Most knowledgeable people acknowledge that theoretically, on paper at least, the concept of infinity has merit, even if it’s difficult to pin down. Some however say that this concept presents a logical contradiction. An actual infinity cannot exist and so there had to have been an “in the beginning”, a first cause, yet 1) how do you create a something from nothing and 2) what was the first cause that caused the first cause? What follows arises out of my point of view in a debate I had with an Accidental Meta-physician which I’ve edited for, hopefully, sake of clarity.
# Defining Infinity
Actually people (philosophers, mathematicians and others) do differ on the definition of infinite series, or rather the concept of infinity. Many tend to go for the philosophical or mathematical definition which has infinity as a concept, not a number. I (and others) have gone for the practical definition which is along the lines of no matter how far you go (in time or space) you can always go even farther, and farther with no end in sight.
I’ll stick to my guns that infinity exists in a practical real world sense even if not in a philosophical sense. I define infinity along the lines that if no matter how far you go (in time and/or in space) you can go farther, and farther and farther yet again and again, that’s a practical, working and real reality definition of infinity. It works for me. I could care less if it doesn’t work for others.
# Infinity and the Maximally Greatest Being (God)
My point of view remains that if the cosmos and all that it contains is infinite (in a practical sense), then there is no need for any first cause and therefore there was nothing that actually created our cosmic something. There is no requirement for a Maximally Greatest Being (i.e. – God)
Our cosmos cannot be infinite according to some like my ‘Accident Meta-physician’ therefore it was created by a Maximally Greatest Being. The cosmos had a beginning. Any Maximally Greatest Being must be eternal but cannot be infinite (since infinity is just a concept). However, any Maximally Greatest Being could NOT in itself have been created (according to my ‘Accident Meta-physician’) since you cannot create yourself. Hence, any Maximally Great Being did NOT have a beginning. Therein lies a contradiction! Two things are linked – the cosmos and your Maximally Greatest Being – as both being NOT infinite, yet one had an “in the beginning” and other did not. That makes no sense so therefore nuts to that!
# Life Eternal?
Someone who “never died” would have an infinite lifespan. An infinite lifespan could deal with an infinite series (just like a finite lifespan can deal with a finite series).
But I note here that those who advocate that an actual infinity is impossible often fail to address the concept an eternal (infinite) afterlife. Do you or do you not get life eternal or life everlasting when and if you go to Heaven? If not, then you only get a Heavenly finite afterlife. So which is it? True believers clearly must believe their Maximally Greatest Being when He says you will get eternal life or everlasting life after you depart this mortal coil, yet on the other hand they also argue or say that everlasting or eternal (synonyms for infinity) isn’t possible. So, they need to kindly clarify which point of view they logically believe in, or don’t they really understand what they are on about since their worldviews are seemingly in contradictory conflict.
Translated, my Accident Meta-physician believes that your afterlife (assuming an afterlife) will be finite which does seem to fly in the face of the Biblical words “eternal” or “everlasting”. So be it. In one sense I hope he is right for an infinite afterlife would be absolutely boring since whatever you do – I assume you do things in an afterlife – you’ll have already done it an infinite number of times before. However, that’s a separate issue from an infinite cosmos or an infinite Heaven. In an infinite cosmos, you may come into and go out of existence an infinite number of times, but you’re blessed by not having to remember all of those previous existences – which you couldn’t do in any event since the memory capacity of the brain is finite and thus couldn’t cope with an infinite number of past or previous memories.
In conclusion, one can transverse an infinite series if one is immortal and thus has an infinite amount of time to play around with. Doesn’t the Maximally Greatest Being promise life everlasting or everlasting life or eternal life or life eternal, or do you only get a finite existence in Heaven? Counting all of the digits in Pi might give those with life eternal something useful to do in their eternal afterlife.
# Infinity in Time and/or Space (i.e. – Spatial Infinity / Temporal Infinity)
If you can’t come across any boundary to the Universe then that establishes that for all practical purposes that the Universe is infinite (in space at least). A rose by any other name seems to apply here.
My little red rose whispers to me that if there are no boundaries then you have a state of foreverness and foreverness is to me and my little red rose synonymous with the term infinity or infiniteness.
Infinity means no endpoint. That in itself doesn’t preclude the cosmos being spatially or temporally infinite. I however don’t adopt the idea that the present moment constitutes an endpoint of all that preceded it. There is no such thing as “the present moment” which has to be a sort of ‘boundary’ between a no longer existing past and a not yet existing future*.
A cause producing an effect slides over an interval of time. You’re driving along, you see the green light change to yellow, you apply the brakes and you stop. You’re the clean-up batter and you see the pitcher wind up and throw the ball and you swing and you hit a home run. Each of these events slides over an interval of time. There was no “present moment”. If there is such a thing as “the present moment”, what is it? Is it five minutes duration; five seconds duration; a half-second duration; 0.05 seconds; 0.005 seconds; 0.005 seconds? Is there such a thing as “the present moment” or does the past slide into the future infinitely fast?
# Infinity in Cosmology
You can never truly know if something, like the cosmos, is infinite since there is always more left to explore. Thus, you can’t conclude either way whether the cosmos is actually infinite or not. Only if you hit a boundary, in space or in time (as in a First Cause) can you absolutely conclude the cosmos is not infinite. Just because you can never achieve an infinite journey to its conclusion doesn’t of necessity mean that infinity isn’t actually the state of affairs.
# Infinity and Cosmologists
Some say the topic of infinity does not lie within the realm of cosmology. The Accidental Meta-physician suggests that the concept of infinity lies outside of the realm of cosmology since it is just a mathematical / philosophical concept without any actual reality. Since there can be no reality to infinity, it has no place in cosmology nor should cosmologists entertain the subject.
Cosmologists might beg to differ, or not. That’s for them to decide, not anyone else.
IMHO, the concept of infinity in space and/or in time falls within the jurisdiction of cosmology and cosmologists. Obviously mathematics / philosophy and their associated mathematicians / philosophers play around with the concept too. The concept doesn’t have to be intellectually confined to this profession or that profession.
Infinity might be a mathematical/philosophical concept, but if it has relevant applications to theories about the nature of the cosmos, then infinity is fair game for cosmologists to ponder and redefine if they so feel it necessary to do so. In any event, just to repeat the obvious, what cosmologists want to ponder or not ponder is absolutely none of the concern of non-cosmologists.
Ah, but are professional cosmologists even academically qualified to ponder the mathematical/philosophical concept of the infinite? Now some cosmologists might disagree with that reasoning, or not. Again, that’s for them to debate with skeptics about. But, I’ll note in passing, to be a professional cosmologist requires extensive coursework in higher or advanced mathematics; no doubt many cosmologists have studied philosophy, especially the philosophy of science, and metaphysics. If cosmologists wish to wax lyrical about the concept of infinity, that’s their right – freedom of speech applies here. If professional mathematicians and/or professional meta-physicists wish to debate them, that’s also their right.
Repeating the obvious, it is the right of cosmologists to wax lyrical about infinity if they wish to. If every cosmologist wrote a textbook about the reality of traversing an infinite series, well somehow I think civilization would cope.
Now there is one interesting “Twilight Zone” aspect to an infinite cosmos as postulated by some cosmologists. All configurations of matter and energy would have to reoccur, and thus you and I would have to reoccur and thus we’ve had this discussion before, and before that and before that right on down the line. That also gives yet another future us something to look forward to!
# Final Thoughts & Conclusions: What Is Infinite?
1: The cosmos is all that is, was or ever will be. REASON: there is no larger structure than all that is, was or every will be. We call that largest structure the cosmos. The cosmos is 100% of all that is, was or ever will be.
2: Space is infinite. REASON: No matter how far you go out into space, you can always go farther, and farther and farther. There is no boundary that you come up against. That may not be a mathematical or metaphysical definition of infinity, but it’s a practical definition, a definition that reflects reality, not philosophical waffle. Speaking of philosophy, it also eliminates that awkward question of “what’s beyond the horizon?” There is always a beyond the horizon.
3: Time is infinite. REASON: No matter how far you go back into time, you can always go back farther, and farther and farther. There is no boundary that you come up against. Again, that may not be a mathematical or metaphysical definition of infinity, but it’s a practical definition, a definition that reflects reality, not philosophical waffle. Speaking of philosophy, it also eliminates that awkward question of “what happened before that?” No matter where you are in time, there is always a before that.
Finally, any ultra-sweeping all-inclusive statement that my pontificating is not upheld by modern science is nonsense since not all modern scientists happen to adopt the particular worldview of my ‘friend’ the Accidental Meta-physician, as interviews for example on the PBS ‘Big Questions’ TV show “Closer to Truth” more than adequately demonstrate. It is crystal clear that others can and have disputed his so-called “indisputable” reasoning.
*The alternative concept being that there is nothing else but “the present moment”. That there exists nothing other than “the present moment” is based on the logical but obvious observation that no one, no organism, nothing at all, living or non-living, has ever existed and experienced anything other than “the present moment”. That’s all she wrote since you no longer have existence in the past nor existence yet in the future.