In my paper I write about numeric values being "derived from measurement" prior to assumptions about arithmetic or magnitude. A measurement involves two things. Typically one is variable and the other is "constant" or in some way standardized. The constant is derived from the variable.
For a range of standardized items (constants) if you can run through them and stop when you find a match, that is one way to measure. Any function from the variables to the constants is a measurement.
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