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• W4285128249 abstract "Examining different cases, I show that, and how, analogies play a variety of roles in the application of mathematics. Different purposes may involve different cognitive and methodological tasks, some more descriptive – clustering –, others more heuristic – problem-solving and guiding metaphors – and others more evidentiary – robustness analysis and statistical inference in single studies and meta-analyses. Classification, generalization and justification cannot be easily reduced to basic standard patterns of analogical reasoning. I discuss two, however, main kinds of cases: the roles of analogy in the application of mathematics and, connectedly, the role of mathematics in the representation and implementation of analogical cognition. Moreover, while the relevant similarities get a mathematical expression, the case of machine learning, including the case of similarity metrics and cluster analysis, shows that analogical cognition is not ultimately mathematical. And what I call the analogical circle is virtuous. But I also point to mathematical metaphors and, in relation to mathematical representations of similarity in clustering analysis, raise the issue of the possibility of mathematical representation of metaphoric function itself. The different cases show in a new way also that the dependence on subjective judgment, research purpose, data characteristics and background information render the application of mathematics and analogical cognition, when connected, unavoidably contextual and plural. The cases I have presented show also how analogy-driven or aided applications of mathematics connect analogical and synthetic tasks, and that they do so in different ways. They show, more specifically, also that each kind of task is a two-sided coin, so to speak, in scientific cognition and methodology. Synthesis involves also some form of differentiation or analysis, and connectedly, similarity is inseparable from dissimilarity." @default.
• W4285128249 created "2022-07-14" @default.
• W4285128249 creator A5053700476 @default.
• W4285128249 date "2022-01-01" @default.
• W4285128249 modified "2023-09-30" @default.
• W4285128249 title "Synthesis and Similarity in Science: Analogy in the Application of Mathematics and Application of Mathematics to Analogy" @default.
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• W4285128249 doi "https://doi.org/10.1007/978-3-030-90688-7_6" @default.
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