The Reign of Quantity and The Signs of the Times

2 Materia Signata Quantitate

The scholastics gave the name materia, generally speaking, to what Aristotle had called ὕλη; but this materia, as has already been said, must in no way be identified with the ‘matter’ of the moderns, for the idea of ‘matter’, complex and even in some ways contradictory as it is, seems to have been as strange to the ancient Westerners as it still is to Easterners. Even admitting that materia can become ‘matter’ in certain special cases, or rather to be more accurate, that the more recent conception can be made to fit into the earlier one, materia nevertheless includes many other things at the same time, and it is these other things that must be carefully distinguished from ‘matter’; but for the purpose of naming them as a group by some comprehensive term like ὕλη or materia, we have no better word at our disposal in Western languages than the word ‘substance’. In any case, ὕλη, as a universal principle, is pure potency in which nothing is distinguished or ‘actualized’, and it constitutes the passive ‘support’ of all manifestation; it is therefore, taken in this sense, precisely Prakriti or universal substance, and everything that has been said elsewhere about Prakriti applies equally to ὕλη thus understood.[5] Substance, understood in a relative sense as being that which represents analogically the substantial principle and plays its part in relation to a more or less narrowly restricted order of existence, furnishes the term ὕλη with a secondary meaning, particularly when this term is correlated with εἶδος, to designate the two sides, essential and substantial, of particular existences.

The scholastics, following Aristotle, distinguish these two meanings by speaking of materia prima and materia secunda, so that it can be said that their materia prima is universal substance and their materia secunda is substance in the relative sense; but, since terms become susceptible of multiple applications at different levels as soon as the relative is considered, what is materia at a certain level can become forma at another, and inversely, according to the more or less particularized hierarchy of the degrees of manifested existence under consideration. In no case is a materia secunda pure potency, although it may constitute the potential side of a world or of a being; universal substance alone is pure potency, and it is situated not only beneath our world (substantia, from sub stare, is literally ‘that which stands beneath’, a meaning also attached to the ideas of ‘support’ and ‘substratum’), but also beneath the whole of all the worlds and all the states comprised in universal manifestation. In addition, for the very reason that it is potentiality, absolutely ‘undistinguished’ and undifferentiated universal substance is the only principle that can properly be said to be ‘unintelligible’, not merely because we are not capable of knowing it, but because there is actually nothing in it to be known; as for relative substances, insofar as they participate in the potentiality of universal substance, so far do they also participate in its ‘unintelligibility’. Therefore the explanation of things must not be sought on the substantial side, but on the contrary it must be sought on the essential side; translated into terms of spatial symbolism, this is equivalent to saying that every explanation must proceed from above downward and not from below upward; and this observation has a special relevance at this point, for it immediately gives the reason why modern science actually lacks all explanatory value.

Before going further it should be noted here that the physicists’ ‘matter’ can in no case be anything but a materia secunda, since the physicists regard it as being endowed with properties, on the nature of which they are incidentally not entirely in agreement, so that their ‘matter’ is not potentiality and ‘indistinction’ and nothing else besides; moreover, as the physicists’ conceptions relate to the sensible world and do not go beyond it, they would not know what to do with the conception of a materia prima. Nonetheless, by a curious confusion, they talk all the time of ‘inert matter’, without noticing that if it were really inert it would have no properties and would not be manifested in any way, so that it could have no part in what their senses can perceive; nevertheless they persist in pronouncing everything that comes within range of their senses to be ‘matter’, whereas inertia can actually only be attributed correctly to materia prima, because it alone is synonymous with passivity or pure potentiality. To speak of the ‘properties of matter’ while asserting at the same time that ‘matter is inert’ is an insoluble contradiction; and, by a strange irony, modern ‘scientism’, which claims to eliminate all ‘mystery’, nonetheless appeals in its vain attempts at explanation only to the very thing that is most ‘mysterious’ in the popular sense of the word, that is to say most obscure and least intelligible!

The question now arises, after setting aside the supposed ‘inertia of matter’ as being really no more than an absurdity, whether ‘matter’, endowed as it is with the more or less defined qualities that enable it to be manifested to our senses, is the same thing as the materia secunda of our world as understood by the scholastics. Doubt will at once arise as to the validity of any such assimilation, if it be noted that the materia secunda in question, if it is to play a part in relation to our world analogous to that played by materia prima or universal substance in relation to all manifestation, must in no way be manifested in this world itself, but can only serve as ‘support’ or ‘root’ to whatever is manifested therein, and that in consequence, sensible qualities cannot be inherent in it, but on the contrary must proceed from ‘forms’ implanted in it; and this again amounts to saying that anything that is quality must necessarily be referred to essence. Here a new confusion makes its appearance: modern physicists, in their efforts to reduce quality to quantity, have arrived by a sort of ‘logic of error’ to the point of confusing the two, and thence to the attribution of quality itself to their ‘matter’ as such; and they end by assigning all reality to ‘matter’, or at least all that they are capable of recognizing as reality: and it is this that constitutes ‘materialism’ properly so called.

Nevertheless, the materia secunda of our world cannot be devoid of all determination, for if it were so it would be inseparable from the materia prima itself in its complete ‘indistinction’; neither can it be a sort of generalized materia secunda, for it must be determined in accordance with the special conditions of this world, in such a way that it can effectively play the part of substance in relation to this world in particular, and not in relation to anything else. The nature of this determination must then be specified, and this is what Saint Thomas Aquinas does when he defines this particular materia secunda as materia signata quantitate; quality is therefore not inherent in it and is not that which makes it what it is, even if quality is considered only in relation to the sensible order; its place is taken by quantity, which thus really is ex parte materiæ. Quantity is one of the very conditions of existence in the sensible or corporeal world; it is the condition that belongs most exclusively of all to that world; therefore, as might have been expected, the definition of the materia secunda in question cannot concern anything other than this world, but it must concern this world as a whole, for everything that exists in this world is necessarily subject to quantity. The definition given is therefore fully sufficient, and there is no need to attribute to materia secunda, as has been done to modern ‘matter’, properties that can in no way really belong to it. It can be said that quantity, regarded as constituting the substantial side of our world, is as it were its ‘basic’ or fundamental condition: but care must be taken not to go too far and attribute to it an importance of a higher order than is justifiable, and more particularly not to try to extract from it the explanation of this world. The foundation of a building must not be confused with its superstructure: while there is only a foundation there is still no building, although the foundation is indispensable to the building; in the same way, while there is only quantity there is still no sensible manifestation, although sensible manifestation has its very root in quantity. Quantity, considered by itself, is only a necessary ‘presupposition’, but it explains nothing; it is indeed a base, but nothing else, and it must not be forgotten that the base is by definition that which is situated at the lowest level, so that the reduction of quality to quantity is intrinsically nothing but a ‘reduction of the higher to the lower’, and some have very rightly attributed this very character to materialism: to claim to derive the ‘greater’ from the ‘lesser’ is indeed one of the most typical of modern aberrations.

One further question presents itself: we meet with quantity under diverse modes, and in particular as discontinuous quantity, which is nothing but number,[6] and as continuous quantity, which is principally represented by spatial and temporal magnitudes; among all these modes, which is the one that can most accurately be called pure quantity? This question has its importance, all the more so because Descartes, whose place is at the starting-point of many specifically modern philosophical and scientific conceptions, tried to define matter in terms of extension, and to make his definition the principle of a quantitative physics, which though not yet quite ‘materialism’, was at least ‘mechanism’, and it might be tempting to draw the conclusion that extension, as being directly inherent in matter, represents the fundamental mode of quantity. On the other hand, Saint Thomas Aquinas, when he says that numerus stat ex parte materiae, seems rather to suggest that number constitutes the substantial basis of this world, and therefore that it is number that must properly be looked on as pure quantity; and the attribution of a ‘basic’ character to number is in perfect agreement with the fact that in the Pythagorean doctrine number is taken, by inverse analogy, as the symbol of the essential principles of things. It should be noted too that the ‘matter’ of Descartes is no longer the materia secunda of the scholastics; it is on the other hand an example, perhaps the earliest in point of date, of the modern physicists’ ‘matter’, although Descartes’ notion did not then include all that his successors were gradually to incorporate in it in order to arrive at the most recent theories of the ‘constitution of matter’. There is therefore reason to suspect that there may be some error or confusion in the Cartesian definition of matter, and that some element not of a purely quantitative order must have slipped into it at that stage, perhaps unsuspected by its originator: the nature of his error will be made clear in chapter 4, where we shall see that extension, although it is obviously quantitative in character, like everything else belonging to the sensible world, cannot be regarded as pure quantity. It may also be observed that the theories which go farthest in the direction of a reduction to the quantitative are generally ‘atomistic’ in one way or another, that is to say they introduce discontinuity into their notion of matter in such a way as to bring it into much closer relation to the nature of number than to that of extension; and the very fact that the material from which bodies are formed cannot in any case be conceived otherwise than as extended is never anything but a source of contradictions in all ‘atomism’. Another cause of confusion is the habit that has grown up of considering ‘body’ and ‘matter’ as nearly synonymous; actually, bodies are in no sense materia secunda, which is not met with anywhere in the manifested existences of this world, bodies only proceeding from it as from their substantial principle. But number, like materia secunda, is never perceived directly and in a pure state in the corporeal world, and it is number that must without doubt be considered primarily as constituting the fundamental mode in the domain of quantity; the other modes of quantity are only derived from number, that is to say they are so to speak only quantity by virtue of their participation in number: and this is implicitly recognized whenever it is maintained, as in fact it always is, that everything quantitative must be expressible in terms of number. In these other modes, even when quantity is the predominant element, it always appears as more or less mixed with quality; thus it is that the conceptions of space and of time, despite the efforts of modern mathematicians, can never be exclusively quantitative, unless indeed it be accepted that they must be reduced to entirely empty notions, without contact with any kind of reality; and is not the science of today in actual fact made up to a large extent of such empty notions, purely ‘conventional’ in character and without the least effective significance? This last question must be more fully dealt with, especially so far as it concerns the nature of space, for this aspect of the question is very closely connected with the principles of geometrical symbolism, while at the same time it provides an excellent example of the degeneration that traditional conceptions must undergo in order to become profane conceptions; the procedure will be to examine first of all how the conception of ‘measure’, the very foundation of geometry, can be transposed, in a traditional sense, in such a way as to give it a significance quite other than that which modern scientists attach to it, for they only see in ‘measure’ a means for getting as near as they can to their topsy-turvy ‘ideal’, which seeks to bring about by degrees the reduction of all things to quantity.