A Simple Interpretation of Quantity Calculus

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A simple interpretation of quantity calculus is given. Quantities are described as 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 notational simplification is that we consider units 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 classically conceived quantities (calculus is invariant to the choice of units and has built-in dimensional analysis). This also shows that the whole metaphysics of the common concept of quantities and their magnitudes is irrelevant to quantity calculus. As an application of this interpretation of quantity calculus, an easy proof of dimensional homogeneity of physical laws is given.
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Archival date: 2020-08-28
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