Utility and Measurement (part 2 beta)

NOTICE

• May contain errors: DO NOT TRUST THE FOLLOWING
• just a survey, no new claims intended
• Blame my wife if this post is more insufficient than previous posts :)

History in Physics

• Like other metaphysical categories (space, time, whole vs. part), distinctions between quality (or intensity) and quantity (or extension) is soon relativized after clarification
• I don't know the very first appearance of "Intensive" and "Extensive" in thermodynamics literature
• Gibbs(1876) introduced "Intensive" concept, but no inclusive concept for extensive values: he just enumerated values which are proportional to volume in equilibrium
• Helmholtz(1887) explicitly referred to old metaphysicians' conception of "Extensive" and "Intensive" contrast, respectively adding "Mr. P. du Bois-Raymond named former as linear magnitude and latter as non-linear"
• Hölder(1901) presented axioms for theory of measurement
• Duhem(1911) assured mediæval roots of this metaphysical distinction (mentioned in part 1)
• Textbooks of thermodynamics: In Duhem(1902) and Planck(1903) these concepts do not appear as such
• (Added Sep 17 2013) Richard C. Tolman proposed terminology of "Extensive" and "Intensive" properties in 1917, as reported in O. Redlich(1970)
• Enswiler(1921), as an product of transitional period, use "intensity factor" and "distribution factor"
• Enswiler(1921), as an product of transitional period, use "intensity factor" and "distribution factor"
• Fermi(1937, 1956) avoids use of "Intensive-Extensive" and use homogeneity (of 0th or 1st degree) instead

History in Mathematics

• After Helmholtz and Hölder, it was widely understood that extensivity is additivity
• Measure in general needs to be built on set theory. Affected by Cantor, Henri Lebesgue and his fellow French researchers tried to define measure
• After WW2, from a order-theoretic viewpoint, Dana Scott and Patrick Suppes contributed to theory of measurement (incomplete differentiation, non-monotonic change of variables, or projection, causes information loss - probably that's the motivation for domain theory)

TODO

• detailed bibliography
• or total refinement of Math part
• Scottish Metaphysician Sir W.Hamilton (1788–1856), who appear in OED entries "Intensive" and "Extensive" is not Irish Physicist Sir William Rowan Hamilton (1805–1865)
• preview for forthcoming: How economists once abandoned ordinal/cardinal utilities and still use them today? Stay tuned