Abstract
My initial strategy is to focus on categorization and its indeterminacy, since they play a role in understanding and using pictures as well as they do in symbolic representation and reasoning. The methodological choice to emphasize categorization is not arbitrary; it is rather motivated by the central role it plays in conceptual and formal accounts of the phenomenon of vagueness as well as in the very practice of its investigation, particularly in philosophical models of linguistic vagueness and the application of formal models of fuzzy sets. I take it to be a stable description of a phenomenon and a practice itself used to guide and explain other forms of behavior. There is some gain in trying to apply the conceptual standards developed around the linguistic cases: it brings out the scope of their relevance and some of their differences in role and interpretation. But, again, this is not to deny the variety of additional or alternative criteria relevant for understanding or establishing representation, or the mechanisms for effecting it; similarly, in the specific case of categorization, for its possible criteria or procedures. The caveat, I repeat, is that, like representation, the role of categorization itself as a label for a cognitive practice and an explanation for cognitive and other practices may very well be reinterpreted, explained away and replaced; that is, in objectivist terms, talk of categorization could be “wrong” and in pragmatic, functional terms, it could prove less efficient than alternatives. Vagueness and fuzzy set theory will have to be reinterpreted accordingly. Either way, applying specific views to new models of specific cognitive phenomena will suggest further developments that I leave the reader to explore.
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- 1.
Cat [1].
- 2.
For a comprehensive discussion of varieties of approaches to conceptualization and attempts at a common framework, see, for instance, Machéry [2].
- 3.
A note on language: as a result of my focus on a generalized empirical notion of categorization that includes properties as well as activities, I often speak of categorizations where the reader might expect a reference to categories or even predicates.
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I call the strategy, methodological nominalism; as a form of methodological minimalism, it ensures the methodological generality that performs the connecting function my argument requires across a number of conceptual divides.
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We can always rule out vagueness by definition, for instance, by adopting standards of rigid designation, in Kripke’s sense, relating naming and necessity within a possible-world semantics.
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One example of a complex approach is the community-based, multi-component vector model of reference in Putnam [5].
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The overlap includes the existence of ideographic alphabets.
- 9.
Goodman [3].
- 10.
Given the relation between content and categorization, one may read IC-EC rules equivalently, as linking intrinsic and extrinsic categorizations.
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- 12.
On the independence of perceptual recognition from belief see Schier [8] and Lopes [9]. Human perception, like machines, might run on a recognition process that follows something like a rule-based iterative algorithm, but if it does, the human algorithm is opaque (Zadeh’s terminology). The IC–EC rule is here a matter of mechanism exercising the capacity that enables the formation of extrinsic categorization stimulated by intrinsic categorization. The transparent machine algorithm models the categorization outcome and along the way postulates a procedure that models also the process.
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For a discussion of the complexity of this formal practice of set-theoretic representation, see Cat [13].
- 16.
Zadeh [14].
- 17.
This is a straight application of Zadeh’s formal extension principle and subsequent generalizations; they are rules for generalizing domains of set-theoretic structures and reasoning based on the notion a variable having precise value must be replaced with that of a variable having a degree of membership to each possible value; Dubois and Prade [15], 36–38. Zadeh’s original formulation is based on a definition of Cartesian product for fuzzy subsets of different classic universes; see Zadeh [16].
- 18.
For a discussion of the role of fuzzy concepts in scientific models see Cat [17].
- 19.
Other things being equal, standards include calibration and replication.
- 20.
Cat [13].
- 21.
See, for instance, Smith [18].
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Cat, J. (2017). From Ordinary to Mathematical Categorization in the Visual World… of Words, Pictures and Practices. 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_2
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