Abstract
In Part 2 I conclude the process of tracking objective conditions of vagueness in representation and categorization: from language to pictures, from philosophy to imaging science, from vagueness to approximation and from representation to reasoning. The scientific focus is the application of fuzzy set theory. The main aim of Part 2 is to analyze fuzziness and the application of fuzzy set theory to imaging as a kind of practice applied to the understanding and control of depiction and categorization as other practices. As practices they are enabled and constrained by a variety of resources such as formal and material technologies, habits and skills, interests, standards and limitations.
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Notes
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- 2.
On such roles in mathematical application see Cat [1, 2]. In connection with the methodological value of ambiguity, Grosholz has defended the notion of productive ambiguity: A systematic use of ambiguity scientific consists in the joint use of a multiplicity of modes of representation and argumentation in problem-solving and persuasion. See Grosholz [3].
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Schlimm [4].
References
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.
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: Routledge.
Grosholz, E. R. (2007). Representation and productive ambiguity in mathematics and the sciences. Oxford: Oxford University Press.
Schlimm, D. (2013). Axioms in mathematical practice. Philosophia Mathematica, 21, 37–92.
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Cat, J. (2017). Introduction: Fuzzy-Set Representation and Processing of Fuzzy Images; Non-linguistic Vagueness as Scientific Practice; Scientific Epistemology, Aesthetics, Methodology and Technology of Fuzziness. 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_12
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