Numbers and Arithmetic: Neither Hardwired Nor Out There

Biological Theory 4 (1):68-83 (2009)

What is the nature of number systems and arithmetic that we use in science for quantification, analysis, and modeling? I argue that number concepts and arithmetic are neither hardwired in the brain, nor do they exist out there in the universe. Innate subitizing and early cognitive preconditions for number— which we share with many other species—cannot provide the foundations for the precision, richness, and range of number concepts and simple arithmetic, let alone that of more complex mathematical concepts. Numbers and arithmetic, and mathematics in general, have unique features—precision, objectivity, rigor, generalizability, stability, symbolizability, and applicability to the real world—that must be accounted for. They are sophisticated concepts that developed culturally only in recent human history. I suggest that numbers and arithmetic are realized through precise combinations of non-mathematical everyday cognitive mechanisms that make human imagination and abstraction possible. One such mechanism, conceptual metaphor, is a neurally instantiated inference-preserving cross-domain mapping that allows the conceptualization of abstract entities in terms of grounded bodily experience. I analyze how the inferential organization of the properties and “laws” of arithmetic emerge metaphorically from everyday meaningful actions. Numbers and arithmetic are thus—outside of natural selection—the product of the biologically constrained interaction of individuals with the appropriate cultural and historical phenotypic variation supported by language, writing systems, and education
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DOI 10.1162/biot.2009.4.1.68
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References found in this work BETA

Metaphors We Live By.George Lakoff - 1980 - University of Chicago Press.
Metaphors We Live By.George Lakoff & Mark Johnson - 1980 - Journal of Aesthetics and Art Criticism 40 (2):208-210.
The Number Sense: How the Mind Creates Mathematics.Stanislas Dehaene - 1999 - British Journal of Educational Studies 47 (2):201-203.

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