The Nature of Infinity

We can assume and differ on base-line assumptions/axioms. But the stance you take (axiom you assume that existence is infinite) is in contradiction with reasoning you extrapolate from this base. You could then reassert your base-line axiom as you have to say that infinity is inherently irrational. This doesn't fix your other point but questions my baseline. This can be done as all baselines when taken back to source reasoning come from assumptions: Humes Problem with Induction.

My assumption is this:
universaldistress said:
I would say how can physical existence not be infinite? Where there is something, how can there be nothing beyond that something? For me nothingness is illogical. How can there not always be something more . . ?
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and this is formative and in concord with/to my corrollaries. I follow my axiological baseline through logically.

But we could assume a different stance as you suggest (though as per my quote I find it displeasing to do so) and assume as you say that infinity is not logical/rational, which you could then use to extrapolate out a different stance on that basis. This doesn't affect my stance within the axiological framework "Existence Is Infinite" though . . .
 
I think it is fair to say that throughout the history of human thought, the notion of infinity and zero have constantly teased the mind(s) with all sorts of inductions. No two notions have caused so much thought than infinity and zero IMO.
And it would also be fair to say that the contributions to this thread aren't going to "put it to bed" either...

Yet funnilly enough I believe the use of infinity can indeed demonstrate the reality of zero.... as zero can not exist in an infinite universe. In fact for zero to be truly zero the universe must be infinite.

Yet paradoxically we use zero every day....and yet zero can only be realised as a notion by induction, or even deductive reasoning. It's non-existence, by default being totally dependant on a infinite universe of "things"

The issue of infinity and zero is paradoxical and one philosophy and science have been struggling with for ages. IMO
 
Quantum Quack said:
Yet funnilly enough I believe the use of infinity can indeed demonstrate the reality of zero.... as zero can not exist in an infinite universe. In fact for zero to be truly zero the universe must be infinite.

Yet paradoxically we use zero every day....and yet zero can only be realised as a notion by induction, or even deductive reasoning. It's non-existence, by default being totally dependant on a infinite universe of "things"

The issue of infinity and zero is paradoxical and one philosophy and science have been struggling with for ages. IMO
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Can the evil have a value in the notion of 'Zero'?
 
If there is something infinitely big, then naturally we must be infinitely small.
 
the nature of infinity is in the nature of the existence of what allows things to exist in the first place , such as energy and matter , which if it becomes devoid in any space becomes problematic in how it can restart its self

so infinity to me becomes really about perhaps a fractal thinking upon infinity

fractal is defined as being about " various extremely irregular curves or shapes to which any suitably chosen part is similar in shape to a given larger or smaller part when magnified or reduced to the same size"
 
QQ,
'The issue of infinity and zero is paradoxical and one philosophy and science have been struggling with for ages. IMO'

Why do not try first to have a look into the inner Universe? It must ‘work’ on the same principle like the outer.

Imagine, the heart and the brain are the two pillars in it that their crossing point forms the ‘Zero point’. As the mind creates the thought and the heart – the feeling. Both are made in exactly the same time so the inner image is one.
Such system cannot be dysfunctional.

There is not any paradox in its work. There is a lack of emotions. There are only pure thought and pure feeling that both match to produce the right image.

Try to find the ‘zero’ in the inner universe. It has a heart shape and flexible borders from one life to another…
 
Quantum Quack said:
I think it is fair to say that throughout the history of human thought, the notion of infinity and zero have constantly teased the mind(s) with all sorts of inductions. No two notions have caused so much thought than infinity and zero IMO.
And it would also be fair to say that the contributions to this thread aren't going to "put it to bed" either...

Yet funnilly enough I believe the use of infinity can indeed demonstrate the reality of zero.... as zero can not exist in an infinite universe. In fact for zero to be truly zero the universe must be infinite.

Yet paradoxically we use zero every day....and yet zero can only be realised as a notion by induction, or even deductive reasoning. It's non-existence, by default being totally dependant on a infinite universe of "things"

The issue of infinity and zero is paradoxical and one philosophy and science have been struggling with for ages. IMO
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So Zero as in "Nothing". I see nothing as only a concept not an actual physicality and so of no regard(axiom I choose to speculatively explore infinity from).

The whole of reasoning philosophy suffers at the hand of assumptions being the source of all observation. How can one assume that the physical properties of the universe will remain stable when history is finite. Tomorrow the rules of physics could be different so how can we assume things will carry on behaving how we ASSUME they will? We simply have to assume certain baseline axioms to function in existence.

I would say that for the notions of Nothing and Infinity one has to choose one's baseline assumptions and get on with it :) We just have to define our POV or context for any given discourse, to ensure we are working through issues from the same page, whatever page we choose for today . . .

We are discussing the fundamentals of existence; of course we can argue about which fundamentals are of most importance from our own assumptive points of view; these fundamentals are a choice we make through our own logical reasoning/assumptions . . .

I choose to base myself in a physical-world-driven logic.
 
BUT, I find the most interesting subjects are not always the fundamentals, but in fact any given frameworks extrapolated out to their frontiers.
 
universaldistress said:
BUT, I find the most interesting subjects are not always the fundamentals, but in fact any given frameworks extrapolated out to their frontiers.
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One of the first and most important steps whe discussing these sorts of concepts or notions is to decide to stringently apply absolutism when appropriate to those notions. IMO
Clearly identifying what is to be considered as absolutely absolute.
Both notions of zero and Infinity are "absolute concepts" and can be managed in discussion, I feel, only if they are maintained as absolutes with out deviation into "vagueness" or "variability".
 
Although it isn't that easy to explain why, complex numbers along with infinity and zero are a way to 'coordinatize' the Riemann sphere. The Riemann sphere though, is just an extension of the Argand plane, which itself is an extension of the real plane.

The Riemann sphere and Riemannian geometry are important in physics; the coordinatized sphere allows for division by zero or infinity (both values are just antipodal points on the sphere), usually mathematically undefined functions. So this extension of the complex field of numbers makes division by zero and infinity, and addition and multiplication of/by infinity, well-defined. To make it more 'concise', numbers in the neighbourhood of infinity (say, the south pole of the sphere) are large, numbers in the neighbourhood of zero (the north pole) are small.

But you still need to ask: "Why does it 'work' with complex numbers?"
 
Infinity and zero are reciprocal concept relative to our perception. In reality it is one continuum only throughout its existence and this is something beyond our perception.
 
arfa brane said:
Although it isn't that easy to explain why, complex numbers along with infinity and zero are a way to 'coordinatize' the Riemann sphere. The Riemann sphere though, is just an extension of the Argand plane, which itself is an extension of the real plane.

The Riemann sphere and Riemannian geometry are important in physics; the coordinatized sphere allows for division by zero or infinity (both values are just antipodal points on the sphere), usually mathematically undefined functions. So this extension of the complex field of numbers makes division by zero and infinity, and addition and multiplication of/by infinity, well-defined. To make it more 'concise', numbers in the neighbourhood of infinity (say, the south pole of the sphere) are large, numbers in the neighbourhood of zero (the north pole) are small.

But you still need to ask: "Why does it 'work' with complex numbers?"
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this is actually an area of future interest for me. Studying the philosophy of mathematics as it evolved over time.. I believe, possibly incorrectly, that contemporary mathematics has a more controversial philosophical premise than what used to be the case in ancient times.. [ the Ancient Greeks for a over generalised example, were great at using mathematics to express a philosophical point of logic or rational in an abreviated form [ aka Mathematics. ]
The premise being that all sciences stem from a philosophical genesis, hence a University Faculty of Philosophy includes all or most sciences [typically]
Some thing to get "in to" in the future for sure....
Riemannian Geometry for example from a man in the early 1800's no doubt had some pretty heavy philosophical premises underpinning it.
 
hansda said:
Infinity and zero are reciprocal concept relative to our perception.
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A very precise reflection on those concepts, I think.

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Infinity seems to provide a useful point of reference against our existence.

We could view the totality of human experience as a point on a continuum of possibility.

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What are the practical implications of the concepts of zero and infinity to philosophy?
 
From my perspective I believe infinity is a real concrete physical thing. A number is a number but an abstract number refers to something that exists in reality. Although it has no real tangible value as a thought, the ideas such as the universe or any object within could be counted as part of this infinite. But it's value as a thought lies in understanding everything that surrounds the concept itself.
 
kx000 said:
Forever in the sky. Forever down the pit. Sealed and shut.

Where do we fit in between infinity big, and infinity small?
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I would guess, exactly in the middle :), on one hand we have the infinitely small which makes us infinitely big, but on the other hand we have the infinitely big which makes us infinitely small. The only thing not spreading everything out into infinity is that those two have equal pressure against the middle (which should be infinitely defined).

Perhaps this means that everything is really inside a infinitely dense point? Perhaps there was no "Big Bang" but just a reconfiguration of the information contained in that point, in such a way that the information began to describe space and time and everything else? In which case we are second nature to reality (we are the description, not the information itself, but the description that the information describes). We could be a tale, but what a great one, and told with such immense expression!
 
Time goes on both ways forever,
despite all mortal human endeavour,
infinity will be reached, never ever.
 
All anyone can actually say is that infinity conceptually exists, since nobody has the empirical means to confirm it in actuality. Sure, theories say this and theories say that, but even the evolution of sciences has yet to uncover this. Sure, the Big Bang theory has a beginning, a Singularity, and a predicted ending, or a "Big Crunch.", but even on top of this, String theorists have conceptualized the multiverse, in which case the beginning and ending of The Big Bang is completely irrelevant to infinity. Of course, that is only infinity in terms of time. There could be infinity in terms of space, as well, or dimensions. Is the Universe infinitely small or infinitely large? Well, if String theory is correct at least the first would be false, since the entire basis of the theory relies on an indivisible part, strings. Anyway... I think you see my point here when I say it's un-confirmable in actuality. But yes, definitely conceptually. And we can discuss those terms since even restricted to a concept it is quite wide spanning contextually, since it is highly abstract (and I feel I have covered some of the main concepts when I asked question related to infinite time, space, or dimension).
 
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I don't necessarily think nothingness is untrue in actuality simply because it is illogical. Simply, I feel that the concept of nothing is impossible to understand, because in ALL of human experience, there is a something. In fact, experience is entirely dependent upon a something. Using that logic, we can conclude that if a nothing can be true then merely it can never be understood. Probably one of the most annoying ideas to contemplate, since it can't actually be contemplated. Ever since I was a kid though I imagined nothingness as complete whiteness. Not that this is an accurate depiction of nothing since after all white is color, and whatever nothing 'is', it's entirely visual-less. I mean, can nothing even be an 'is'? Well, 'is' is an existence, and existence=something, so no. I feel more confused now than when I started this, with no conclusion in sight, so uhh there you go I guess. Bam your mind's a poofy balled. Or maybe it isn't since you KNOW. Whatever I really need to stop typing.
 
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