You cannot start counting 1,2,3,4,... ad infinitum and reach somewhere, anywhere. Infinity has neither a start or an end — Alkis Piskas
Then, counting (natural) numbers you can never reach infinity because that infility would be also a number, and infinity is not a real or natural number. — Alkis Piskas
A set is a collection of objects (elements, members). I'm not sure if we can talk about an infinite set — Alkis Piskas
All this raises questions about the infiniteness of the Universe, whether it started (created) from something or it always existed, etc. And, as I see it, since we don't have a proof that it is created from nothing, it must have always existed, even in the form of extremely high density and temperature, which at some point exploded (re: Big Bang), or in any other form. But I'm not the right person to talk about these things. — Alkis Piskas
But Euclidian triangles don't exist in nature. — Lionino
To me, the nature of Existence/Infinity accounts for this awareness. — Philosopher19
Suppose that the universe has infinite space, and let's also say that there is an infinite number of particles in this space. For there to be space between the particles, would that not make space a bigger infinity than the infinite number of particles in the infinite space?
Suppose someone produces an axiom. Will it not be the case that that axiom will either be contradictory in relation to certain truths or consistent in relation to certain truths? Existence determines what is true and what is false. Whether any belief or axiom highlights truths or is contradictory to truth is determined by Existence/Truth. If not, there is no truth or semantics to work with to deduce further truths. — Philosopher19
Right.I don't believe we can talk about different infinite sets because it will lead to contradictions. — Philosopher19
I see what you mean. Well, the words "exist" and "existence" can be used in different ways. And it can be used strictly (substantially, concretely) and loosely (insubstantially, abstactly). And I guess the second form applies to what you say above.I do believe Infinity and Existence denote the same Entity. I see Infinity/Existence as the set of all existents. I see there being no end to the number of existents purely because the nature of Infinity/Existence allows for such possibilities. — Philosopher19
Right. Or, impossible. Yet, we stiil can use the expression "something from nothing" loosely or figuratively. But there are always some conditions (something) that allow the creation of some other thing (something). This is the universal law of cause and effect.It is clearly contradictory for something to come from nothing. — Philosopher19
But doesn't an expanding universe mean that this process is infinite and thus the universe itself is limitless? It is not much different than if we consider the universe as being static, in which case it can also be infinite.And since I have heard some say that the universe is expanding, my view is that the universe is not infinite (if it's expanding, it's not infinite). — Philosopher19
But doesn't an expanding universe mean that this process is infinite and thus the universe itself is limitless? It is not much different than if we consider the universe as being static, in which case it can also be infinite. — Alkis Piskas
What the Universe's expansion means, whether it is infinite or not, is that its local energy density is decreasing. In other words, there is more spatial structure between each of its internal field excitations (particles, energy). — DanCoimbra
Doesn't infinity mean endless? i.e. unreachable eternal continuation in concept?How would a difference in size be established between them when there is no counting involved? And if there is counting involved, how would infinity be reached? — Philosopher19
"Let us not forget: mathematician's discussions of the infinite are clearly finite discussions. By which I mean, they come to an end." - Philosophical grammar, p483. Wittgenstein.One can talk about infinity conceptually, as one does in mathematics, without reference to its empirical verifiability. — DanCoimbra
Some of the advanced math theories are maybe just some mental showboating of things the math people can do with their brains. — Mark Nyquist
How? — Lionino
infinity is a concept considering continuity, not size. — Vaskane
As an analogy, consider looking at a dictionary and judging how truthfully the definitions represent how people are actually using the words which are defined there. — Metaphysician Undercover
It may well be the case that existence determines truth, like you say, but that's not relevant to the selection of mathematical axioms. — Metaphysician Undercover
The axioms do not give mathematicians rules for how to do things, because the mathematicians get to create and choose their own axioms. So the axioms simply provide a representation of what mathematicians are doing. Since they are descriptions, "truth" is to be found in how well the axioms represent what the mathematicians are actually doing — Metaphysician Undercover
for mathematicians to be using the label "infinity" — Philosopher19
from what I've seen of mathematicians — Philosopher19
I see what you mean. Well, the words "exist" and "existence" can be used in different ways. And it can be used strictly (substantially, concretely) and loosely (insubstantially, abstactly). And I guess the second form applies to what you say above. — Alkis Piskas
But doesn't an expanding universe mean that this process is infinite and thus the universe itself is limitless? It is not much different than if we consider the universe as being static, in which case it can also be infinite. — Alkis Piskas
"Let us not forget: mathematician's discussions of the infinite are clearly finite discussions. By which I mean, they come to an end." - Philosophical grammar, p483. Wittgenstein.
When it comes to the empirical application of the concept of infinity, it is indeed reasonable to think that it is fundamentally unverifiable whether something is infinite — DanCoimbra
Not 'infinity' as a noun, as if there is an object named 'infinity', but rather 'is infinite' as an adjective to name a property. — TonesInDeepFreeze
What you've seen is what you've allowed yourself to see, which is virtually nothing about the actual mathematics you've not even bothered looked up. — TonesInDeepFreeze
But from what I've seen of mathematicians, they either have no part for infinity, or they're using infinity wrong. I believe they're doing the latter which leads to the former (which I think is why I have heard it said before that "maths is incomplete") — Philosopher19
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