I think you would get stuck on that issue of whether 1 = .999…
If you take 1 away from an infinite count, you still have an infinite count. So are you going to say that an infinite count doesn’t go to infinity?
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In my opinion, taking one away from an infinite count or quantity, does not = infinity. It equals absurdity. An infinite number of books does not go to infinite in quantity, it IS infinite in quantity. I know you are talking about infinity and not existence, but I cannot separate these two concepts from each other. Just as I think it absurd to take 1 book away from Existence, I think it absurd to take 1 book away from an infinite number of books. Which is why I feel the need for the label of semi-infinite to fill in the following semantical gap:
I can have a library that goes on forever containing an endless number of books. But this library can never expand to the point of infinity in the same way that I can never count to infinity. But despite this, it still goes on forever. Infinity is true and meaningful. This is the only reason why counting to infinity forever without reaching infinity is possible. Or why a semi-infinite library can contain an endless/semi-infinite number of books without the number of books it contains reaching infinity. Infinity is also why reaching infinity is impossible. Infinity is not a hypothetical possibility. It just necessarily is infinite and nothing can become it. Infinity reaches all things. It encompasses all things. All that is in it will never see it, reach it, or become it. Of course, this does not mean that we have no understanding of it.
So the set of all real numbers except 0 is not an infinite set?
I think the world of maths will strongly disagree.
So why not just use one of the terms for sake of the rest of us who try to understand what you are saying?
It is. But you cannot take anything away from this set.
Because maths claims that you can take away from Infinity and be left with Infinity. How have mathematicians come up with this??? You go to someone and ask can you take anything from Infinity? They may not be sure about the answer. You go to someone and ask can you take anything away from Existence? Again, they may not be sure about the answer. Make clear to them the semantical/logical implications of something exiting or entering Existence, and they will say no, you cannot add or take away from Existence. Further make clear to them that by definition, Existence is Actually/Truly Infinite, and then ask them, can you take away from Infinity? They will surely then answer no.
You can take finite books out of a finite library, but you cannot take these books out of x (the set of all books). You can even burn these books and turn them into ashes, but x is still infinite. Those books that you burnt, did not cease to exist in Existence for you to say x -1 occurred. Nor did they exit Existence. The past does not go out of Existence. So those books that were books at that point in time and reality, are still books at that point in time and reality.
We look to the stars, and what we see is their past state. This is because of the speed of light.
I just did, didn’t I?
All I am trying to say is that you are using words that means differently to others than what you mean by them. That is leading to others being confused by what you say as well as some logic mistakes you make because logic requires consistency in your words.
But I didn’t mean to distract. I have said enough on this - for now anyway.
Certainly Real says:
"The past does not go out of Existence. So those books that were books at that point in time and reality, are still books at that point in time and reality.
We look to the stars, and what we see is their past state. This is because of the speed of light…"
Existence has no being as a foundation, and Being as a foundation negates Russell’s idea in the philosophycal foundations as logico-mathematical, and destroys his ’ sense-data idea by incrementally shortening out the overbearing data, by enscription.
In other words, the symbolic structure creates memory gaps, as it has to generalize programs of relevance, but the epigrams do not somehow ‘leak’ that information
Therefore the reductive process of stored data can not be a foundation in. ’ real’ sense, when sensation in the instant can not connect the sufficient number of frequency of those illusive stills, that are at the very bottom , or required repetition of assimilated epigrams.
The eye can only capture a still and it is by the means of internal simulation , that those tiny ‘beings’ can coalesce into motion.
Cantor can only imagine an all inclusive set, but he can actually quantify an infinite series where every set underneath , not unlike an infinite set of turtles, are one on top of another
In this instance, you can imagine a calculus of fed back epigrams, which creates the illusion of flow…
That is where the difference between the two differentials on both sides of a gap, or a memory loss, due to symbolic generalization.
This IDEA formation harbors a push for learning( conscious), because projective (or objective) ideas can not create anything but illusions of movement.
A retrograde process of forming constant , epigram ‘gaping’ is the result of a universal move , toward a all inclusive foundation,where ‘gravity’ is the unmoved moved.
It is a set that can , or can not include It’s self at
in that instant. I think somewhere along described it as ‘eigenblick’
That is not God, but it is a power that enables it to connect a the gaps between what slips out of these gaps…So God becomes that power, which includes as own source.( of power)
ref: K .Polanyi:The Great Transformation
"Embeddedness” centers around Karl Polanyi’s concept of … from a set of social mechanisms that resolve underlying problems.
"Understanding, comprehension – this is the cognitive faculty cast aside by a positivistic theory of knowledge, which refuses to acknowledge the existence of comprehensive entities as distinct from their particulars; and this is the faculty which I recognize as the central act of knowing. For comprehension can never be absent from any process of knowing and is indeed the ultimate sanction of any such act. What is not understood cannot be said to be known. (p. 240)
Like many other philosophers I enjoy, Polanyi stresses the movement of a knowing mind rather than any static state of knowledge.
The dynamic impulse by which we acquire understanding is only reduced and never lost when we hold knowledge acquired and established by this impulse. The same impulse sustains our conviction for dwelling in this knowledge and for developing our thoughts within its framework. Live knowledge is a perpetual source of new surmises, an inexhaustible mine of still hidden implications. (p. 244)"
Right, I think I’ve reached a definitive decision on this.
Call the set of all lions x. Call the set of all animals y. Neither x nor y can be Infinite in quantity for the following reason:
It cannot be denied that y is greater in quantity than x. This is because y encompasses the quantity of x. Thus, it is absurd to say x and y are equal in terms of quantity when y wholly encompasses x’s quantity. There are more things than just lions and animals. A greater quantity than that which is representative of the quantity of animals exists. A greater number/quantity exists than the quantities that x and y denote.
There is no quantity greater than Infinity. What is there an Infinite number/quantity of? Things. There are an Infinite number of things. The semantic of thing encompasses all things (this includes numbers). There are more things than there are animals. There are no more things than there are things. Thus, Infinity is only representative of the total number of things, or the set of all things. Not the total number of lions or the set of all animals.
Thus, you cannot have an infinite number of lions or animals. You have an infinite number of things.
It is true that you can have an endless number of animals and lions. But it is also true that there are more animals than there are lions. Thus, semi-infinite is an appropriate word to use here to describe that which is not Infinite in quantity, but still endless and can come in varying sizes. You can have different sizes of finite and semi-infinite. But you cannot have different sizes of Infinity. That implies that you can have different size of the greatest quantity. Or that you can have different sizes of that which no greater quantity can be conceived of.
If x is infinite and y is infinite yet y is larger in quantity than x, then x is certainly not infinite. y is only infinite when there is nothing larger in quantity than it.
Infinity is NOT a quantity.
I could present more if those aren’t enough. I hate to keep harping on this but I don’t think you are going to get anywhere until you face it.
I agree that “infinity” means “an infinite number of things”. However, I do not agree that “an infinite number of things” means the same as “the whole of existence”. In other words, if you say that the something is infinite in size, it does not mean that its size is equal to the size of the universe (i.e. that it occupies every bit of physical space.) The word “infinite” simply means “a number greater than every integer” (that’s the definition I prefer since it’s the clearest one.) By definition, it is unrelated to what exists.
There may be some repetition here. It’s a product of me trying to convey my understanding as effectively as I can. My apologise if it’s in excess.
It doesn’t really matter who said x. What matters is that x be non-paradoxical. I know what Cantor said and I see a paradox in what he said. He also saw this himself. Thus, clearly, what he said was problematic/paradoxical. I think we should solve this in a genuine manner. Not ignore it and settle for some clearly unfulfilling theory (as all other forms of set theory have attempted to do).
Is there something actually infinite? Yes. Call this x. Does the potentially ‘infinite’ ever become x? No. So why treat them the same when they are clearly different? Which do you deny? x being x? Or the potentially ‘infinite’ never becoming x? If you deny neither, then you must acknowledge that they are clearly different. I will illustrate their difference more clearly:
Now if there was nothing Infinite (x) (as opposed to the paradoxical idea of something becoming ‘infinite’), there would be no solution to Cantor’s paradox. There wouldn’t even be a potential ‘infinity’. But since infinity is that which encompasses all potential infinites as well as finites, we can solve the following: In set theory, Cantor’s paradox states that there is no set of all cardinalities. This is derived from the theorem that there is no greatest cardinal number.
For the sake of argument, take Infinity to be the greatest cardinal number. This does not imply an end to the numbers that forever try to get to Infinity (but never do), it just implies that it is greater than all those numbers that try to get (of which the list is endless), but never do. In this fact alone, should we not separate the infinite from the potentially ‘infinite’? Again, a potentially ‘infinite sequence’ does not contain this greatest number. It tries to reach this number, but never does. Can we really say that this number or quantity does not exist when we are trying to count to it? We know there is nothing beyond infinity. A number that cannot be reached even if one counts forever. Again, one does not reach infinity. Infinity just is infinity. It encompasses all numbers that try to reach it. It cannot be reached even if a number sequence goes on forever. This does not mean it does not exist. Nor does it imply a final end point of the endless.
The word infinity implies the potential for an endless set of numbers (of which the number of these sets could be endless). It does not imply the potential for another infinity, or for multiple or different sizes of infinity. It and only It, IS Infinity.
You say Infinity is not a quantity. This seems to be in line with Cantor saying ‘there is no set of all cardinalities. This is derived from the theorem that there is no greatest cardinal number.’. Yet, he acknowledged this to be paradoxical. Per the dictates of pure reason, paradoxes are just cases of misunderstanding semantics or lack of reasoning. Call Infinity the greatest cardinal number. Call Infinity the set of all cardinalities…and you will have no paradoxes. Right? If wrong, where is it wrong? How would any paradox arise from it? And if not wrong, why not adopt it?
For me, Existence and the universe are not the same. I think there is more to Existence than just our universe. I think this for the following reason: The universe had a beginning. It is paradoxical for something to come from nothing, or to have had a beginning in non-existence/nothingness. To avoid the paradox of something coming from nothing, we need an entity/being/thing/Universe, that is actually infinite. I call this thing Existence. If Existence was temporally finite, then that implies that it came from non-existence. If it was spatially finite, then that implies it is surrounded by non-existence. But then that paradoxically implies that non-existence exists. For how can non-existence surround Existence if it does not exist? In other words, how can x be surrounded by that which does not exist? It cannot.
Paradoxes are all the same. They must not be accepted on any level. We do not accept triangles being four-sided. We do not accept x being in two different places at the same time. We do not accept something coming from nothing. Given the paradoxes in the aforementioned paragraph, I see myself as rationally obliged to acknowledge Existence as being actually/truly Infinite.
“The universe had a beginning.”
you’ont know that, bro.
True. If it did, then it does not represent the whole of Existence.
You seem to have it stuck in your head that infinity is an actual thing. It isn’t. It is an oxymoron intended to just imply the “direction toward the infinite”. Infinity itself does exist any more than “up” exists as an actual height. It is nonsense to keep treating infinity as though it was actual existence and then compare it to real existence.
And who said anything about “becoming infinite”? We have all agreed that there is no “becoming infinite”. Why are you even bringing it up?
“Potentially infinite” can ONLY mean - “something that might be infinite but we don’t know yet”. It has nothing to do with growing to become infinite.
There is no “trying to reach”. The issue is that the very definition of “infinite” already means that there is no end to be reached whether anything is trying or not - no such thing as “infinity” - a “square-circle” - the “end of the endless”.
No. That is NOT what it means in English. If you want to make up your own language please try to use different words than English.
Wrong. You are claiming that “infinity is the universe” and at the same time claiming that a nonexistent concept, an oxymoron, “infinity” IS that universe that clearly exists.
That would definitely be a paradox as you ignore your word confusions.
You seem to have this list of discoordinate liberal concepts and their words that refute logic and rationality. With your words, you are saying that the universe itself and all reality is a square-circle - balderdash.
But for others, the two words are almost synonymous with each other. The universe is merely the set of all that has existed, that exists and that will exist. Existence is merely whatever exists.
Doesn’t that mean it is surrounded by nothing? What exactly is the problem with that idea?
How? Not that it’s relevant. It doesn’t appear related to Cantor and infinity but . . . just wondering.
For the sake of argument, I will try your approach and say there is no actually infinite thing.
Given that you say there is no actually infinite thing, then it follows that you don’t believe the universe to be an infinite thing. Did the universe have a beginning? Did it come from nothing? Is the universe surrounded by nothing/non-existence (as in is it spatially finite)?
To make a distinction between that which has no end, but has a beginning, and that which has no beginning and no end. x can go on forever, but because it had a beginning, it will never become that which has no beginning and no end (I’ve refrained from using the word infinity here, though I think it necessary to have a separate label for that which has no beginning and no end, versus that which has a beginning but no end)
Ok, I will not say trying to reach infinity. I will say, it goes on forever, but because it had a beginning, it is distinct from that which had no beginning and no end (which I will refrain from calling Infinity).
Ok, let me know what your take is on the following:
Is the universe such that it had no beginning and has no end? If no, do you consider there to be another existing thing x that encompasses the universe such that x had no beginning and has no end?
Personally, I don’t view the universe as infinite. I think the universe had a beginning, therefore, I don’t think it is infinite.
I’m keen to find out what your view on reality is. I look forward to your answers to the questions I’ve asked.
If x is surrounded by y, then that logically implies that y exists. If y does not exist, then y does not surround x (because it does not exist to surround x). If the universe is surround by nothing, then that logically implies that nothing exists. Is it not paradoxical to say that nothing/nothingness or non-existence exists?
First I have to make clear that something that has no beginning and no end (which I would label as actually/truly Infinite) exists and that it is paradoxical to reject this. Once I do this, I can then show that that which is actually/truly Infinite, encompasses all things that have a beginning, but no end. I can then make a distinction between this thing which is actually Infinite, and the things that have a beginning but no end (which I would label semi-infinite). I can then show that Cantor’s paradox can be solved by acknowledging that that which has no beginning and no end, encompasses all things that have a beginning but no end (which mathematicians are calling infinite). Since Infinity encompasses semi-infinities, we have a set that contains the set of all semi-infinities, whilst it Itself, is Infinite.
It is paradoxical to say that non-existence exists. That’s not what I dispute. What I dispute is what the statement “X is surrounded by nothing” implies. This has to do with what that statement means. I interpret that statement the same way I interpret “X is not surrounded by anything” and I simply don’t see how that statement implies that non-existence exists.
That is NOT what I said.
I said “infinity” as a actual thing or location does not exist. Infinity is an oxymoron of concepts - a bogus word - a square-circle.
Of course there are things that are infinite in scope, such as an “infinite line” or total number of stars or total number of natural numbers or the entire universe.