Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-24T23:12:05.810Z Has data issue: false hasContentIssue false
  • English
  • Français

Numbers as a cognitive and social technology: on the nature of conventional number sequences used in economic systems

Published online by Cambridge University Press:  06 May 2010

DAVID A. HARPER
DAVID A. HARPER*
Affiliation:
Department of Economics, New York University, New York, USA
*
*Email: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract:

This paper examines the fundamental nature of numbers as they are used in economic systems. In the framework proposed, number sequences are technological objects (‘tools’) that are constituted by both form and function. To do their job, number sequences have to have the necessary internal structure – all elements (e.g. symbols) of the sequence must be distinct from one another, and the sequence must be a progression. In addition, numerical toolkits have to have the right external structure – they must be situated in a social network of economic agents that confers on them quantitative functions (e.g. identifying set sizes). Number sequences are the product of multilevel evolutionary processes, including psychological selection that screens sequences for their learnability by human users. Number tools are a kind of capital; they are material systems that are as real as other everyday objects. Just as changing physical tools alters the structure of productive activity, so too changing number sequences alters cognitive, behavioral, and social routines.

Type
Research Article
Information
Journal of Institutional Economics , Volume 6 , Issue 2 , June 2010 , pp. 167 - 190
Copyright
Copyright © The JOIE Foundation 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abler, W. L. (1989), ‘On the Particulate Principle of Self-Diversifying Systems’, Journal of Social and Biological Structures, 12 (1): 1–13.CrossRefGoogle Scholar
Aubrey, J. (1972), Aubrey on Education: A Hitherto Unpublished Manuscript by the Author of ‘Brief Lives’, edited by Stephens, J. E., London: Routledge. [Based on Aubrey's late seventeenth-century manuscript ‘Ideas on Education’].Google Scholar
Barwise, J. and Moss, L. (1991), ‘Hypersets’, Mathematical Intelligencer, 13 (4): 31–41.CrossRefGoogle Scholar
Beller, S. and Bender, A. (2008), ‘The Limits of Counting: Numerical Cognition Between Evolution and Culture’, Science, 319 (5860): 213–215.CrossRefGoogle ScholarPubMed
Benacerraf, P. (1965), ‘What Numbers Could Not Be’, The Philosophical Review, 74 (1): 47–73.CrossRefGoogle Scholar
Boulding, K. E. (1993), ‘The Economics of the Coming Spaceship Earth’, in Daly, H. E. (ed.), Valuing the Earth: Economics, Ecology, Ethics, 2nd edition, Cambridge, MA: MIT Press, Chapter 16, pp. 297–310.Google Scholar
Boyer, C. B. (1944), ‘Fundamental Steps in the Development of Numeration’, Isis, 35 (2): 153–168.Google Scholar
Bratman, M. E. (1999), Faces of Intention: Selected Essays on Intention and Agency, Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Brownell, W. A. (1939), Learning as Reorganization: An Experimental Study in Third-Grade Arithmetic, Durham, NC: Duke University Press.Google Scholar
Bruner, J. S. (1973), Beyond the Information Given: Studies in the Psychology of Knowing, New York: W. W. Norton.Google Scholar
Cajori, F. (1896), A History of Elementary Mathematics, New York: Macmillan.Google Scholar
Campbell, J. I. D. (1994), ‘Architectures for Numerical Cognition’, Cognition, 53 (1): 1–44.CrossRefGoogle ScholarPubMed
Campbell, J. I. D. and Epp, L. J. (2004), ‘Architectures for Arithmetic’, in Campbell, J. I. D. (ed.), Handbook of Mathematical Cognition, New York: Psychology Press.Google Scholar
Christiansen, M. H. (1994), ‘Infinite Languages, Finite Minds: Connectionism, Learning and Linguistic Structure’, Ph.D. thesis, University of Edinburgh, available at http://cnl.psych.cornell.edu/papers/mhc-phd-dissertation.pdfGoogle Scholar
Clark, A. (2003), Natural-born Cyborgs: Minds, Technologies, and the Future of Human Intelligence, Oxford: Oxford University Press.Google Scholar
Clark, A. (2006), ‘Material Symbols’, Philosophical Psychology, 19 (3): 291–307.CrossRefGoogle Scholar
Cohen Kadosh, R. (2008), ‘Numerical Representation: Abstract or Nonabstract?’, Quarterly Journal of Experimental Psychology, 61 (8): 1160–1168.CrossRefGoogle ScholarPubMed
Cohen Kadosh, R., Cohen Kadosh, K., Kaas, A., Henik, A., and Goebel, R. (2007), ‘Notation-Dependent and –Independent Representations of Numbers in the Parietal Lobes’, Neuron, 53 (2): 307–314.CrossRefGoogle ScholarPubMed
Crosby, A. W. (1997), The Measure of Reality: Quantification and Western Society, 1250–1600, Cambridge: Cambridge University Press.Google Scholar
Debreu, G. (1984), ‘Economic Theory in the Mathematical Mode’, American Economic Review, 74 (3): 267–278.Google Scholar
Dennett, D. C. (1987), The Intentional Stance, Cambridge, MA: MIT Press.Google Scholar
Dennett, D. C. (1991), Consciousness Explained, Boston: Little Brown.Google Scholar
Dopfer, D. and Potts, J. (2008), The General Theory of Economic Evolution, New York: Routledge.Google Scholar
Dretske, F. (1988), Explaining Behavior: Reasons in a World of Causes, Cambridge, MA: MIT Press.Google Scholar
Edwards, J. R. (1989), A History of Financial Accounting, London: Routledge.Google Scholar
Faulkner, P. and Runde, J. (2009), ‘On the Identity of Technological Objects and User Innovations in Function’, Academy of Management Review, 34 (3): 442–462.CrossRefGoogle Scholar
Fibonacci, L. (1202), Liber Abbaci [Book of Calculation].Google Scholar
Field, H. (1989), Realism, Mathematics and Modality, New York: Basil Blackwell.Google Scholar
Frege, G. (1959), The Foundations of Arithmetic: A Logico-Mathematical Enquiry into the Concept of Number, 2nd revised edition, translated by Austin, J. L., Oxford: Basil Blackwell.Google Scholar
Gelman, R. and Gallistel, C. R. (1978), The Child's Understanding of Number, Cambridge, MA: Harvard University Press.Google Scholar
Giaquinto, M. (2001), ‘What Cognitive Systems Underlie Arithmetical Abilities’, Mind and Language, 16 (1): 56–68.CrossRefGoogle Scholar
Gibilisco, S. and Crowhurst, N. H. (2008), Mastering Technical Mathematics, 3rd edition, New York: McGraw Hill.Google Scholar
Gordon, P. (2004), ‘Numerical Cognition without Words: Evidence from Amazonia’, Science, 306 (5695): 496–499.CrossRefGoogle ScholarPubMed
Harper, D. A. (2008), ‘A Bioeconomic Study of Numeracy and Economic Calculation’, Journal of Bioeconomics, 10 (2): 101–126.CrossRefGoogle Scholar
Hersh, R. (1986), ‘Some Proposals for Revising the Philosophy of Mathematics’, in Tymoczko, T. (ed.), New Directions in the Philosophy of Mathematics, Boston: Birkhäuser, pp. 9–28.Google Scholar
Hodgson, G. M. (2002a), ‘The Evolution of Institutions: An Agenda for Future Theoretical Research’, Constitutional Political Economy, 13 (2): 111–127.CrossRefGoogle Scholar
Hodgson, G. M. (2002b), ‘Reconstitutive Downward Causation: Social Structure and the Development of Individual Agency’, in Fullbrook, E. (ed.), Intersubjectivity in Economics: Agents and Structures, London: Routledge, pp. 159–180.Google Scholar
Holzknecht, S. (1986), ‘A Morphology and Grammar of Adzera (Amari dialect), Morobe Province, Papua New Guinea’, Pacific Linguistics, A70: 77–166.Google Scholar
Hurford, J. R. (1987) Language and Number: The Emergence of a Cognitive System, Oxford: Basil Blackwell.Google Scholar
Hurford, J. R. (1999), ‘Artificially Growing a Numeral System’, in Gvozdanovic, J. (ed.), Numeral Types and Changes Worldwide, Trends in Linguistics: Studies and Monographs 118, Berlin: Mouton de Gruyter, pp. 7–41.CrossRefGoogle Scholar
Hutchins, E. (1995), Cognition in the Wild, Cambridge, MA: MIT Press.Google Scholar
Hutchins, E. (2001), ‘Cognition, Distributed’, in Smelser, N. J. and Baltes, P. B. (eds.), International Encyclopedia of Social and Behavioral Sciences, Oxford: Elsevier, pp. 2068–2072.CrossRefGoogle Scholar
Jackendoff, R. (1996), ‘How Language Helps Us Think’, Pragmatics and Cognition, 4 (1): 1–34.CrossRefGoogle Scholar
Jenkinson, H. (1926), ‘The Use of Arabic and Roman Numerals in English Archives’, The Antiquaries Journal, 6: 263–275.CrossRefGoogle Scholar
Kaput, J. J. and Shaffer, D. W. (2002), ‘On the Development of Human Representational Competence from an Evolutionary Point of View’, in Gravemeijer, K., Lehrer, R., van Oers, B., and Verschaffel, L. (eds.), Symbolizing, Modeling and Tool Use in Mathematics Education, Dordrecht: Kluwer, pp. 277–293.CrossRefGoogle Scholar
Klaes, M. (2004), ‘Ontological Issues in Evolutionary Economics: Introduction’, Journal of Economic Methodology, 11 (2) (Special Issue): 121–124.CrossRefGoogle Scholar
Lachmann, L. M. (1977), Capital Expectations, and the Market Process: Essays on the Theory of the Market Economy, edited by Grinder, W. E., Kansas City: Sheed Andrews & McMeel.Google Scholar
Lachmann, L. M. (1978), Capital and Its Structure, Kansas City: Sheed Andrews & McMeel.Google Scholar
Lawson, C. (2008), ‘An Ontology of Technology: Artefacts, Relations and Functions’, Techné: Journal of the Society for Philosophy and Technology, 12 (1): 48–64.Google Scholar
Lean, G. A. (1992), ‘Counting Systems of Papua New Guinea and Oceania’, Ph.D. thesis, Papua New Guinea University of Technology.Google Scholar
Liebowitz, S. J. and Margolis, S. E. (1994), ‘Network Externality: An Uncommon Tragedy’, Journal of Economic Perspectives, 8 (2): 133–150.CrossRefGoogle Scholar
Mäki, U. (2001), ‘The What, Why, and How of Economic Ontology’, in Mäki, U. (ed.), The Economic World View: Studies in the Ontology of Economics, Cambridge: Cambridge University Press, pp. 3–14.CrossRefGoogle Scholar
McLaughlin, P. (2001), What Functions Explain: Functional Explanation and Self-Reproducing Systems, Cambridge: Cambridge University Press.Google Scholar
Menninger, K. (1969), Number Words and Number Symbols: A Cultural History of Numbers, Cambridge, MA: MIT Press.Google Scholar
Millikan, R. G. (2003), ‘In Defense of Public Language’, in Antony, L. and Hornstein, N. (eds.), Chomsky and His Critics, Oxford: Blackwell, pp. 215–237.CrossRefGoogle Scholar
Millikan, R. G. (2004), Varieties of Meaning: The 2002 Jean Nicod Lectures, Cambridge, MA: MIT Press.CrossRefGoogle Scholar
Mises, L. von (1966), Human Action: A Treatise on Economics, third revised edition, San Francisco: Fox &Wilkes.Google Scholar
Murray, A. (1978), Reason and Society in the Middle Ages, Oxford: Clarendon Press.Google Scholar
Nesher, P. (1988), ‘Precursors of Number in Children: A Linguistic Perspective’, in Strauss, S. (ed.), Ontogeny, Phylogeny, and Historical Development, Human Development Series, Volume 7, Norwood, NJ: Ablex Publishing, pp. 106–124.Google Scholar
Nunes, T. (1999), ‘Mathematics Learning as the Socialization of the Mind’, Mind, Culture and Activity, 6 (1): 33–52.CrossRefGoogle Scholar
Nunes, T., Schliemann, A. D., and Carraher, D. W. (1993), Street Mathematics and School Mathematics, Cambridge: Cambridge University Press.Google Scholar
Peirce, C. S. (1960), Collected Papers of Charles Sanders Peirce, Volumes I and II, Cambridge, MA: Belknap Press of Harvard University Press.Google Scholar
Plunkett, S. (1979), ‘Decomposition and all that Rot’, Mathematics in School, 8 (3): 2–5.Google Scholar
Popper, K. R. (1979), Objective Knowledge: An Evolutionary Approach, revised edition, Oxford: Clarendon Press.Google Scholar
Popper, K. R. (1992), In Search of a Better World: Lectures and Essays from Thirty Years, London and New York: Routledge.Google Scholar
Potts, J. (2000), The New Evolutionary Microeconomics: Complexity, Competence and Adaptive Behaviour, Cheltenham, UK: Edward Elgar.Google Scholar
Quine, W. V. (1960), Word and Object, New York: Wiley.Google Scholar
Ross, S. and Pratt-Cotter, M. (2000), ‘Subtraction in the United States: An Historical Perspective’, The Mathematics Educator, 10 (1): 49–56.Google Scholar
Saxe, G. B. and Esmonde, I. (2004), ‘Making Change in Oksapmin Tradestores: A Study of Shifting Practices of Quantification under Conditions of Rapid Shift towards a Cash Economy’, South Pacific Journal of Psychology, 15 (1): 11–28.CrossRefGoogle Scholar
Searle, J. R. (1990), ‘Collective Intentions and Actions’, in Cohen, P. R., Morgan, J., and Pollack, M. E. (eds.), Intentions in Communication, Cambridge, MA: MIT Press, pp. 401–415.CrossRefGoogle Scholar
Searle, J. R. (1995), The Construction of Social Reality, New York: Free Press.Google Scholar
Searle, J. R. (2005), ‘What is an Institution?’, Journal of Institutional Economics, 1 (1): 1–22.CrossRefGoogle Scholar
Seidenberg, A. (1962), ‘The Ritual Origin of Counting’, Archive for History of Exact Sciences, 2 (1): 1–40.CrossRefGoogle Scholar
Sfard, A. (2008), Thinking as Communicating: Human Development, the Growth of Discourses, and Mathematizing, Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Smith, D. E. (1925), History of Mathematics, Volume 2: Special Topics of Elementary Mathematics, Boston: Ginn & Company.Google Scholar
Thomas, K. (1987), ‘Numeracy in Early Modern England’, Transactions of the Royal Historical Society, 37: 103–132.Google Scholar
Van Egmond, W. (1976), ‘The Commercial Revolution and the Beginnings of Western Mathematics in Renaissance Florence, 1300–1500’, Ph.D. thesis, Department of History and Philosophy of Science, Indiana University.Google Scholar
Vermaas, P. E. and Houkes, W. (2006), ‘Technical Functions: A Drawbridge between the Intentional and Structural Natures of Technical Artefacts’, Studies in History and Philosophy of Science, 37 (1): 5–18.CrossRefGoogle Scholar
Whitehead, A. N. (1911), An Introduction to Mathematics, New York: Henry Holt & Company.Google Scholar
Whitman, D. G. (1998), ‘Hayek Contra Pangloss on Evolutionary Systems’, Constitutional Political Economy, 9 (1): 45–66.CrossRefGoogle Scholar
Wiese, H. (2003), Numbers, Language and the Human Mind, Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Wiese, H. (2007), ‘The Co-Evolution of Number Concepts and Counting Words’, Lingua, 117 (5): 758–772.CrossRefGoogle Scholar
Zúñiga, G. L. (1999), ‘An Ontology of Economic Objects: An Application of Carl Menger's Ideas’, American Journal of Economics and Sociology, 58 (2): 299–312.CrossRefGoogle Scholar