Cooper 2012 Synthese

From Bioblast
Publications in the MiPMap
Cooper G, Humphry SM (2012) The ontological distinction between units and entities. Synthese 187:393–401.


Cooper G, Humphry SM (2012) Synthese

Abstract: 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 HΓΆlder; 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.

β€’ Bioblast editor: Gnaiger E

Selected quotes

  • "Few scientific arguments are stated more forcefully than those on nomenclature which is always rooted in history and respected by tradition. New insights give new meanings which may not always fit with earlier concepts. One should not underestimate the importance of relevant discussions. Clear words impose a discipline on mind and expressions of ideas. They help to clarify concepts until they are formulated clearly and unequivocally. Thus, names and definitions have a strong influence on thinking and analysis, and should therefore occupy a foremost place in education. They assist logical thinking in all professional activities and original work" (BiΓ©vre and Peiser 1992, p. 1536).
  • To use a specific example, 6 electrons is an aggregate of entities, whereas 6.22 kg is a magnitude of the continuous quantity called mass. This distinction holds whether we consider an electron as a materialistic entity or in terms of detectable phenomena in quantum physics; i.e. whether we are focusing on the wave or particle nature of matter.
  • Indeed, assuming a realist position, the distinction between measurement and counting is the basis of the distinction between natural numbers and real numbers.
  • In short, we enumerate aggregates of entities and measure their quantitative properties.
  • Considerable confusion is evident in metrological definitions and nomenclature regarding the distinction between entities and units.

Cited by

Gnaiger 2024 Ambiguity crisis.jpg
Gnaiger E (2024) Addressing the ambiguity crisis in bioenergetics and thermodynamics. MitoFit Preprints 2024.3.


Amount of substance, Avogadro constant, Count, Dimension, Elementary entity, Entity, International System of Units, Mass, Number, Unit, Gnaiger 2024 MitoFit 

Cookies help us deliver our services. By using our services, you agree to our use of cookies.