Can infinity have parts? What is meant by parts of infinity? If you reason it out, you will find that it is impossible. Infinity cannot be divided, it always remains infinite. If it could be divided, each part would be infinite. And there cannot be two infinites. Suppose there were, one would limit the other, and both would be finite. Infinity can only be one, undivided. Thus the conclusion will be reached that the infinite is one and not many, and that one Infinite Soul is reflecting itself through thousands and thousands of mirrors, appearing as so many different souls. It is the same Infinite Soul, which is the background of the universe, that we call God. The same Infinite Soul also is the background of the human mind which we call the human soul.

The infinite... happens to subsist in a way contrary to what is asserted by others: for the infinite is not that beyond which there is nothing, but it is that of which there is always something beyond. ...But that pertaining to which there is nothing beyond is perfect and whole. ...that of which nothing is absent pertaining to the parts ...the whole is that pertaining to which there is nothing beyond. But that pertaining to which something external is absent, that is not all ...But nothing is perfect which has not an end; and the end is a bound. On this account... Parmenides spoke better than Melissus: for the latter says that the infinite is a whole; but the former, that the whole is finite, and equally balanced from the middle: for to conjoin the infinite with the universe and the whole, is not to connect line with line.

Aristotle says the infinite is imperfect, unfinished, and therefore unthinkable; it is formless and confused. Only as objects are delimited and distinct do they have a nature.

This feature is reminiscent in my opinion, of certain features of some paintings, where each part reflects other parts and even the whole, with regard to colour, form, composition and other elements which go to make up the picture.

The above idea of the infinite shows already the breakdown of the notion that the world can be divided into separately existing parts. For already, even in this very simple view, an essential aspect of what each part is that it reflects the other parts.

The further extension of the idea of infinity to time leads to an even more radical change. Here, what is suggested is to reverse the usual idea of first imagining time and then saying that things exist and move in time. Rather, we begin with existence and process, and say that time is the order in this process. Thus we define each time concretely as the 'time when' such and such existed, or changed, and each position as the 'place where' it was etc. to carry such a view consistently, we should begin with the concept of totality, which is infinite and eternal. This includes all that there is, was and will be. If we knew this, we would all know reality. We would all know every concrete existent, every law(relationship) and the limits of every law. Of course, we can only select out certain aspects of this totality. Each science reflects some aspect, the arts another, the poet another and so on...

I protest against the use of infinite magnitude as something completed, which is never permissible in mathematics. Infinity is merely a way of speaking

Twelfthly, there is no reason or sense-perception which, since we accept an infinity undivided, utterly simple and all-embracing, will not permit also a corporeal and extended infinity.

Thirteenthly, our own surrounding space which appeareth to us so immense is neither part nor whole in relation to the infinite; nor can it be patient of infinite activity; compared to such activity, indeed, that which can be comprehended by our imbecile minds is merely nonbeing. And to a certain objection it may be replied that we base our argument for infinity not on the dignity of space but on the dignity of the natures [of worlds], since for the same reason that our space doth exist, so also should exist every other possible world; and their power of being is not actuated by our world's being, just as Elpino's power of being is not actuated by the existence of Fracastoro.

SALV. I will now say something which may perhaps astonish you; it refers to the possibility of dividing a line into its infinitely small elements by following the same order which one employs in dividing the same line into forty, sixty, or a hundred parts, that is, by dividing it into two, four, etc. He who thinks that, by following this method, he can reach an infinite number of points is greatly mistaken; for if this process were followed to (37) eternity there would still remain finite parts which were undivided.

Indeed by such a method one is very far from reaching the goal of indivisibility; on the contrary he recedes from it and while he thinks that, by continuing this division and by multiplying the multitude of parts, he will approach infinity, he is, in my opinion, getting farther and farther away from it. My reason is this. In the preceding discussion we concluded that, in an infinite number, it is necessary that the squares and cubes should be as numerous as the totality of the natural numbers [tutti i numeri], because both of these are as numerous as their roots which constitute the totality of the natural numbers. Next we saw that the larger the numbers taken the more sparsely distributed were the squares, and still more sparsely the cubes; therefore it is clear that the larger the numbers to which we pass the farther we recede from the infinite number; hence it follows [83] that, since this process carries us farther and farther from the end sought, if on turning back we shall find that any number can be said to be infinite, it must be unity. Here indeed are satisfied all those conditions which are requisite for an infinite number; I mean that unity contains in itself as many squares as there are cubes and natural numbers [tutti i numeri].

After these came to be relished, an infinite scale of infinites and s (ascending and descending always by infinite steps) was imagined and proposed to be received into geometry, as of the greatest use for penetrating into its abstruse parts. Some have argued for quantities more than infinite; and others for a kind of quantities that are said to be neither finite nor infinite, but of an intermediate and indeterminate nature.

[B]ecause that which is finite is always bounded with reference to something... it is necessary that there should be no end... [N]umber also appears to be infinite, and mathematical magnitudes, and that which is beyond the heavens. And since that which is beyond is infinite, body also appears to be infinite, and it would seem that there are infinite worlds; for why is there rather void here than there? ...If also there is a vacuum, and an infinite place, it is necessary that there should be an infinite body: for in things which have a perpetual subsistence, capacity differs nothing from being. The speculation of the infinite is, however, attended with doubt: for many impossibilities happen both to those who do not admit that it has a subsistence, and to those who do. ...It is ...especially the province of a natural philosopher to consider if there be a sensible infinite magnitude.

There is finitude — unless this were true, infinity would have no meaning. The contrast of finitude and infinity arises from the fundamental metaphysical truth that every entity involves an indefinite array of perspectives, each perspective expressing a finite characteristic of that entity. But any one finite perspective does not enable an entity to shake off its essential connection with totality. The infinite background always remains as the unanalysed reason why that finite perspective of that entity has the special character that it does have. Any analysis

Philotheo: All of this is true, and contradicts nothing we've said, rather to the contrary we've said that there are dissimilar finite parts in one infinity, and have offered considerations how this might be true. Perhaps it might be expressed proportionately, how one might have many continuous parts which form a unity, using the example and simile of liquid mud, which, though water is contiguous with water in every part, and earth with earth, smaller than we can apprehend sensibly, these are called neither discrete nor continuous, not water nor earth, but only a continuum of mud; another might like to say that since the atoms of water are not actually continuous with one another, nor earth with earth, but perhaps water with earth and earth with water; a third might disagree with both and say only mud is continuous with mud. Following these reasons it can be stated that the infinite universe is a continuum, in which discreteness is not created by the interposition of ether between the great celestial bodies, than it would be were air to be mixed and interposed among the dry and watery particles, the difference being only in the consistency of the smallest parts of the mud, beneath the level of our sensible apprehension, or in the size, greatness, and sensibility of the parts that make up our universe: and so, contrary and diverse moving parts cooperate and compose a single immobile continuum, where contraries converge to make up a single whole, achieve single order, and become one. Certainly, it would be inconvenient and impossible to imagine two infinities distinct from one another, since it would be impossible to imagine the dividing line between them, where one infinity would end and the other begin, or in what way each would terminate against the other. Moreover, it is extremely difficult to imagine two bodies which are finite and bounded on one side and infinite on the other.

Infinity, in its first form (the improper-infinite) presents itself as a variable finite [veranderliches Endliches]; in the other form (which I call the proper infinite [Eigentlich-unendliche]) it appears as a thoroughly determinate [bestimmtes] infinite.

The notion of infinity had long since been introduced into mathematics, but this infinity was what philosophers call a becoming. Mathematical infinity was only a quantity susceptible of growing beyond all limit; it was a variable quantity of which it could not be said that it had passed, but only that it would pass, all limits.

The notion of infinity had long since been introduced into mathematics, but this infinity was what philosophers call a becoming; Mathematical infinity was only a quantity susceptible of growing beyond all limit; it was a variable quantity of which it could not be said that it had passed, but only that it would pass, all limits.