control and exploit it. If vagueness is best understood objectively, from the standpoint of fuzziness, objectivity must be understood more broadly than an ontic commitment to the reality of autonomous preexisting properties in the world. This extends to the case defended here of vagueness or uncertainty in pictures.

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Notes

  1. 1.

    Smith [1].

  2. 2.

    Zadeh [2, 3], McNeill and Freiberger [4], Seising [5], Cat [6, 7].

  3. 3.

    Turner [8].

  4. 4.

    Cat [6].

  5. 5.

    Maji and Pal [9], 2.11.

  6. 6.

    Ibid., 2.8.

  7. 7.

    Maji and Pal [9], 2.1–2.

References

  1. Smith, N. J. J. (2010). Vagueness and degrees of truth. Oxford: Oxford University Press.

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  2. Zadeh, L. A. (1962). From circuit theory to system theory. Proceedings of Institution of Radio Engineers, 50, 856–865.

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  3. Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 201, 240–256.

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  4. McNeil, D., & Freiberger, P. (1993). Fuzzy logic. New York: Touchstone.

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  5. Seising, R. (2007). Fuzzification of systems: The genesis of fuzzy set theory and its initial applications. New York: Springer.

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  6. Cat, J. (2015). An informal meditation on empiricism and approximation in fuzzy logic and fuzzy set theory: Between subjectivity and normativity. In R. Seising, E. Trillas, & J. Kacprzyk (Eds.), Fuzzy logic: Towards the future (pp. 179–234). Berlin: Springer.

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  7. Cat, J. (2016). The performative construction of natural kinds: mathematical application as practice. In C. Kendig (Ed.), Natural kinds and classification in scientific practice (pp. 87–105). Abingdon and New York: Routledge.

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  8. Turner, S. P. (2010). Explaining the normative. Malden, MA: Polity Press.

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  9. Maji, P. & Pal, S. K. (2010). Rough-fuzzy clustering algorithm for segmentation of brain MR images. In: Pal, S. K., Peters, J. F. pp 2.1–21.

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Authors and Affiliations

  1. Department of History and Philosophy of Science, Indiana University, Bloomington, USA

    Jordi Cat

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  1. Jordi Cat
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Cat, J. (2017). Pictorial Vagueness as Scientific Practice: Picture-Making and the Mathematical Practice of Fuzzy Categorization. In: Fuzzy Pictures as Philosophical Problem and Scientific Practice. Studies in Fuzziness and Soft Computing, vol 348. Springer, Cham. https://doi.org/10.1007/978-3-319-47190-7_21

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  • DOI: https://doi.org/10.1007/978-3-319-47190-7_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-47189-1

  • Online ISBN: 978-3-319-47190-7

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