A forgotten lesson ...

Aristotle

Aristotle (Metaphysics XIII) on the reification of the mathematical:

'It is said that the objects of mathematics—i.e. numbers and lines and the like—are substances,' and some say moreover 'that the mathematical substances are the only substances.' But conclusions contrary to the truth follow, 'if one supposes the objects of mathematics to exist thus as separate entities. For if they exist thus they must be prior to sensible spatial magnitudes, but in truth they must be posterior; for the incomplete spatial magnitude is in the order of generation prior, but in the order of substance posterior, as the lifeless is to the living ...'

'Grant that they are prior in formula. Still not all things which are prior in formula are prior in substance. For those things are prior in substance which when separated from other things surpass them in the power of independent existence, but those arc prior in formula out of whose formulae the formulae of other things are compounded; and these two properties are not coextensive. For if attributes, such as "moving" or "white," do not exist apart from their substances, the white is prior to the white man in formula, but not in substance. For it cannot exist separately, but is always along with the concrete thing; and by the concrete thing I mean the white man. Therefore it is plain that neither is the result of abstraction prior nor that which is produced by adding determinants posterior; for it is by adding a determinant to the white that we speak of the white man.'

Chomsky on today's materialism ...

Chomps

What Kind of Creatures Are We? (Columbia UP, 2016) is Noam Chomsky's latest (and perhaps last-est) word on philosophy's big questions. The final chapter of the book is an exercise in what Aristotelians call philosophy of nature, an intermediary discipline between metaphysics and science. There Chomsky argues that the terms material, physical, natural (et al) are basically meaningless nowadays. (And what, then, is it to be a materialist, a physicalist, a naturalist? Cf. the  posts on Galen Strawson here, here, and here.) See, 'we speak of the "physical" world much as we speak of the "real" truth: for emphasis, but adding nothing' (What Kind of Creatures Are We?, p. 105).

'[T]he notions of body, material, physical are hardly more than honorific designations for what is more or less understood at some particular moment in time, with flexible boundaries and no guarantee that there will not be radical revision ahead, even at its core' (ibid., p. 102).

'[T]he concept "physical facts" means nothing more than what the best current scientific theory postulates, hence should be seen as a rhetorical device of clarification, adding no substantive content' (ibid., p. 125). 

Whatever happened to the 'substantive content'? As metaphysicians of matter, the early modern revolutionaries were mechanists.* What does that mean? Chomsky understands the mechanical as that which 'an artisan could construct' (ibid., p. 91). This is correct, inasmuch as all that's mechanical is (theoretically) constructible, but it doesn't get to the centre of the question. At the centre is this: the early modern understanding of matter (or of that which is material) was dysteleologico-nominal. What does that mean? It's helpful to look back to the later mediæval metaphysics, against which Kepler, Galileo, Descartes (and so on) positioned themselves. For Aristotelian metaphysicians, such as Aquinas and Scotus, the difference between an organism and an artefact is teleologico-essential. That is to say, an organism (an example of physis) has an intrinsic teleology and a substantial form, and is in this sense autotelic; whereas an artefact (a product of techne) has an extrinsic teleology and an accidental form, and is in this sense exotelic. The bisect that's made here isn't at all trivial. Its consequences are both intensive and extensive. (Take an example: the causation manifest in an organism is both immanent and transient—immanent in that it begins with the organism and terminates in the organism for the sake of the organism, to adapt David Oderberg—whereas that manifest in an artefact is transient simpliciter.) But here's the kicker, these teleologico-essential concepts (themselves the centuries-absent 'substantive content') are irreducibly qualitative, and the early moderns argued that the material world is to be understood in a reductively quantitative way. They therefore rejected these concepts as immaterial, nonphysical, supernatural, etc., necessitating substance dualism. The upshot is that, armed with mathematism, techne drove physis out of the cosmos altogether, and God was demoted from actus purus to artifex maximus, a supersmart artificer-demiurge. (Whence Pascal's criticisms of  Cartesianism qua proto-deism, a philosophy which would've liked to do without God, but 'couldn't help allowing him a flick of the finger to set the world in motion.' Cf. Kierkegaard: 'In scientific distraction people made God into a rather stupid God.') There are inferior man-made machines (e.g. levers and pulleys and cathode-ray tubes) and there are superior God-made machines (e.g. molecules and plants and animals)—that's all.†

[Off-piste addendum: 'History is written by the winners.' We're repeatedly told in the textbooks that scientists (qua scientists) discovered that the world was dysteleologico-nominal. But how could that be? No, that the world is thus-and-so was a conceptual decision, not (per absurdum) an empirical discovery.]

Note that we're still mechanists today, inasmuch as we're still dysteleologico-nominal. The atomistic (or corpuscular) push-pull causation, the Cartesian contact mechanics, and so on, gave place to the conclusions of the Newtonian and quantum-theoretic revolutions. But these are internal revolutions, internal to a subsisting mathematism.

What's frustrating is that the same philosophers who tell us that the terms 'material,' 'physical,' 'natural' are empty husks, e.g. Bertrand Russell, try to feed them to us as good eating nonetheless—an aporia. Chomsky picks up on this, noting that when Russell says 'experience is "part of the material of the physical world," ' this means 'no more than "part of the world" ' (ibid., p. 102). Thus Chomsky suggests 'simply dropping the words "matter" and "physical" ' (ibid., p. 105), and that's a start. What comes next?

In the end Chomps himself retires to a mysterianism, believing that there are probably 'ultimate secrets that will ever remain in obscurity, impenetrable to human intelligence' (ibid., p. 127). For 'if we are biological organisms, not angels, much of what we seek to understand might lie beyond our cognitive limits ... There is no reason to believe that humans can solve every problem they pose or even that they can formulate the right questions; they may simply lack the conceptual tools, just as rats cannot deal with a prime number maze' (ibid., pp.104-5). His position is not unlike Pascal's:

'Let us then realise our limitations. We are something and we are not everything ... Our intelligence occupies the same rank in the order of intellect as our body in the whole range of nature. Limited in every respect, we find this intermediate state between two extremes reflected on all our faculties. Our senses can perceive nothing extreme; too much noise deafens us, too much light dazzles; when we are too far or too close we cannot see properly; an argument is obscured by being too long or too short; too much truth bewilders us ... In a word, extremes are as if they did not exist for us nor we for them; they escape us or we escape them.' 

'Such is our true state. That is what makes us incapable of true knowledge or absolute ignorance. We are floating in a medium of vast extent, always drifting uncertainly, blown to and fro; whenever we think we have a fixed point to which we can cling and make fast, it shifts and leaves us behind; if we follow it, it eludes our grasp, slips away, and flees eternally before us. Nothing stands still for us. This is our natural state and yet the state most contrary to our inclinations. We burn with desire to find a firm footing, an ultimate, lasting base on which to build a tower rising up to infinity, but our whole foundation cracks, and the earth opens up into the depth of the abyss.' (Pensée 199)

* 'The label "mechanistic philosophy" or "mechanicism" should be handled with care, as it was not employed by the novatores themselves' (Cees Leijenhorst, The Mechanisation of Aristotelianism, p. 6).

†A difference of degree, not kind; the definition of God-made machines is comparatively compounded (e.g. 'machinam hydraulico-pneumatico-pyriam'). Leibniz: 'An organism is formally nothing other than a mechanism, even if it is more exquisite and divine.' Herr Leibniz would later try to restore full godhead (to the all-too-human demigod of the moderni) by infinitizing the mechanical complexity of God's machines. See, for example, Guido Giglioni's Automata Compared.

Pointer readings ...

Eddington and friends

From Sir Arthur Eddington's The Nature of the Physical World:

'Let us then examine the kind of knowledge which is handled by exact science. If we search the examination papers in physics and natural philosophy for the more intelligible questions we may come across one beginning something like this: "An elephant slides down a grassy hillside…" The experienced candidate knows that he need not pay much attention to this; it is only put in to give an impression of realism. He reads on: "The mass of the elephant is two tons." Now we are getting down to business; the elephant fades out of the problem and a mass of two tons takes its place. What exactly is this two tons, the real subject matter of the problem? It refers to some property or condition which we vaguely describe as "ponderosity" occurring in a particular region of the external world. But we shall not get much further that way; the nature of the external world is inscrutable, and we shall only plunge into a quagmire of indescribables. Never mind what the two tons refers to; what is it? How has it actually entered in so definite a way into our experience? Two tons is the reading of a pointer when the elephant was placed on a weighing-machine. Let us pass on. "The slope of the hill is 60˚." Now the hillside fades out of the problem and an angle of 60˚ takes its place. What is 60˚? There is no need to struggle with mystical conceptions of direction; 60˚ is the reading of a plumb-line against the divisions of a protractor. Similarly for the other data of the problem. The softly yielding turf on which the elephant slides is replaced by a coefficient of friction, which though perhaps not directly a pointer reading is of kindred nature. No doubt there are more roundabout ways used in practice for determining the weights of elephants and the slopes of hills, but these are justified because it is known that they give the same results as direct pointer readings.' 

'And so we see that the poetry fades out of the problem, and by the time the serious application of exact science begins we are left with only pointer readings. If then only pointer readings or their equivalents are put into the machine of scientific calculation, how can we grind out anything but pointer readings? But that is just what we do grind out. The question presumably was to find the time of descent of the elephant, and the answer is a pointer reading on the seconds’ dial of our watch.' 

'The triumph of exact science in the foregoing problem consisted in establishing a numerical connection between the pointer reading on the weighing-machine on one experiment on the elephant and the pointer reading on a watch in another experiment. And when we examine critically other problems of physics we find that this is typical. The whole subject matter of exact science consists of pointer readings and similar indications' (p. 127).