Abstract
A simple interpretation of quantity calculus is given. Quantities are described as two-place functions from objects, states or processes (or some combination of them) into numbers that satisfy the mutual measurability property. Quantity calculus is based on a notational simplification of the concept of quantity. A key element of the simplification is that we consider units to be intentionally unspecified numbers that are measures of exactly specified objects, states or processes. This interpretation of quantity calculus combines all the advantages of calculating with numerical values (since the values of quantities are numbers, we can do with them everything we do with numbers) and all the advantages of calculating with standardly conceived quantities (calculus is invariant to the choice of units and has built-in dimensional analysis). This also shows that the standard metaphysics and mathematics of quantities and their magnitudes is not needed for quantity calculus. At the end of the article, arguments are given that the concept of quantity as defined here is a pivotal concept in understanding the quantitative approach to nature. As an application of this interpretation of quantity calculus, an easy proof of dimensional homogeneity of physical laws is given.
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Notes
These advantages and disadvantages of computing with numerical values are clearly seen in Bridgman’s book (Bridgman 1922), which alternates masterful parts, where numerical values are important, and burdened parts, when units of measure must be included in the discussion.
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Čulina, B. A Simple Interpretation of Quantity Calculus. Axiomathes 32 (Suppl 2), 393–403 (2022). https://doi.org/10.1007/s10516-021-09609-9
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DOI: https://doi.org/10.1007/s10516-021-09609-9