, Volume 187, Issue 2, pp 393–401 | Cite as

The ontological distinction between units and entities

  • Gordon CooperEmail author
  • Stephen M. Humphry


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.


Measurements Quantity Units Count of entities Ontology Epistemology 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Andrich D. (2003) On the distribution of measurements in units that are not arbitrary. Social Science Information 42: 557–589CrossRefGoogle Scholar
  2. Berka K. (1983) Measurement: its concepts, theories and problems. Boston series in the philosophy of science, 72. Reidel Publishing Company, HollandGoogle Scholar
  3. Biévre P. D., Peiser H. S. (1992) ‘Atomic Weight’: the name, its history, definition and units. Pure and Applied Chemistry 64: 1535–1543CrossRefGoogle Scholar
  4. BIPM (2006). Bureau International des Poids et Mesures—Système International d’Unité s (SI). (Organisation Intergouvernementale de la Convention du Mètre).Google Scholar
  5. BIPM (2008). Bureau International des Poids et Mesures—Vocabulaire international de métrologie (VIM) (Organisation Intergouvernementale de la Convention du Mètre).Google Scholar
  6. de Boer J. (1994/95) On the history of quantity calculus and the International system. Metrologia 31: 405–429CrossRefGoogle Scholar
  7. Duncan O. D. (1984) Notes on social measurement: Historical and critical. Russell Sage Foundation, New YorkGoogle Scholar
  8. Emerson W. H. (2004a) One as a ‘Unit’ in expressing the magnitudes of quantities. Metrologia 41: 26–28CrossRefGoogle Scholar
  9. Emerson W. H. (2004b) On the algebra of quantities and their units. Metrologia 45: 134–138CrossRefGoogle Scholar
  10. Emerson W. H. (2008) On quantity calculus and units of measurement. Metrologia 45: 134–138CrossRefGoogle Scholar
  11. 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: 1–64Google Scholar
  12. Michell J. (1999) Measurement in psychology. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  13. Michell J. (2003) Measurement: A beginner’s guide. Journal of Applied Measurement 4: 298–308Google Scholar
  14. Michell, J. (2007). Measurement. In P. T. Turner & W. R. Mark (Eds.), Handbook of the philosophy of science. Elsevier.Google Scholar
  15. 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.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.The University of Western AustraliaCrawleyAustralia

Personalised recommendations