I wanted to write a post on the problem of atheism (and for some conversely theism). Atheism requires a proof comprehensively regarding reality of the non-existence of God, and that cannot be done any more than one can express all possible numbers, geometries and possible maths in some kind of order of non-order or non-cardinality.
One wonders about the relationship of mathematics to physics and expressions of the real construction of the Universe(s) and of what is the progenitor of Universes and temporality. The idea that time can be all wrapped up inside the Planck epoch with space, and that perhaps space has all potential energy then is fascinating, yet one believes that the relationship of mathematic's all-potential-maths that exist as pluralist pieces of an infinite whole or One isn't restricted to any finite context such a a very tiny bubble of space smaller than the Planck length.
As I believe God is a non-locality, so perhaps might one regard the One truly infinite mathematical series as non-local in character.
Logical sets comprising a theoretical ontology are implicity incapable of providing comprehensive evidence for atheism. Logical sets of trans-finite concepts are transfonly in relation to other infinite sets, none of which can be shown to contain all others including itself. Atheism would need to provide exhaustive data representation accurately regarding all Universal, trans-temporal and pre-Universal, before the big inflation and before any possible inflation or virtual loop, before anything ever was until the end of anything that could ever be (because of Wheeler's retro-causaliity idea) ways wherein God might exist to offer even minimal credibility (and it hasn't). Atheists to attain even a shred of credibility-for-others would need to demonstrate that human logic is capable of grasping the idea of God for-himself and negate that idea.
In the Bible the prophet Moses was allowed a small glimpse of the glory of God passing before him before he died. It isn't evident that even human philosophers are able to comprehend the nature of God or even of one Universe, as if it were a dot in infinite non-space less significant than a period at the end of a sentence.
Without such a logical set of inferences of the absolute trans-finite set that captures all sets and ideas that might be represented in sets, no reasoning about the non-existence of God could be anything more than conditional, contingent and wrong. Atheism cannot be logically proven except as an existential belief for itself held by an individual in error.
Infinite mathematical series of numbers are of much interest to philosophically inclined people. Do they really exist and what value are they since it is possible only to use a finite portion?
Gregory Cantor developed the idea of trans-infinite numbers. That means that not all infinite series are created equal, though we may be biased to believe that all truly infinite series must be eternal since if they are simply in progress of increase they are not really infinite with some sort of beginning and present terminus even if only for a fraction of an instant of time.
The series of natural numbers (positive integers) are finite in one direction; to the right, and I believe that Cantor would regard that as a trans-infinite series. What does that mean? In regard to the infinite set between the numbers 2 and 3 for example where smaller and smaller rational numbers can be expressed in fractions, the natural numbers breezes beyond it.
Infinite number series though seem to be limited and finite in some respect simply because they are not a set of all sets of any kind of number that can be represented. Even number series do not include odd numbers, and positive numbers don't include negative numbers, in fact any series of numbers or geometry is a finite slice of the infinite continuum of numbers in all forms and size.
One of the interesting characteristics of infinite sets of rational numbers is that they seem to have the potential for being implictly contradictory in time as they are expressed. Because they cannot seemingly exist a priori in infinite numbers without continuing to diminish in proportionate size retroactively from the beginning, with a kind of reverse causality, they might need to exist just in a finite temporaly context.
Numbers seem be nominal finite, proportional sets of true infinity encompassing all directions, dimensions, ordinal and cardinal sets and so forth that is inexpressible. The relationship of that infinity non-contingent One to the expression of forms in the 'real world' studied by physicists makes one wonder of the expressions of possible cosmologies in space-time by The One.
The experience of a finite element of space-time or a given Universe is a provision of from the realm of Absolute Spirit evidently, at least as a point of faith and logical inference.
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