Parodites mentioned this video and I think this is worthy of discussion. Professor Doron here is saying that infinity doesn’t exist and is not meaningful, and that mathematics can be and needs to be reconstructed solely based on finitisms.

As far as I can tell his only evidence or explanation for the non-existence and meaninglessness of infinity either as a reality or as a concept is that it doesn’t make sense to him. He (seems to) think it is really that simple. He sees infinity as analogous to belief in God, a kind of dogma without evidence. Maybe useful at times, but unnecessary and ultimately wrong. But where is his actual explanation for this? I haven’t been able to find it yet.

To me, infinity seems more like a conceptual placeholder, an idea we use because we are able to understand the notion of something continuing without an end, at least in theory. It’s quite easy to say there is no such thing as infinity in reality, while still using infinity as a concept to represent the idea of “continuing without an end”.

Dr. Doran thinks there are a finite number of integers, for example, and he says there is one “largest possible integer” although he admits not knowing what it is. To me this is crazy, since we can define integers based on their additive property. An integer can always be added to another previous integer that came before it, to produce a still-larger integer, thus expanding the sequence. We don’t need to limit the concept of numbers or integers to representing real things in reality, as if every number has to mean “represents X things in reality”. I can say “2” without needing this “2” to refer to any two specific things in the world. 2 can simply mean 2, which also means 1+1, which also means 3-1, etc.

@Parodites, can you explain why you think Dr. Doron is correct? And how would we rescue things like calculus if we throw out the notion of infinity? Infinity can simply represent the notion of approaching a limit, an asymptote, or a series without a defined terminus. Calculus makes use of infinity as a limit in order to allow us to figure out area under a curve, for example. This is highly useful and apparently is perfectly accurate, so what is the objection to this use of “infinity”? And what alternative is there to find the area under a curve if we don’t use calculus, and why would this alternative be superior if the calculus method gives the correct answer?

Another point that needs addressing: what about the supposed “actual” infinity of existence itself? We can reject ideas of first cause or original cause, at least insofar as this means to imply an Ultimate Beginning before which there was literally nothing. Such a notion is irrational and supposes a contradiction as violation of the principle of sufficient reason. No “uncaused” things can exist, period. That is pretty much the basis for the foundation of logic/reason itself.

But as Kant pointed out, the idea of an infinite past or infinite future is also irrational, or at least it SEEMS irrational. Just because it seems irrational doesn’t mean it is, and I could argue that infinite past or future is the only rational option because of 1) the irrationality of first cause and 2) no other possibility exists except for infinite past/future [[although there is a possible (3) in self-causation, as if perhaps existence caused its own existence, but this appears to be irrational too since it violates the idea of time as relates to what causation means (how can something cause itself, if at the point it is acting as a cause for itself “itself” doesn’t yet exist? It would need to exist before it exists). This might be resolved by removing the typical understanding of time and replacing it with something like a pure logical abstraction of spatiality in a higher dimension where “time” is irrelevant. But then we would need to actually find what this higher dimensional plane of pure logic is and why it is the case that it is self-causing. Perhaps there is some kind of blueprint in existence at the level of pure logic that explains exactly how existence itself is self-causing on a higher pure spatiality dimension, thus declining in steps into lower dimensions until finally arriving at the existence of “time” and the formation of our actual universe.]]

But I do understand the counter-point that this doesn’t make sense, and infinity itself is nonsensical insofar as we are required to more or less suspend our critical thinking and just abstract a vague idea of “continues without end…” without really thinking more about it. In that way it does seem similar to a dogma, as Dr. Doron was saying.

So, is it the case that existence in the most general and basic sense has “always” existed? To me it seems like we need to accept this as true, if for no other reason that the alternative seems insane and unthinkable. Then what? We can attempt to re-evaluate our understanding of infinity to help smooth out the difficulties, for example perhaps a paradigm shift is needed similar to moving from a visualization of a flat plane to one of a sphere, and “infinity” might simply mean “the ability to keep going in one direction forever and never arrive at a terminus beyond which you cannot keep going”. That is true if you were to travel around a sphere, no matter what direction you go or any changes in direction you take you will never reach an end-point. Is there a sense in which this an accurate analogy for existence itself? If so, then the notion of infinity can certainly be rescued at least a little bit.

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The Universe was said to be a lemniscate, in antiquated times… which would then explain the cyclical notion of Aeons/Yugas, but it could well be a Kline shape, which would make the Universe self-containing… clearing up the matter of what is the Universe in/what contains it.

I don’t know what you mean by that, except to suppose that existence is a kind of ouroboros, which is just another type of “sphere” in the sense that you can keep going and never reach an end. Any closed shape can be useful in this way. But even a sphere can be flawed if we assume one can travel along a z’ axis up and away from the sphere… which, if the sphere is all that exists, would not be possible and therefore might represent a terminus point. Say we invent a technology that allows us to lift-off from the sphere and travel along the z’ axis, suddenly we reach the terminus and cannot move anymore in that direction because the “sphere” is all of existence itself. What would this imply about infinity? At least it would imply that using a sphere is perhaps not an adequate analogy for the “shape” of existence itself (and maybe it doesn’t even make sense to think about existence itself as having a shape?).

Well… a lemniscate/mobius strip, has no beginning or end, and allows for a never-ending progression of movement on/through it / through space/time… it’s shape, making the Universe one big eternal rollercoaster ride. A ride that cannot be stopped, so there’s no getting off.

…but the Kline shape, the Kline shape accommodates that explanation and much much more… it, being a 4-dimensional object, perpetually enclosing a 3-dimensional one… so the Universe, being in and of itself/the container and the contained. But was it always there…

It is likely that both views are correct, the case being that a limited quanta( died) space time implies a paradoxical halving of nearing the horizon of perceptual possibility.

That jives with leibnitz’ calculations of the two folded up sheets , does with Einstein’s cosmic curvature, as well as with the meta quantum mobius configuration. Equating those three conceptual analogs, do give pause to affirm more likelihood to it then not, but does not negate the equally debatable infinity quest, because, even the idea of getting closer to the horizon have a doubly asserted proof.

One is the cosmological Schwarzkopf limit of black holes, as that idea is analogous to the ancient race between the turtle and the hare.

That is exactly what infinity is, the concept of continuation without end. You nailed it!

Consider 1 divided by 3 in long division. 3 goes into 1.0 .3 times…WITH A REMAINDER OF .1.
.3 X 3 = .9 and add the remainder of .1 to equal 1.0.

Now to attempt to finish the division equally you have to divide the remainder of .1 by 3, which means .03 added to the previous unfinished answer of .3, so the unfinished answer is .33, WITH A REMAINDER OF .01.

Any sane individual will conclude that this nonsense will continue in the same manner, ALWAYS putting another 3 in the next decimal place, and ALWAYS having a remainder of 1 in that decimal position.

The division continues on and on and on, NEVER to end. We shall call this concept of never-ending continuation “INFINITY.”

Infinity is not a number or destination, it is the concept of continuation without end!

MagsJ
(..a chic geek -all thoughts are my own-)
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An ever-expanding Universe -expanding into who knows what, originating from who knows where, just doesn’t compute- so if the universe was always there, then the question of “how” and “why” still arises.

No beginning… no end… eternal… the Universe, as a lemniscate/klein, and not a new notion at that.

[quote=“MagsJ”]
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Can you clarify/elaborate, on that ^^^?[/But it does recur,? Infinitely since an infinite permutation of finite existential observation is impossible, at least from this vantage , MagsJ

This is sooooo difficult , but give it that old 1-2-3.

The observation is methodically a presumption of a limited numbered ser(s) of observable data. It is an existentially ( phenomenologically) reduced set(s), otherwise the permutations of x number of conclusions remain as unlimited as any other possible conclusion which can be drawn from the result.

Infinity? Belongs into the separable set of unaccounted for possible sets, and those sets subsumed under those sets- as they are open ended by definition, the sun summation reduces to a conceivable absolute-self inclusion .

That is not saying much, only that a conceivable infinity can only account for all possible conceptual worlds- which is a pantheistic reduction to an unaccountable infinity, or something like that.

Existential reduction of phenomena is limited and can not mirror the vast self inclusive absolute that conceived a limitless infinite.

So two kinds of infinity are incompatible with each other, and Leibnitz is aware of this diffference with his two identical sphere configuration, which he knows is not reasonable, but differentiator by calculating it, placing such calculus subsumed under the absolute general criteria , because he could then not sustain his alleged position of trying to create sandcastles calculations that match ‘reality’, and so being a staunch religious, he voins it under the general condition that even if not arguable from a human point of view, God withstands such critical argument by grounding the calculation under , the presumption that this is the best of all possible worlds.

I thought you learned that 1.0 can not be divided into 3 equal parts, in ANY base?

…and it’s not about my example, it’s about defining the term infinity, which is clearly pointed out in my example. Feel free to apply the concept of infinity in any base you please.

Heck, no need for numbers or math, just go outside and point your finger in ANY direction. That direction has INFINITE DISTANCE. There is no end to that direction along that line. There is no sign saying “Turn around now, you have reached the end of space.”

Although I am certain things can be infinite - infinity - certainly doesn’t exist.

Infinity is a reference to the end of the endless - an oxymoron - of course it doesn’t exist. It was never intended to be a existence - rather merely a concept for “all the way down an infinite path” such as in maths “as X approaches infinity” - the end of the endless.

Infinity isn’t a thing or a location - merely a compass heading.

If the Universe always existed, was never created, will never be destroyed, then wave good bye to Abrahamism/Christianity/Judaism/Islam.

Because Creationism is the core belief of their major religions. Most humans will reject this premise outright, because of this factor alone. It repudiates their entire belief system.

When it comes infinite Addition, the problem as I see it, is conceptualization. Infinitely large or small numbers, require computation, and ever increasing energy to understand. There is a limit to this understanding, to the energy required to compute math on those levels. So infinity would be forever Unknown. There’s simply no way to know whether there is an ‘End’ or not. But there is an End to human understanding, conceptual and knowledge limits, Epistemology.

I think a Universe without beginning and without end, is more ‘Rational’ than a theoretical beginning and end.

Anthropomorphism is a logical fallacy, hence Creationism is irrational.