Abstract
The standard notion of iconicity, which is based on degrees of similarity or resemblance, does not provide a satisfactory account of the iconic character of some representations of abstract entities when those entities do not exhibit any imitable internal structure. Individual numbers are paradigmatic examples of such structureless entities. Nevertheless, numerals are frequently described as iconic or symbolic; for example, we say that the number three is represented symbolically by ‘3’, but iconically by ‘\(|||\)’. To address this difficulty, I discuss various alternative notions of iconicity that have been presented in the literature, and I propose two novel accounts.
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Notes
- 1.
This differs from other conceptions of numbers, e. g., Euclid’s [6, Bk. 7, Def. 2].
- 2.
This view of analogy also underlies the structure-mapping theory of analogy [3].
- 3.
See [5, pp. 52–57] for a general discussion of exemplification in the context of representations.
- 4.
The exact measure of simplicity that is applied here is difficult to make precise, but it might correlate with the notion of naturalness invoked in Sect. 3.1.
- 5.
Note that some of the caveats about the assessment of operational iconicity discussed at the end of Sect. 2 also apply to the notion of systematic iconicity.
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Acknowledgments
I would like to thank Viviane Fairbank, David Waszek, Jessica Carter, and two anonymous reviewers for fruitful discussions and helpful comments on a draft of this paper. This research was supported by the Social Sciences and Humanities Research Council of Canada.
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Schlimm, D. (2021). How Can Numerals Be Iconic? More Varieties of Iconicity. In: Basu, A., Stapleton, G., Linker, S., Legg, C., Manalo, E., Viana, P. (eds) Diagrammatic Representation and Inference. Diagrams 2021. Lecture Notes in Computer Science(), vol 12909. Springer, Cham. https://doi.org/10.1007/978-3-030-86062-2_53
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