I have not ventured outside our universe yet. Will tell you if and when I do.

Are there an infinite number of dimensions higher than the 4d spacetime that defines our universe outside of our universe? — an-salad

You seem to be using "our universe" in two different ways.

I don't think there's a mathematical constraint that limits the number of dimensions to a finite number. I wonder though how infinite axes, all mutually perpendicular to my reckoning, and all meeting at one single point, the origin, would look like? A sphere?

Are there an infinite number of dimensions higher than the 4d spacetime that defines our universe — an-salad

Given the conditions under which the conception of infinity is thought by us, the question is irrational with respect to our universe.

Given the conditions under which the conception of infinity is thought by us, the question is irrational with respect to our universe — Mww

My two cents worth:

Firstly, that's an odd thing to say. Aren't we part of this universe?

Secondly, our relationship with infinity had modest beginnings: the natural numbers - keep adding 1 and voila! you get infinity. Remember, the "natural" numbers - nothing exotic or highfalutin or, in your terms, other-worldly.

What say you? :chin:

What say you? — TheMadFool

What say I? Nothing more than.......

........to keep adding implies infinity hasn't been “gotten”, and infinity “gotten” implies there is no adding, “gotten” tacitly understood to indicate “arrived at”;
.......the pure a priori concept of quantity is far the more a beginning, than the schemata subsumed under it;
......the notion of “other-worldly” is impossible to derive from the predicates contained by the concepts given in “our universe” and “thought by us”, which the emphasis in the originals should have illustrated.

Rhetorically speaking, of course.

What say I? Nothing more than.......

........to keep adding implies infinity hasn't been “gotten”, and infinity “gotten” implies there is no adding, “gotten” tacitly understood to indicate “arrived at”;
.......the pure a priori concept of quantity is far the more a beginning, than the schemata subsumed under it;
......the notion of “other-worldly” is impossible to derive from the predicates contained by the concepts given in “our universe” and “thought by us”, which the emphasis in the originals should have illustrated.

Rhetorically speaking, of course. — Mww

That was too complicated but grant me one question: how do you know this, our, universe isn't, you know, infinite? If I misread you, where?

how do you know this, our, universe isn't (...) infinite? — TheMadFool

It is impossible to know, which makes it irrational to ask how I know.

It is impossible to know, which makes it irrational to ask how I know. — Mww

:ok:

I'd just like to run something by you for your views:

What's the difference between an actual infinity and a potential infinity? I got the impression that you were headed in that direction.

Are there an infinite number of dimensions higher than the 4d spacetime that defines our universe outside of our universe? — an-salad

Yes. And I have been there. Believe me. :nerd:

I'd just like to run something by you for your views: What's the difference between an actual infinity and a potential infinity? — TheMadFool

I’d say mathematicians might hold with actual completed sets of infinite members, but philosophers tend to hold with the potential of infinitely continuous series.

I favor Enlightenment continental metaphysics, which holds with the actual infinity of space and time, but also with the potential infinity of limitless sequential natural numbers, so I guess it just depends on the context of its use, which kind of infinity is to be considered.

Truth be told, Everydayman doesn’t have much use for either one, and I am that before all else.

But anyway.....my views thank you for asking about them.

Just wondering about a certain inconsistency that's bothering me. In all likelihood, it's a failure on my part and not in the rationale behind the distinction, actual and potential infinity. If infinity can be viewed as potential there must be a reason to it; my personal view is that 1) infinity is, by definition, endless 2) something endless can't be completed, obviously.

How then the notion of an actual infinity, completed as it must be?

How then the notion of an actual infinity, completed as it must be? — TheMadFool

I suppose....keyword, notion. An actual infinity would have to be thought as a concept in and of itself, merely to represent that of which the totality is either incomprehensible or altogether impossible, under the auspices of a particular cognitive system. Problem is, every conception must have an object at least thought as belonging to it, from which follows, in certain idealist doctrines, those objects may be merely another conception. But even then, metaphysical reductionism, or, which is the same thing.....logic.... mandates that eventually, we absolutely must rely on experience to ground all of those conceptions. Hence, we have the concept of actual infinity, justified by the a priori conception of time, which is justified in turn by the a priori conception of change, which can be given to us by sensibility, from which we finally arrive at experience. So...we haven’t experienced infinity, but only justified, logically validated, the conception of it, completed in itself. In effect, a bottom-up systematic rendition of the actually infinite.

On the other hand, if the complementary nature of human reason is granted, re: yes/no, right/left, right/wrong, up/down....for any conception its negation is given immediately.....then because bounded things are known with certainty, otherwise we could never even talk about that which is perceived as real, unbounded things are given necessarily by it, otherwise our cognitive system is inherently inconsistent. In such cases, what those unbounded things are is irrelevant, only that they must be possible. In effect, a top-down systematic rendition of the potentially infinite.

my personal view is that 1) infinity is, by definition, endless 2) something endless can't be completed, obviously.

How then the notion of an actual infinity, completed as it must be? — TheMadFool

Putting another philosophical spin on things, infinity does, or at least can, translate into “without limit” or “without boundary”.

This creates a misnomer of sorts. For example, most all mathematical infinities are infinities that are limited in some way. A line has infinite extension, but only in one direction; in the perpendicular direction it is bounded and thereby holds the finitude specific to a line (thereby for example distinguishing it from a geometric plane). Likewise with 1/3: the limitless series of 3s that results is nevertheless bounded to the number specified by the fraction, and thereby results in the finitude of 3s following the decimal point.

These, then, are all limited infinities. In effect, when claiming the infinity of X, the X specified remains bounded and, thereby, limited to X. So the infinity addressed in all such cases can be deemed equivocal: “without limit” in some way but “with limit(s)” in another.

We as humans can however also fathom the notion of an absolute infinity (what some term "The Absolute"): that which unequivocally is without limit. But, since even our concepts are by necessity limited to the concept specified, no one can conceptually understand what (absolute) infinity might actually be.

And it is in this fuzzy, else mystical, notion of absolute infinity (infinity proper?) that the notion of God as actual infinity unfolds for many, or at least some. For example:

Cantor linked the Absolute Infinite with God,[1] and believed that it had various mathematical properties, including the reflection principle: every property of the Absolute Infinite is also held by some smaller object.[2] — https://en.wikipedia.org/wiki/Absolute_Infinite

So...we haven’t experienced infinity — Mww

I'm here in my room. It was 11:00 AM when I got here. Now, the second time I look at my watch, it's 11:01 AM. Exactly 1 minute has passed. How many instances/moments of time are there between 11:00 AM and 11:01 AM? Infinite right? I then, like you and everyone else, actually experience infinity all the time. No?

Also, what about Zeno's Achilles' and the tortoise paradox?

for any conception its negation is given immediately — Mww

This, for me, is a key insight into the nature of our world, also our mind if the distinction must be made. If there's a something then, necessarily its negation, the not-something. Ergo, finite, necessarily infinite.

Also, it seems you didn't quite understand my take on the issue. I meant to say that infinity, by definition, is endless which, in other words, means it can't be completed; it, infinity, is necessarily incomplete. Hence, the idea of an actual infinity is...well...something doesn't add up. If an actual infinity is self-contradictory, as it is, then your argument that it has to be experienced is asking for the impossible. It's like saying valhalla must be experienced despite knowing full well it doesn't exist.

Well, let's figure out what this mother of all infinity is then? That infinity that's truly, in every sense and in all dimensions, truly infinite. Such an infinity would possess an infinite colors, an infinite size, an infinite mass, an infinite of every conceivable property.

Here's the interesting bit. Every property, as implied by @Mww' post comes in pairs - opposites as it were. So, imagine this mother of all infinity - it would possess, for every property, both the positive sense of the property, infinite in "extent", and also the negative sense of the property, also infinite in "extent". So, it would be, for example, infinitely red and also infinitely not-red. You get the picture. The opposite properties would cancel each other and will, in computer parlance, return the value 0, null, void, cipher, nought. Imagine this for every single property and the same thing will happen.

It appears that, paradoxical and self-contradictory as it sounds, the mother of all infinity, the be all and the end all of infinity, the infinity of infinities, is the humble zero!

Also, it seems you didn't quite understand my take on the issue. — TheMadFool

Wasn’t trying to. You asked, I answered. Using my understanding.

I meant to say that (....) the idea of an actual infinity is...well...something doesn't add up. — TheMadFool

Ok, fine. You’re entitled to that. Still, the infinity of space or time makes perfect sense to me. Doesn’t make it a fact, only that I don’t contradict myself by thinking it, as far as my knowledge currently permits.

The way in which you frame your argument misses the mark. For example: A property, any property, is bound to the property specified. And so it cannot specify - be it part or in whole - that which is without bounds, else without limits.

As to the conclusion that it returns the "value 0, null, void, cipher, nought", I don't know what (absolute) infinity is other than via description of what it cannot be, which isn't saying much. As an interesting tidbit, though, the description of being without any limit (e.g., as in volumeless, period; neither infinitesimally small nor infinitely large, but volumeless) is ascribed by some in the field of physics to the supposed gravitational singularity from which the Big Bang is supposed to have commenced. (Not a cosmology I subscribe to, but, all the same, the idea goes that finitude causally emerged from lack of finitude via the Big Bang.)

At any rate, given your conclusion that:

It appears that, paradoxical and self-contradictory as it sounds, the mother of all infinity, the be all and the end all of infinity, the infinity of infinities, is the humble zero! — TheMadFool

In assuming that absolute infinity is the humble zero, the question remains: Is the humble zero something potential, something actual, or something other?

:razz: