Philosophy Of The Cosmos - From Transcendental Idealism To Cosmology
For the intended point of this post, let us consider the view of transcendental idealism, the view in which we derive all the manners in which we can perceive, represent and imagine things, according to the categories and intuitions of our own minds ' that is, although there is a reality, we can only intuit and think of it in such ways as are dictated by the respective laws of those functions which are already _inside_ the subject, as a grounds for the grounded (the perceptible).
From this view, we can derive both the infinite and general, and the finite and discrete as categories of mind (or, "of the understanding"). It makes sense, then, that in order for them to consistently coexist, considering their maximum extent in the empirical world, both an infinite universe and finite demarcations within the universe exist. Similarly, infinite discrete parts exist, themselves defined by their finite demarcations within the spacetime continuum. Additionally, as the general and discrete are categories of mind (or, "of the understanding"), both distinct parts and non-distinct wholes exist ' in effect, the reason for the existence of the particle/wave duality, as well as providing the backdrop for deduction and induction.
However, this is a working out both from the categories of mind (or, "of the understanding"), and of an assumed principle of necessary harmony ' being assumed, of course, due to the necessary unity of the understanding. Hence, if it is the case that our representations are wholly conditioned by our _a priori_ understanding, this harmony of parts with wholes, and finites with infinites, seems quite assured. And so from it, we can, in a sense, explain the order we see in the universe, from necessary conceptual grounds.
As an example of how attempting to invert the previous picture of the universe, brought together by the categories of our understanding, would be less harmonious, and more contradictory, consider the following description of such an inversion. If it is assumed that the universe is finite, with infinite divisions, then it would turn out, indeed, that the universe is infinite. Indeed, it ends up that this starting point, taken to its results, rather than assuming the assumptions without further investigation, actually leads one, necessarily, to the original picture of the universe given ' hence, they are actually identical, except the latter "inversion" is engaged in equivocation. And if we assumed all things were necessarily finite, we would be disregarding the categorical existence of infinity. And just the same, then, if we assume that the universe is infinite, without being able to place finites within that infinity, since we would then be disregarding the categorical existence of the finite.
Thus I conclude the mutual existence of finite and infinite, general and discrete, as necessary attributes of the entire spacetime in which all things must occur.
Feel free, of course, to discuss further.
'
Kyle, u 4686832.

This is kind of a side comment to Kyle's interesting main topic. In the event that there exist minds that will see this and were unaware of such a thing (assuming that other minds exists and that they indeed have awareness) then let this item be as a small contribution to them; our friend Descartes used the concept of infinity or rather that we have a concept of infinity together with the inherent and obvious limitation of our reason to bring about a currently widely rejected but nice proof for the existence of God. It is a variant on Anselm's old ontological argument and was executed like this:
Firstly, Descartes concludes that all ideas must have as much reality in their cause as in their effect. By this he means that if we have a certain idea (in this case, 'infinity'), then the thing which caused that idea must have enough power ('reality') to produce such an idea in the first place (i.e. the thing which produced the idea of 'infinity' must itself be infinite). The way he phrases this is to talk about the 'formal' and 'eminent' properties of a thing. So, if I possess a quality formally, I have it as a consequence of the way I look (my form) - such as having black hair. However, if I possess a quality 'eminently', then I possess the power to produce that quality (an example would be the quality of being strong - I do not display it all the time, but I can when I want to. So, whatever produces the idea of God must either have the quality of infinity formally (it is itself infinite), or else eminently (be able to produce that idea). Therefore, if Descartes can prove that the idea does in fact contain a real idea of infinity, then he can prove that it must have come directly from God.
This he does by arguing that the idea of God cannot be linked to ideas he has of himself, because he (Descartes) is not infinite. He also rejects the idea that the idea he has of an infinite being may have arisen by simply thinking of the opposite of a finite being (i.e. the opposite of himself), because the idea of infinity seems both more real than that of being finite, and also to have originated first (since the idea of infinity is more clear and distinct, it is a more fundamental idea than that of a finite thing, which is imperfect). He then also rejects the idea that he himself might have created an idea of his own potential infinity - i.e. becoming eventually infinitely powerful, knowledgeable, etc. - arguing that something can never become infinite by degrees, because it would only ever increase in knowledge bit by bit (and, like Zeno's arrow, never reach it's target), whereas something infinite is actually without limit.
Therefore, the idea must come from outside him, cannot have come from nowhere, must have originated from an infinite being, and must have been left there almost like a trademark when the craftsman (God) made the object (Descartes himself). Therefore, God - who contains the quality of infinity both formally (he is infinite) and eminently (he can produce the idea of infinity) is the cause of the idea.
—(Daniel u 4587729).