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The ontological distinction between units and entities

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The base units of the SI include six units of continuous quantities and the mole, which is defined as proportional to the number of specified elementary entities in a sample. The existence of the mole as a unit has prompted comment in Metrologia that units of all enumerable entities should be defined though not listed as base units. In a similar vein, the BIPM defines numbers of entities as quantities of dimension one, although without admitting these entities as base units. However, there is a basic ontological distinction between continuous quantities and enumerable aggregates. The distinction is the basis of the difference between real and natural numbers. This paper clarifies the nature of the distinction: (i) in terms of a set of measurement axioms stated by Hölder; and (ii) using the formalism known in metrology as quantity calculus. We argue that a clear and unambiguous scientific distinction should be made between measurement and enumeration. We examine confusion in metrological definitions and nomenclature concerning this distinction, and discuss the implications of this distinction for ontology and epistemology in all scientific disciplines.

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  • Andrich D. (2003) On the distribution of measurements in units that are not arbitrary. Social Science Information 42: 557–589

    Article  Google Scholar 

  • Berka K. (1983) Measurement: its concepts, theories and problems. Boston series in the philosophy of science, 72. Reidel Publishing Company, Holland

    Google Scholar 

  • Biévre P. D., Peiser H. S. (1992) ‘Atomic Weight’: the name, its history, definition and units. Pure and Applied Chemistry 64: 1535–1543

    Article  Google Scholar 

  • BIPM (2006). Bureau International des Poids et Mesures—Système International d’Unité s (SI). (Organisation Intergouvernementale de la Convention du Mètre).

  • BIPM (2008). Bureau International des Poids et Mesures—Vocabulaire international de métrologie (VIM) (Organisation Intergouvernementale de la Convention du Mètre).

  • de Boer J. (1994/95) On the history of quantity calculus and the International system. Metrologia 31: 405–429

    Article  Google Scholar 

  • Duncan O. D. (1984) Notes on social measurement: Historical and critical. Russell Sage Foundation, New York

    Google Scholar 

  • Emerson W. H. (2004a) One as a ‘Unit’ in expressing the magnitudes of quantities. Metrologia 41: 26–28

    Article  Google Scholar 

  • Emerson W. H. (2004b) On the algebra of quantities and their units. Metrologia 45: 134–138

    Article  Google Scholar 

  • Emerson W. H. (2008) On quantity calculus and units of measurement. Metrologia 45: 134–138

    Article  Google Scholar 

  • Hölder O. (1901) Die Axiome der Quantität und die Lehre vom Mass. Berichte über die Verhandlungen der Königlich Sachsischen Gesellschaft der Wissenschaften zu Leipzig. Mathematische-Physicke Klasse 53: 1–64

    Google Scholar 

  • Michell J. (1999) Measurement in psychology. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Michell J. (2003) Measurement: A beginner’s guide. Journal of Applied Measurement 4: 298–308

    Google Scholar 

  • Michell, J. (2007). Measurement. In P. T. Turner & W. R. Mark (Eds.), Handbook of the philosophy of science. Elsevier.

  • Petley, B. W. 1992. The continuing evolution in the definitions and realizations of the SI units of measurement. In: L. Crovini & T. J. Quinn (Eds.), Proceedings of the international school of Physics, course CX. North-Holland: Elsevier Science Publishers B.V.

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Correspondence to Gordon Cooper.

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Cooper, G., Humphry, S.M. The ontological distinction between units and entities. Synthese 187, 393–401 (2012).

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