Abstract
In this chapter I relate the ideas of fuzziness and accuracy of pictorial depiction to the complexity of approximation. Attention to approximation contributes to my focus on the application of fuzzy set theory as a contextual practice, bringing out some of its aspects as an expression of the practice of approximating. Fuzziness in pictures, then, adds another dimension of approximation; and vice versa, approximation adds another dimension to the analysis of fuzziness. In particular, it contributes a helpful way to understand the contrast between inaccuracy and imprecision.
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Notes
- 1.
To repeat the qualification, I have already insisted on the plurality of uses and values of images beyond representation and its own uses.
- 2.
Siegel [1].
- 3.
- 4.
Bachelard [4].
- 5.
I introduce this account in Cat [5].
- 6.
An encyclopedia of formal conditions for measurement is Krantz et al. [6], vol. 1.
- 7.
- 8.
- 9.
For a defense of the more restrictive criterion, see Hopkins [9].
- 10.
Cat [5].
- 11.
Pawlak [10].
- 12.
Ibid.
- 13.
In this sense a measurement may be quantitatively imprecise or fuzzy before it can be determined to be inaccurate by some margin; see Duhem [11]. Duhem appeals to the linguistic semantic of symbolic denotation to claim that predicate standing for qualities denote like a symbol, but do not picture empirical facts and that quantitative theoretical laws can be neither true nor false, only fuzzy approximations.
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Cat, J. (2017). Pictorial Approximation: Pictorial Accuracy, Vagueness and 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_20
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DOI: https://doi.org/10.1007/978-3-319-47190-7_20
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