Some time ago, I was discussing the qualitative-quantitative divide with a friend, a medical doctor, who happens to be very interested in the philosophy of science. The discussion became a debate, where we trying to get to the bottom of whether it was as I said, that the world is a qualitative entity, wherein the mind supplies quantity; or as he said, that the world has a mathematical ontology, something like the worldview championed by Meillassoux or Galileo. To be clear, I was just arguing that it could be either way, with some slightly greater likelihood that the world may not have quantity in it, apart from that supplied by the mind. By contrast, my colleague, the M.D., did not understand how it could be that there is no such thing as quantity in the world, in the sense that he could not envisage as scenario in which number does not inhere in the world. Between us was the barrier of language and experience, which was constituted in the difference between education of a physicist —though I did do a pre-med track and have interests in the philosophy of medicine— and that of a physician. We ended up settling on an example that is grounded in physiology. I will set up the groundwork for the discussion, then, give the example, and, finally, provide the resolution that has come to me only recently.
There are three good sources for anyone interested in the process of quantification: Pierre Duhem’s The Structure and Aim of Physical Theory, Enrico Fermi’s Thermodynamics, which was a lecture series given at Columbia University, and Hasok Chang’s Inventing Temperature. Primarily at issue is the fact that the process of quantification, in establishing a measurement, requires an arbitrary move in scaling. The best way to explain it in only a few words is to use Fermi’s example: What does one need to establish the amount of gravitational potential energy in an object? The beautiful subtlety that Fermi points out, and which so few others realize is that you do not simply need a location with respect to which the object has a measured height; one needs an absolutely, positively arbitrarily chosen reference point, in addition to the interval. That is, in the equation, U=mgΔy, where ‘U’ is the potential energy, ‘m’ is mass, ‘g’ is the acceleration due to gravity, and ‘Δy’ is the change in height between some surface, line, or point and the object. Most high school or undergraduate physics students —and, quite probably, not having given any thought to it, graduate students— of physics would think that everything needed is entailed in the ‘Δy’. Not so. This, now, is Fermi’s point: we often take for granted that the surface is a ‘y’ of zero units, but it might be 10 or 20, or anything, and so a third point, an arbitrary point, is required in establishing a uniformity of scale between the points of ‘Δy’, call them ‘yo’. for the object’s height, and ‘ys’, for the surface height. There is need for a ‘y*’ an arbitrary reference point, which is often implicit in problem setups and smuggled in. Here is how. By making ‘ys’ zero units, the ‘ys’ is taken to be both the arbitrary point of reference and the point from which the scaling across the interval will be performed.
There is one very important point to take away from this, that extension is a quality, unless an arbitrary point is applied to the problematic setup for determining something like gravitational potential energy. In other words, the world appears to be a qualitative entity, not inherently quantitative, which is quite an issue for the Galileos, Meillassouxs, and Tegmarks.
The example/scenario that was developed between myself and the M.D. was in regards to how the body maintains temperature. The argument posed by my counterpart was that, while the central nervous system (CNS) is an analog circuit of ions and ion channels, the hypothalamus acts like a discriminator, providing (to his knowledge) critical cutoff currents. Presumably, this has to be a quantitative relation, being that that is what a discriminator does, providing a current bias, above which a binary ‘1’ is given, below which a binary ‘0’ is given. The argument might also extend to the body surface, being that, at the time, neither of us was sure how the skin determines heat-quality sensations. A similar sensory discrimination may occur, or there may be a unit-for-unit conveying of information from environment into the body. The argument was strong, and the presumption seemed a good one. If the body qua integral part of nature was the source of quantity, then it would have seem to eliminate the implementation of quantity by consciousness, which is really what we are talking about when we say that the mind, through a constructed process, generates the notion. The sequestration of part of the world away from itself as a unit, a separate wholeness, is what quantity is. The process we have described, as it pertains to measurement (e.g., of temperature, gravitational potential energy, etc.), is the methodical process of quantification.
The key idea that wrecks the discrimination idea is proportionality. Here’s how, but an explanation of how a few physiological apparati work is necessary. That bit, above, regarding the black box of skin sensors, remember that? It turns out that heat transfer from the environment (and adjacent to the environment, i.e., the peripheral temperature of the human body) is sensed by the folding and unfolding of proteins, called TRVP1. Commensurate with the warmth and coolth of the environment/body interface, the proteins will unfurl and curl up proportionally. That’s where the proportionality issue comes in. The quality of “this” bigger than “this” does not require quantity. This should be commonsensical. For instance, visually observing that one building is taller than another requires a qualitative judgment, not measurement or any other kind of quantification. The power in science is in uniformity and method, and, being that simple sensations can be mistaken, measurements are much less likely to be in error, and so that is the purpose of quantification, so far as science is concerned. There is a pragmatic function through uniformity. In saying this, one should realize that the bodily sensorium, in all its organic capacities, can and does make errors in qualitative assessment of circumstances. The point, here, is that proportionality does not require quantification. For the sake of example, we can see this in regard to two values, call them ‘z’ and ‘x’. If for all values of ‘z’ the relation to ‘x’ remains the same, then they share a proportionality. Place rice on a balance scale. If the scale is balanced between the two sides and rice is falling onto both, we don’t know how much is falling on either, but we can determine if the amount is proportional, if the beam, for instance, remains balanced. All that is needed are placeholders, not quantities, to determine proportionality (or an inverse relation).
Coincidentally, the same argument extends to the hypothalamus, which employs proteins to determine its received signals. The denaturing of proteins and proportionalities of reactions determine hypothalamic responses in temperature regulation. So when the hypothalamus sends out signals, indicating that the vessels undergo vasoconstriction or vasodilation, proportionalities, not strict measures, are all that is needed. Without strict modes of measurement, no quantification, per se, is necessary.
What is fascinating about all of this is the consideration that the arbitrary function of “end fixing,” as Hasok Chang calls it, or arbitrary reference-point interpolation (maybe “instantiation” is a better word, here?) is necessary for the notion of quantity, yet the universe does not appear to have an Archimedean point. An Archimedean point needs to be supplied, it seems, and the human mind seems to be a natural provider of this, and so to the point of first nature, as a matter of course, and at a commonsense level. Nature does not appear to do it of its own volition, though it almost assuredly supplies the conditions for it.
The upshot to be considered is that quantity does not, it seems, appear in nature.
Note: I would like to remark upon the fact that some of the information and leads to information for this blog post were garnered from Dr. Steven A. Fink’s website, at www.professorfink.com. The site has a wealth of information, including lecture videos and other materials, as well as a little bit on the philosophy of science as it pertains to religion.
 A thorough discussion is given of these points by Fermi, so, to eliminate any lack of clarity I may have brought in trying to be terse, revert to that text.
 The astute reader, or not-so-astute reader who is familiar with my interests, will realize that this is a thoroughly Kantian mode of thought.
 This idea of quantification, built ground up, requires a very complex sort of metaphysics, which includes such ideas as “not-sameness” and other very raw and bare notions. I leave it at that, not going any further into the idea, with the understanding that these do not, in and of themselves provide quantity, due to the arbitrary step in scaling.
 This does not mean that there is necessarily something special about mind, such as suggesting dualism. What this means is that it is a possibility, but that pluralism is a real possibility. The reason for thinking so is that there are, as we find in quantification, infinitely many points of reference, all of which viable, which means that there is an infinitude of Archimedean points, not just one; and that anyone of them maybe used to ground measure and quantity.