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Surprisingly, I have not yet found a good philosophical work on the concept of "measuring" things. Though I assume one exists.

In quantum theory, of course, we encounter measurement problems, and similar problems go all the way back to Zeno or, most intriguingly to me, the fractal "Coast of England" problem. Or the evolution of a measurement for heat.

A "measurement" must take the form of an interval between two "points" or limits. And be seen from "outside" those limits, which is where infinite regresses seem to leak in. This could relate to a host of philosophical problems, but I'd like to know if there are any theories or texts that treat them as problems of "how to measure" things. Or what "measurement" means.

I feel, as usual, that there is something very basic that I'm not quite getting.

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    Measurement is a topic of philosophical interest. See for example work by Suppes suppes-corpus.stanford.edu/browse.html?c=mpm there are many articles on measurement there. See also: plato.stanford.edu/entries/measurement-science – Johannes Feb 2 '16 at 1:55
  • Thanks, I admit I haven't done my homework. But I'm looking for some reductive overview not scattered throughout philosophy of science. I'll look at your leads, thanks again. – Nelson Alexander Feb 2 '16 at 2:25
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    The three volumes of D. H. Krantz, R. D. Luce, P. Suppes, and A. Tversky. "Foundations of Measurement" are still a standard. Definitely have a look at those. – user3451767 Feb 2 '16 at 6:12
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The act of 'measuring', limiting or slowing down is something that the philosopher Gilles Deleuze has written about quite extensively. He seems to have inherited this particular concept from Leibniz, who is in some ways the inventor of the limit (which, as you correctly note, is the ground for the possiblity of measurement), and who also wrote quite a bit on the subject. It also takes on a Kantian aspect in Deleuze (like most of his concepts), whose Critique of Pure Reason (in particular the chapter 'Transcendental Aesthetic') can also be seen as a meditation on the idea of measurement (for Kant, space [and therefore measurement] is no longer a relation [e.g. between bodies] as it is in Leibniz, but the form of appearances itself).

According to Deleuze, measuring (although its not a term he uses himself, nor does it appear to have any significance in English translations of his work) is the defining gesture of science and scientific thought, and is related to the primary functives of science (functives are the things which a scientific function is made of, and functions are the objects of science):

The first functives are therefore the limit and the variable, and reference is a relationship between values of the variable or, more profoundly, the relationship of the variable, as abscissa of speeds, with the limit (What is Philosophy?: 'Functives and Concepts')

For Deleuze, the universe consists of infinitely many forms appearing and dissappearing at infinite speeds ('chaos' or 'chaosmos'). Science uses measurement to help us deal with the utterly incomprehensible chaos (hence the 'Kantian aspec') by slowing it down:

It is these first limits thaat constitute a slowing down in the chaos or the threshold of suspension of the infinite, which serve as endoreference and carry out a counting: they are not relations but numbers, and the entire theory of functions depends on numbers. We refer to the speed of light, absolute zero, the quantum of action, the Big Bang: the absolute zero of temperature is minus 273.15 degrees Centigrade, the speed of light, 299,796 kilometers per second, where lengths contract to zero and clocks stop. Such limits do not apply through the empirical value that they take on solely within systems of coordinates, they act primarily as the condition of primordial slowing down that, in relation to infinity, extends over the whole scale of corresponding speeds, over their conditioned accelerations or slowing-downs.

So to answer your question, Deleuze might say that the requirement for measuring (and he would be pleased that this question is indeed a Kantian question) is precisely the limit:

Yet it is not the limited thing that sets a limit to the infinite [thereby allowing for the possiblity of measurement] but the limit itself that makes possible a limited thing. Pythagoras, Anaximander, and Plato understood this: the limit and the inifite clasped together in an embrace from which things will come.

  • Thanks, this is a very good lead. I have all those texts, but never would have put together the right sections or flushed that out of Deleuze. Stacks at its best! – Nelson Alexander Feb 2 '16 at 13:51
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    This is also, when taken in contrast to physics and experimental sciences, a good illustration of the distinction between explanations given by philosophers and non-philosophers. – Rex Kerr Feb 2 '16 at 21:13
  • @NelsonAlexander Glad to hear it. I just remembered a volume of Leibniz's writings (translated into English) called 'The Labyrinth of the Continuum'. This contains some very interesting ideas regarding limits, measuring and length. It also reveals that the work of Galileo as an important influence on this aspect of Leibniz's thought. – M. le Fou Feb 2 '16 at 22:36
  • @RexKerr Yes, a good point. Although perhaps in this case its an explanation that could not be given within the sciences, as it takes as its object something which science presupposes and requires (measurement, or really the selection of at least two variables) – M. le Fou Feb 2 '16 at 22:45
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    @user259242 - One can still revert to examining internal consistency and simplicity of explanation for one's ideas of measurement. For example, state entanglement a la QM better explains data than pre-QM notions of measurement. You can't get outside the system, of course, but you can still find that some of your within-the-system ideas are more wrong / unhelpful than others. – Rex Kerr Feb 2 '16 at 23:42
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Surely order, and the stability of that order is neccessary for a measurement to occur? This seems to be at least a precondition for most sciences.

After all, if I measure a shoe, and it's 30cm long; and then again and it's 33cm, and then again and find it's no longer a shoe but an elephant - it's would seems then no measurement is made possible.

  • But this is precisely the problem of modern physics. Newton had to work out the calculus to "measure" motion, indeed the motion of motion or "acceleration." The measurement of heat too, it turns out, is a measure of "motions." And all motion is relative to... something. To me, the indeterminacy problem in QM carries forward the paradoxes of Zeno in the attempt to "measure" a motion. – Nelson Alexander Feb 3 '16 at 13:24
  • @nelson Alexander: Aristotle managed to analyse motion without modern calculus; actually the first part of his Physics touch on exactly 'relative to something'; you should check it out. – Mozibur Ullah Feb 4 '16 at 3:20

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