The Infinite = The Infinitesimal

“Life is certain to the will-to-live; the form of life is the endless present”

This statement seems to contain within it the answer to a question I posed recently, namely, that if the will can equally be called the will-to-live, then how is the will’s purposelessness to be reconciled with its apparent striving for life? Well, in fact this issue has revealed itself to be one of semantics and, more particularly, translation. Some commentators have noted the inadequacy of the translation will-to-live as it seems to indicate that the Will is striving towards vital organic living beings and have attempted to remedy this situation by denoting it instead as “will-to-life”, which perhaps carries the same implication in it too. The resolution to this question lies in understanding that life is not the result of the Will’s willing but rather only the appearance of its willing in knowledge. It is only the second side of the Will and is taken by Schopenhauer to be completely identical with Will. This is one of my most frequent errors regarding the Schopenhauer’s metaphysics and ontology and consists simply of misapprehending the relation between the dual aspects of the world, namely, Will and representation. The relation between the two is not a causal relation as causality only obtains in the realm of representation and does not extend to relations regarding representation as a whole. Representation, as a whole, is related to the Will as mirror is related to mirrored, namely, one of manifestation, or appearance, or objectification, and the two are, in this sense, identical.

“The form of life is the endless present”

This present moment of which Schopenhauer speaks cannot be truly well defined as it is an infinitesimal occurrence, a vanishing nothingness stuck somewhere in between the vastness of both the dead past and the uncertain future. An intriguing idea is that of the identity of what is infinitesimal with what is infinite. This seems like one good conceptual way of eliminating time and space as it reduces the infinity of the universe to a particle and the eternity of time to a moment. And, it also seems to resonate nicely with mystical experience, particularly William Blake’s, which prompted his immortal utterance, “to see the world in a grain of sand, to hold eternity in my hand”. But how can this identity be demonstrated, in light of the immediate absurdity of such an idea? Well, to begin with, I posit that we do not ever truly comprehend the idea of the infinite – or even the infinitesimal – as there is no percept from life that we can draw on in order to give content to the concept of infinity. It remains perceptually no more than the upper limit to all conceivable quantity or duration. And, it is so also with the infinitesimal, which simply represents to us an empty concept designating only that lower limit of all quantity/duration. In the pursuit of clarity what, starting here, is denoted quantity is to be understood as the more general quantity/duration that allows for the treatment of both space and time in one breath. Now, the problem of quantity/duration is precisely that there does not seem to be a sensible “barrier”, so to speak, beyond which there can be no further addition or subtraction of quantity. This “seeming” that I speak of regards the intuitive a priory intellectual apprehension of the forms of space and time and it is this intuitive faculty from whence I draw my judgments concerning space and time. In other words, in our a priory apprehension of space and time, there is no reason to suspect that quantity can be limited, either from increase or decrease. So, in fact, this shows our normal conception of the infinite and the infinitesimal to be ungrounded, as it requires some sort of upper or lower limit to quantity, the very thing we have established cannot be limited at all. So, while we try to define the infinite as the largest conceivable quantity, or the limit of largeness, in truth, infinity denotes limitlessness itself. Therefore, we cannot arrive at a working and grounded conception of the infinite at all as there is nothing we can observe from our very limited point of view which can be said to be limitless. Again, the same argument hold for the infinitesimal. This concept, then, only really comes about through language and the dualities inherent in language; as there is a well grounded concept for the limited, there must equally exist a concept for the limitless, though it is never observed.

So, the identity of the infinite with the infinitesimal can perhaps be shown in that both consist of attempts to arrive at infiniteness from finiteness. A finite quantity becomes infinite in the same way as it becomes infinitesimal, that is, by losing its localization in a particular position in space and/or a moment in time. Conversely, it can be argued that to become infinitesimal is to become precisely ONE position in space and precisely ONE moment in time. However, even “one” is a quantity capable of subdivision and being infinitesimal, as we have shown, is the limitless shrinking down of quantity, or the lower limit of all quantity, and if required to sum up to anything at all would be decidedly ZERO rather than ONE. So, the argument holds that the infinite and the infinitesimal stand outside of space and/or time and signify the same thing, namely, limitlessness. However, there seems to be an inconsistency in this view as it seems to indicate that the increase of a quantity is identical with its decrease, which is assuredly absurd. But this inconsistency does not hold if we recall that increase and decrease are only ways to reach larger or smaller quantities, and by extrapolation, the hypothetical limits of quantity at both ends of the scale, which we have shown to be untenable in accordance with our basic definition of space and time. It is not increase and decrease of quantity that leads a limited thing to limitlessness, but rather the exit from space and/or time altogether. This takes place for us limited humans at those extreme ranges of our senses where no more data can be observed and recorded. So, looked at this way, the whole observable universe, taken as a whole, is outside of space, since nothing larger than it can be known, and thus we say of it that it is infinite. And equally, this present moment with which we are so familiar is, in actuality, outside of time since no smaller moment of time can be known, and thus we say of it that it is infinitesimal. This is why the mystics frequently state that the present moment is timelessness itself. And finally, this is perhaps the reason why Schopenhauer states that “the form of life is the ENDLESS present,” effectively identifying the infinitesimal with the infinite, as I have just attempted to demonstrate. “End” can only be attributed to things which have a definite duration, such that there may be other things shorter or longer than that duration with which to compare them. However, an infinitesimal moment cannot be said to be short or long and cannot even be spoken to have any duration at all, and hence, it is endless, as it is beginningless.

Leave a Reply

Your email address will not be published. Required fields are marked *