Axiomathes (online first) (2022)

Boris Culina
University of Applied Sciences Velika Gorica, Croatia
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.
Keywords Quantities  Units  Quantity calculus  Dimensional homogeneity
Categories (categorize this paper)
Reprint years 2022
DOI 10.1007/s10516-021-09609-9
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

 PhilArchive page | Other versions
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Absolutism Vs Comparativism About Quantity.Shamik Dasgupta - 2013 - Oxford Studies in Metaphysics 8:105-150.
Quantitative Properties.M. Eddon - 2013 - Philosophy Compass 8 (7):633-645.
Foundational Aspects of Theories of Measurement.Dana Scott & Patrick Suppes - 1958 - Journal of Symbolic Logic 23 (2):113-128.
Zero-Value Physical Quantities.Yuri Balashov - 1999 - Synthese 119 (3):253-286.
A Set of Independent Axioms for Extensive Quantities.Patrick Suppes - 1951 - Portugaliae Mathematica 10 (4):163-172.

View all 7 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Quantity and Quantity Value.Luca Mari & Alessandro Giordani - 2012 - Metrologia 49 (6):756-764.
Quantity and Quantity Value.Alessandro Giordani & Luca Mari - 2011 - Proc. TC1-TC7-TC13 14th IMEKO Joint Symposium.
Dimensions.S. Sterrett - 2021 - In Eleanor Knox & Alistair Wilson (eds.), The Routledge Companion to Philosophy of Physics. Routledge.
Invariance, Interpretation, and Motivation.Thomas Møller-Nielsen - 2017 - Philosophy of Science 84 (5):1253-1264.
Quantities, Magnitudes, and Numbers.Henry E. Kyburg - 1997 - Philosophy of Science 64 (3):377-410.
Quantity and Number.James Franklin - 2014 - In Daniel D. Novotný & Lukáš Novák (eds.), Neo-Aristotelian Perspectives in Metaphysics. New York, USA: Routledge. pp. 221-244.
On the Input of a Measurement Process.Luca Mari & Alessandro Giordani - 2015 - Journal of Physics: Conference Series 588:1-6.
Metaphysics of Quantity and the Limit of Phenomenal Concepts.Derek Lam - 2018 - Inquiry: An Interdisciplinary Journal of Philosophy (3):1-20.
Quantities in Quantum Mechanics.John Forge - 2000 - International Studies in the Philosophy of Science 14 (1):43 – 56.
Properly Extensive Quantities.Zee R. Perry - 2015 - Philosophy of Science 82 (5):833-844.
Definitions and Units in Mechanics.J. Gibson Winans - 1976 - Foundations of Physics 6 (2):209-219.
Intrinsic Explanations and Numerical Representations.M. Eddon - 2014 - In Robert M. Francescotti (ed.), Companion to Intrinsic Properties. De Gruyter. pp. 271-290.


Added to PP index

Total views
219 ( #51,752 of 2,506,156 )

Recent downloads (6 months)
79 ( #9,955 of 2,506,156 )

How can I increase my downloads?


My notes