Numbers and Arithmetic: Neither Hardwired Nor Out There

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

Abstract
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
Keywords No keywords specified (fix it)
Categories (categorize this paper)
ISBN(s)
DOI 10.1162/biot.2009.4.1.68
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 44,327
Through your library

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.

View all 23 references / Add more references

Citations of this work BETA

Mathematical Knowledge and Naturalism.Fabio Sterpetti - 2019 - Philosophia 47 (1):225-247.

View all 10 citations / Add more citations

Similar books and articles

A Conversation About Numbers and Knowledge.Charles Sayward - 2002 - American Philosophical Quarterly 39 (3):275-287.
Platonic and Fregean Numbers.N. White - 2012 - Philosophia Mathematica 20 (2):224-244.
Relevant Robinson's Arithmetic.J. Michael Dunn - 1979 - Studia Logica 38 (4):407 - 418.
Reason’s Nearest Kin.Michael Potter - 2000 - Oxford University Press.
Recantation or Any Old W-Sequence Would Do After All.Paul Benacerraf - 1996 - Philosophia Mathematica 4 (2):184-189.
Kant’s Theory of Arithmetic: A Constructive Approach? [REVIEW]Kristina Engelhard & Peter Mittelstaedt - 2008 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 39 (2):245 - 271.

Analytics

Added to PP index
2010-09-14

Total views
51 ( #164,936 of 2,271,492 )

Recent downloads (6 months)
19 ( #42,954 of 2,271,492 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature