What Laws Explain the Infinitude of the Universe?

[Moni]

In many articles I have found that : Universe is (in time & space) infinite.......

But I don't understand what is the law or formula behind this ?

Can anybody explain it further ?

 

[quantum]

That's just the thing, there is really no formula behind whether or not the universe is infinite... It's all simply speculation. However, there are many modern cosmological readings that strongly suggest the universe is infinite because it so well satisfies certain theories...

 

[The Grimmus]

it isent infinite as i under stand it it is constanly exspanding so

hey how do they even know that infitey exist have they ever counted to it?

 

[Moni]

Yes! I wanted to know how they are so sure about it's infinitiness ?

 

[subtillioN]

Originally posted by Moni
Yes! I wanted to know how they are so sure about it's infinitiness ?

The question is how can it NOT be infinite?

 

[Mr. Robin Parsons]

First, I would respectfully suggest, you know what it means, "infinity" hence, I would suggest you read the https://www.physicsforums.com/showthread.php?threadid=1438&perpage=15&pagenumber=11" at the Fourth post down, (My posting) and then you/we can discuss it better(?)

EDIT *LINK*

 

[subtillioN]

Originally posted by Mr. Robin Parsons
First, I would respectfully suggest, you know what it means, "infinity" hence, I would suggest you read the https://www.physicsforums.com/showthread.php?threadid=1438&perpage=15&pagenumber=11" at the Fourth post down, (My posting) and then you/we can discuss it better(?)

Ok so let's discuss it.

 

[Mr. Robin Parsons]

Originally posted by subtillioN
Ok so let's discuss it.

If I assume you have read it then you should ralize that it is not a concept that anyone can think of, hence a formula for infinity is impossible.

The only thing that is left, by that posting I made, is admittance to Belief, you either belive in an infinity, or you don't, but it cannot be proven out, not one way, nor the other.

Hows that?

 

[subtillioN]

Originally posted by Mr. Robin Parsons
If I assume you have read it then you should ralize that it is not a concept that anyone can think of, hence a formula for infinity is impossible.

So you are saying that because we can't calculate to infinity then it cannot exist? Do you consider that a proof?

I find thinking of infinity quite easy. I just can't fit it completely inside my mind, but so what? There are MANY complex phenomena that I cannot imagine in their entirety.

The only thing that is left, by that posting I made, is admittance to Belief, you either belive in an infinity, or you don't, but it cannot be proven out, not one way, nor the other.

Ok, but it requires an extra assumption that space suddenly stops and is therefore finite.

Hows that?

Needs a bit of work.

 

[Hurkyl]

Ok, but it requires an extra assumption that space suddenly stops and is therefore finite.

It doesn't require a sudden stop to be finite.

 

[subtillioN]

Originally posted by Hurkyl
It doesn't require a sudden stop to be finite.

oh yeah the curved space thing... another hyper-pathetical

 

[Mr. Robin Parsons]

Originally posted by subtillioN
So you are saying that because we can't calculate to infinity then it cannot exist? Do you consider that a proof? No, not a "proof" but you cannot prove, noor disprove it.

I find thinking of infinity quite easy. I just can't fit it completely inside my mind, but so what? There are MANY complex phenomena that I cannot imagine in their entirety.

Well apparently you are willing to decieve yourself, as if it is NOT a thought, then no one can 'think' of it, partially or in it's entirey.

No delineations, NO boundaries, NO edges, No appearance of space, NO visuals, ergo, No Conceptualization available.

 

[subtillioN]

Originally posted by Mr. Robin Parsons
Well apparently you are willing to decieve yourself, as if it is NOT a thought, then no one can 'think' of it, partially or in it's entirey.

You can think of it logically. Infinity simply has no edges or boundaries.

No delineations, NO boundaries, NO edges, No appearance of space, NO visuals, ergo, No Conceptualization available.

non sequiter

Just because a substance has no ultimate boundaries does not mean it has no internal structure.

 

[Mr. Robin Parsons]

Originally posted by subtillioN
You can think of it logically. Infinity simply has no edges or boundaries.
Just because a substance has no ultimate boundaries does not mean it has no internal structure. HOGWASH!

As I stated, just because you are willing to decieve yourself, doesn't mean you got it right.

Al thoughts are bounded, ergo you cannot have an unbounded thought, but you can fool yourself into thinkng that you have had one.

 

[subtillioN]

Originally posted by Mr. Robin Parsons
As I stated, just because you are willing to decieve yourself, doesn't mean you got it right.

Just because you can state that I am decieving my self does not mean that I actually am.

Care to explain how you wash the hog?

Al thoughts are bounded, ergo you cannot have an unbounded thought, but you can fool yourself into thinkng that you have had one.

I never said that I could have an unbounded thought. The mind is certainly finite. That is why the imagination is useless to understand infinity. Infinity must be understood through logic not imagination.

If I say Infinity has no boundaries, I have said a true statement about infinity. Do you suppose that this statement must be infinite?

To understand something you need not replicate it in your mind. The mind is capable of generalization and abstraction.

 

[Hurkyl]

I am with subtillioN that you can certainly think logically about infinity...

but I'm at odds with his definition; infinity is typically used in contexts where we may (at least sometimes) ascribe quantities to entities in question, such as sizes of sets, lengths, or volumes. We use infinte/infinity when either we have "transfinite" numbers which are larger than any real number (such as the case of sizes of sets), or when there is no upper bound to the quantities in question (such as distances in the euclidean plane)

subtillioN is thinking in a context where "no edges or boundries" is a sufficient condition for there to be no upper bound on distances or volumes, but that is not in general a sufficient condition.

 

[subtillioN]

Originally posted by Hurkyl
but I'm at odds with his definition; infinity is typically used in contexts where we may (at least sometimes) ascribe quantities to entities in question, such as sizes of sets, lengths, or volumes. We use infinte/infinity when either we have "transfinite" numbers which are larger than any real number (such as the case of sizes of sets), or when there is no upper bound to the quantities in question (such as distances in the euclidean plane)

In mathematics there can be infinities of different magnitude. That is because they are dealing with the indefinite division of continuity.

I do not consider this to be infinity proper, but the transfinite.

True infinity can have no magnitude.

 

[Mr. Robin Parsons]

It becomes the paradox of presentation of the universe, inasmuch as you can count things in the first place, because, if you were truly observing, or thinking, of the infinite, you would have nothing in your head, absolutely nothing, ergo not even the beginning of counting anything!

Think of it in the sense of looking at the surface of a perfectly lit/illuminated sphere all at once, the entire surface, observant thinkers will realize that visually you can see nothing because unless the surface of the sphere is lit in an asymetrical manner, all you will "see" is 'flat space' with nothing to distinguish anything from anything else.

Infinite is NOT a concept in your head, it cannot be, because, your imagination is limited, as well as is your thinking ability. (other then the typicono'graphic that is the word itself)

To be human is to experience these limitations.

That you seem to wish to refuse to accept them, little I can do about that one.

In an infinite system you cannot even begin to count, as there is not one thing that is distinguished. (Neither beginning, nor end)

(Yes, I know, sounds contradictory, but in the complete understanding of the universes construction it ends up making sense...go Figure!)

 

[subtillioN]

Originally posted by Mr. Robin Parsons
It becomes the paradox of presentation of the universe, inasmuch as you can count things in the first place, because, if you were truly observing, or thinking, of the infinite, you would have nothing in your head, absolutely nothing, ergo not even the beginning of counting anything!

First of all you make the error of equating observation with thought. I am talking logic not observation or imagination. This distinction is critical.

Think of it in the sense of looking at the surface of a perfectly lit/illuminated sphere all at once, the entire surface, observant thinkers will realize that visually you can see nothing because unless the surface of the sphere is lit in an asymetrical manner, all you will "see" is 'flat space' with nothing to distinguish anything from anything else.

I am not talking about homogeneity whatsoever. Infinity is not equivalent to homogeneity.

Infinite is NOT a concept in your head, it cannot be, because, your imagination is limited, as well as is your thinking ability.

Of course the infinite cannot be contained in the finite mind and the infinite is not a thought. This does not mean that logic can not define the infinite without encapsulating it.

That you seem to wish to refuse to accept them, little I can do about that one.

You have simply misunderstood them.

In an infinite system you cannot even begin to count, as there is not one thing that is distinguished. (Neither beginning, nor end)

Again you are confusing infinity with homogeneity.


"Everyone regards the question of the infinite as most difficult, if not insoluble, through not making a distinction between that which must be infinite from its very nature, or in virtue of its definition, and that which has no limits, not in virtue of its essence, but in virtue of its cause; and also through not distinguishing between that which is called infinite, because it has no limits, and that, of which the parts cannot be equalled or expressed by any number, though the greatest and least magnitude of the whole may be known; and, lastly, through not distinguishing between that, which can be understood but not imagined, and that which can also be imagined. If these distinctions, I repeat, had been attended to, inquirers would not have been overwhelmed with such a vast crowd of difficulties. They would then clearly have understood, what kind of infinite is indivisible and possesses no parts; and what kind, on the other hand, may be divided without involving a contradiction in terms. They would further have understood, what kind, of infinite may, without solecism, be conceived greater than another infinite, and what kind cannot be so conceived. All this will plainly appear from what I am about to say."

--Spinoza

 

[Hurkyl]

The great thing about human thought is that we can think about what we can think. Recursive logical structures are exceedingly powerful...

At "first order", you may be right and we cannot conceptualize infinity at all.

However, at "second order" we can talk about first order thought itself. We can talk about things that fail to be conceptualized at the first order level and analyze how and why we can't conceptulaize it at that level, allowing us to synthesize second order concepts.

In particular, I can think about infinity without having to simultaneously think about everything "in" that infinity.



That addresses your argumentation, but I think you're thinking about infinity in entirely the wrong way. Most of these arguments that we cannot conceptualize infinity, et cetera, et cetera, are highly dogmatic; if you refuse to step boldly forward and try to figure out what you mean by "infinity", then, by golly, you will not be able to talk logically about it!

On the other hand, mathematicians do step boldly forward. We distill the "essential elements" out of peoples' vague ideas about infinity until we get a nice, precise definition appropriate to the context, and we get a lot of useful mathematics out of it.

 

[Mr. Robin Parsons]

Originally posted by subtillion
First of all you make the error of equating observation with thought. I am talking logic not observation or imagination. This distinction is critical.

So you seem to think that you can separate logic, which is a process, from thought/imagination/concept.

In order for you to follow logical thought, (the process of logic) you must have a thought, "infinite" defies that, as it cannot be thought of, logically, or otherwise, you simply self decieve.

Originally posted by subtillion
I am not talking about homogeneity whatsoever. Infinity is not equivalent to homogeneity.

Neither am I, and you cannot prove your second statement because you cannot concieve of infinite! (period!)

Originally posted by subtillion
This does not mean that logic can not define the infinite without encapsulating it.

This is a contradiction of terms, you cannot 'encapsulate' that which is defined as 'un-ecapsulable'

You can fool yourself as long as you might like to, but it doesn't fool me, nor will it.
(unimaginable & unthinkable, ergo no logic available!)

 

[subtillioN]

Originally posted by Hurkyl
The great thing about human thought is that we can think about what we can think. Recursive logical structures are exceedingly powerful...

At "first order", you may be right and we cannot conceptualize infinity at all.

However, at "second order" we can talk about first order thought itself. We can talk about things that fail to be conceptualized at the first order level and analyze how and why we can't conceptulaize it at that level, allowing us to synthesize second order concepts.

In particular, I can think about infinity without having to simultaneously think about everything "in" that infinity.



That addresses your argumentation, but I think you're thinking about infinity in entirely the wrong way. Most of these arguments that we cannot conceptualize infinity, et cetera, et cetera, are highly dogmatic; if you refuse to step boldly forward and try to figure out what you mean by "infinity", then, by golly, you will not be able to talk logically about it!

On the other hand, mathematicians do step boldly forward. We distill the "essential elements" out of peoples' vague ideas about infinity until we get a nice, precise definition appropriate to the context, and we get a lot of useful mathematics out of it.

Well spoken! I couldn't agree more.

 

[subtillioN]

Originally posted by Mr. Robin Parsons
So you sem to think that you can separate logic, which is a process, from thought/imagination/concept.

There are many modes of thought and yes they can be functionally seperated.

In order for you to follow logical thought, you must have a thought, "infinite" defies that as it cannot be thought of logically or otherwise, you simply self decieve.

Infinite is just a word which means "unbounded". Quite a finite thought really.

Neither am I, and you cannot prove your second statement because you cannot concieve of infinite! (period!)

Why should I prove that infinity is not equivalent to homogeneity if you are not even talking about it?

I can concieve of an infinite substance which is entirely inhomogenous. That is not a proof it is a thought.

This is a contradiction of terms, you cannot 'encapsulate' that which is defined as 'un-ecapsulable'

That is precisely what I said. I can logically understand it without encapsulating it.

You can fool yourself as long as you might like to, but it doesn't folo me, nor will it.
(unimaginable & unthinkable, ergo no logic available!)

You continue to misunderstand my point.

 

[Mr. Robin Parsons]

Originally posted by Hurkyl
The great thing about human thought is that we can think about what we can think. Recursive logical structures are exceedingly powerful...
At "first order", you may be right and we cannot conceptualize infinity at all.
However, at "second order" we can talk about first order thought itself. We can talk about things that fail to be conceptualized at the first order level and analyze how and why we can't conceptulaize it at that level, allowing us to synthesize second order concepts.
In particular, I can think about infinity without having to simultaneously think about everything "in" that infinity.
That addresses your argumentation, but I think you're thinking about infinity in entirely the wrong way. Most of these arguments that we cannot conceptualize infinity, et cetera, et cetera, are highly dogmatic; if you refuse to step boldly forward and try to figure out what you mean by "infinity", then, by golly, you will not be able to talk logically about it!
On the other hand, mathematicians do step boldly forward. We distill the "essential elements" out of peoples' vague ideas about infinity until we get a nice, precise definition appropriate to the context, and we get a lot of useful mathematics out of it.

Just because you can 'second order think' about something doesn't mean that you can achieve the 'first order answer'.

Math might boldly go where no man went before, but it is not capable of mathematizing 'infinite' either, as it too, must start somewhere.

Define infinite, "no beginning, no end" so tell me, logically, where do you start?

 

[subtillioN]

Originally posted by Mr. Robin Parsons
Math might boldly go where no man went before, but it is not capable of mathematizing 'infinite' either, as it too, must start somewhere.

You are correct. No system of thought can encapsulate infinity. In mathematics and logic, "infinity" is an ideal. A mere symbol representing a train of thought.

 

[Mr. Robin Parsons]

Originally posted by Subtillion
Of course the infinite cannot be contained in the finite mind and the infinite is not a thought. This does not mean that logic can not define the infinite without encapsulating it.

These two statements, are contradictions of each other.

I can concieve of an infinite substance which is entirely inhomogenous. That is not a proof it is a thought.

 

[subtillioN]

Originally posted by Mr. Robin Parsons
These two statements, are contradictions of each other.

I am talking about generalizations through logic not replication or exact and complete simulation in the mind.

 

[Hurkyl]

Define infinite, "no beginning, no end" so tell me, logically, where do you start?

Define what it means to have a beginning.
Define what it means to have an end.
Define infinite to be anything without a beginning and without an end.

 

[Mr. Robin Parsons]

Originally posted by Hurkyl
Define what it means to have a beginning. Delineation
Define what it means to have an end. Delineated
Define infinite to be anything without a beginning and without an end. Done with the circle 'joke'

Any more questions?

Yes, it is an Ideal, hence no comport in reality(?) which is exactly why I stated that it ends up with a responce that is equalling your belief systems, you either believe that infinity exists, or not, but there is no proving it one way, or the other.

Inconcievable.

 

[subtillioN]

Originally posted by Mr. Robin Parsons
Yes, it is an Ideal, hence no comport in reality(?)

Not necessarily. Infinity is simply non-computable and non-simulatable in the imagination. The only way to deal with it is through logic and reason.

which is exactly why I stated that it ends up with a responce that is equalling your belief systems, you either believe that infinity exists, or not, but there is no proving it one way, or the other.

There ARE logical proofs for infinity. See Spinoza, for example.

 

[Mr. Robin Parsons]

Originally posted by subtillioN
Not necessarily. Infinity is simply non-computable and non-simulatable in the imagination. The only way to deal with it is through logic and reason.

There ARE logical proofs for infinity. See Spinoza, for example.

Logical proofs of Infinity do NOT prove that Infinity exists, they simple demonstrate an indicator that suggests that infinity is possible, nothing more.

Logic is "of" the imagination.

 

[subtillioN]

Originally posted by Mr. Robin Parsons
Logical proofs of Infinity do NOT prove that Infinity exists, they simple demonstrate an indicator that suggests that infinity is possible, nothing more.

Well they show that infinity is the only rational alternative and that a finite universe is nonsensical.

Of course they are not scientific proofs. They are logical proofs and there is a difference as you are keenly aware.

Logic is "of" the imagination.

Yes, logic is built on language which adds structure and symbolic generalizability to the imagination. This gives the imagination a very powerful set of abilities as we can see in science and all theory and rationality.

I distinguish logic from the pure imagination, however, for obvious reasons. Logic can take powerful symbolic shortcuts and metalevel reasoning, but the imagination must visualize everything in its minute details. Both have their own unique power and applicability and BOTH are critical for an understanding of reality.

 

[Mr. Robin Parsons]

Originally posted by subtillioN

Of course they are not scientific proofs. They are logical proofs and there is a difference as you are keenly aware.

Might I indulge the subtlety of them being Logical Conclusions, as opposed to proofs?

 

[subtillioN]

Originally posted by Mr. Robin Parsons
Might I indulge the subtlety of them being Logical Conclusions, as opposed to proofs?

sure. We both know what they are beyond the words.

 

[Mr. Robin Parsons]

Originally posted by subtillioN
sure. We both know what they are beyond the words.

Not quite sure what you mean by that, as I know that both have different meanings.

An end is not neccesarily a proof, and a proof is not nessecarily an end, but an end can be a proof and a proof can be an end, but in my usage herein when I say it is the "end", it is without proof.

 

[radagast]

Originally posted by Mr. Robin Parsons
Logical proofs of Infinity do NOT prove that Infinity exists, they simple demonstrate an indicator that suggests that infinity is possible, nothing more.

It depends on your definition of exists, I suppose. In a defined mental construct, such as the mathematics of real numbers, the proof of an infinite number of real numbers between the number 1.0 and 2.0 is a proof of the existence of an infinity, at least constrained to within that mathematical construct.

Since common dictionary definitions of existence and exist do encompass mental constructs as well as external reality, I see this as proof of existence within the above given context.

I do not say this says anything about external, objective reality.

 

[Mr. Robin Parsons]

Originally posted by radagast
It depends on your definition of exists, I suppose. In a defined mental construct, such as the mathematics of real numbers, the proof of an infinite number of real numbers between the number 1.0 and 2.0 is a proof of the existence of an infinity, at least constrained to within that mathematical construct.

Since common dictionary definitions of existence and exist do encompass mental constructs as well as external reality, I see this as proof of existence within the above given context.

I do not say this says anything about external, objective reality.

Since infinity cannot be a concept, it cannot be a number, other then to state that 'one' of them exists.

The emboldened is only a proof that we cannot count to infinity, but suggests to us that it is a possibility, ergo neither a conclusion, nor a proof.

 

[radagast]

Originally posted by Mr. Robin Parsons
Since infinity cannot be a concept, it cannot be a number, other then to state that 'one' of them exists.

The emboldened is only a proof that we cannot count to infinity, but suggests to us that it is a possibility, ergo neither a conclusion, nor a proof.

Agreed that, by definition, an infinity isn't and cannot be a number. Your above comment seems to fall into the category of a Bifurcation Fallacy. Implicit is the assumption that an infinity has to be a number or concept to exist. Either delineate the reasons behind this assumption, or I can't see any reason to consider that argument anything but flawed.

In trying to ascertain if an infinity exists, it's definition might be important, so I've included it below:.

Infinity
NOUN: Inflected forms: pl. in·fin·i·ties
1. The quality or condition of being infinite.
2. Unbounded space, time, or quantity.
3. An indefinitely large number or amount.
4. Mathematics The limit that a function is said to approach at x = a when (x) is larger than any preassigned number for all x sufficiently near a.
5a. A range in relation to an optical system, such as a camera lens, representing distances great enough that light rays reflected from objects within the range may be regarded as parallel. b. A distance setting, as on a camera, beyond which the entire field is in focus


Now, given (by the proof) that the numeric space, or the quantity of real numbers between 1.0 and 2.0 corrosponds to an Unbounded space, time or quantity, given (by the proof) there are An indefinitely large number or amount of real numbers between 1.0 and 2.0, and given that defn 4 also seems to apply, then, inferred from the definitions and proofs given, an infinity of real numbers exists between 1.0 and 2.0.



Being you liked the word Concept, I thought I'd explore that path too.

Concept
NOUN: 1. A general idea derived or inferred from specific instances or occurrences.
2. Something formed in the mind; a thought or notion. See synonyms at idea.
3. A scheme; a plan: “began searching for an agency to handle a new restaurant concept” (ADWEEK

From how I read the definition of infinity, defn 2 does seem to also encompass the term, given it's a thought, a notion, and/or something formed in the mind. FWIW


With regards to your second paragraph, the proof does prove that the number of real numbers from 1.0 to 2.0 is unbounded - falling into the definition of infinity.

Regards,

 

[Mr. Robin Parsons]

radagast, did you read the link that I have posted on these pages? as that explains why the "concept thingy" doesn't work at all, infinity is not conceivable, that is what my linked explanation proves!

 

[Mr. Robin Parsons]

Originally posted by Radagast

Implicit is the assumption that an infinity has to be a number or concept to exist. Either delineate the reasons behind this assumption, or I can't see any reason to consider that argument anything but flawed.

As per my original explanation, (the link on the first page) I make no assumptions, because, all you can do is profess a belief; either it exists, or it doesn't, there is "NO proving"!

EDIT /SWITCH

 

[subtillioN]

Originally posted by Mr. Robin Parsons

The emboldened is only a proof that we cannot count to infinity, but suggests to us that it is a possibility, ergo neither a conclusion, nor a proof.

The proof that I am talking about is quite different indeed. It is not a mathematical proof but a metaphysical proof. (relating to the true nature of physical reality vs. a mere quantification of it)

 

[radagast]

Irrespective of your previous link (which I haven't read, yet), I fail to see the problem with the logic I've presented.

Just an impression, but it almost as if you're (only from the posts in this thread, since I haven't read your link), trying to define terms such that infinities cannot exist under your definitions.

 

[Mr. Robin Parsons]

Originally posted by radagast
Irrespective of your previous link (which I haven't read, yet), I fail to see the problem with the logic I've presented.

Just an impression, but it almost as if you're (only from the posts in this thread, since I haven't read your link), trying to define terms such that infinities cannot exist under your definitions.

Might I then suggest you read it, https://www.physicsforums.com/showthread.php?threadid=1438&perpage=15&pagenumber=11" at the Fourth post down, (My posting) and then you/we can discuss it better(?)

 

[radagast]

Originally posted by Mr. Robin Parsons
As per my original explanation, (the link on the first page) I make no assumptions, because, all you can do is profess a belief; either it exists, or it doesn't, there is "NO proving"!

EDIT /SWITCH

But this goes back to my initial statement that it depends on how you define exists.

Given the mathematical induction proofs, the standard definitions of the words exists, and infinity, it can be shown to exist.

Perhaps I'm missing some subtle way in which you are approaching this, but it seems fairly straightforward to me.

You do have me a little baffled at your use of words though, either it exists, or it doesn't, there is "NO proving"!

My right hand exists or it doesn't, but that doesn't keep me from proving it. You seem to be using the term exists as if it implicitly refers to objective reality, rather than (in this case) a conceptual construct, such as mathematics. If so, then I concede (and have already) that none of my arguments have been intended to reflect objective reality, with respect to infinities.

Profession of beliefs, as you use it, refers to things that cannot be known, via proof (if I get what you're saying), yet mathematical constructs are ideas delineated, with rules of interaction, which enable us to determine, thru the use of said rules, along with logic, if certain things are true or not. In this case, I cannot see anything but that it's been proven.

 

[radagast]

Having read your post, I still fail to see your point on infinities and their existence.


First:
All of the thoughts in our heads are 'delineations of space', hence we can conclude that an 'undelineated space', a 'space without boundaries', is something that we cannot conceive of.


A) the above is a definition designed to prevent a specific conclusion, I'm sure it's an argument flaw, but don't have the time to look it up at the moment. To say that all the thoughts in our heads are 'delineations of space', is not something I would concede.

Disregarding that point -
B) This may be a matter of semantics, i.e. how you define conceive differing from mine, but I have had little problem in conceiving the Euclidean 'line', which is infinite. That my mind cannot completely encompass it's entire space doesn't mean I cannot conceive of a line.

 

[Mr. Robin Parsons]

Originally posted by radagast
Having read your post, I still fail to see your point on infinities and their existence.

A) the above is a definition designed to prevent a specific conclusion, I'm sure it's an argument flaw, but don't have the time to look it up at the moment. To say that all the thoughts in our heads are 'delineations of space', is not something I would concede.

Disregarding that point -
B) This may be a matter of semantics, i.e. how you define conceive differing from mine, but I have had little problem in conceiving the Euclidean 'line', which is infinite. That my mind cannot completely encompass it's entire space doesn't mean I cannot conceive of a line.

Yes, and your concept of a line is a delineation of space, ergo "concievable"

And as per the Emboldened part of the quote of you, you sort of have that wrong it is designed to reach a specific conclusion that being the Proving of the fact of the in-conceivability of infinite.

EDIT /switch

 

[radagast]

Yet I can conceive Euclidean line, which by definition is infinite.

 

[Mr. Robin Parsons]

Originally posted by radagast
Yet I can conceive Euclidean line, which by definition is infinite.

Yes! in your imagination you can conceive of a Euclidian line, but as anyone who studies reality, by structures, knows that the 'straight' line is a misnomer, it is a series of POINTS, as all structures, in physics, at atomic levels, currently known, are spherical.

3D

Yes, and in your imagination you can fool yourself into thinking that it is infinite, but in the reality that physics studies, well, proving that one is admitted as impossible, soooo...

 

[subtillioN]

Originally posted by Mr. Robin Parsons
Yes! in your imagination you can conceive of a Euclidian line, but as anyone who studies reality, by structures, knows that the 'straight' line is a misnomer, it is a series of POINTS, as all structures, in physics, at atomic levels, currently known, are spherical.

3D

Yes, and in your imagination you can fool yourself into thinking that it is infinite, but in the reality that physics studies, well, proving that one is admitted as impossible, soooo...

I thought the point was clear that the mind was not infinite and thus could not contain an infinite thought.

The point is then can we logically understand (not replicate in the imagination) the concept of infinity.

There is a HUGE difference here that you keep getting confused about. In the understanding of infinity one must resort to logic NOT the PURE imagination that you keep referring to...and no logic is not infinite but that is beside the point. The point is that one can define a concept in such a way that it includes the concept of boundlessness. To do this it does not have to replicate this boundlessness within itself. The same way that you can concieve of a mountain without actually trying to fit it within your brain!

 

[Mr. Robin Parsons]

Originally posted by subtillioN

(SNIP) one must resort to logic NOT the PURE imagination (SNoP)

Logic is of the ImagInatIon, inseperable.

Originally posted by subtillioN
(SNIP) The point is that one can define a concept in such a way that it includes the concept of boundlessness. (SNoP)

Not if 'one'concedes that all concepts are, inherently, "bounded" things, the only other manner is the typicono'graphic that is the word "Infinite" itself, but that word incapable of describing that which it attempts to tell of/describe. (fun eh?)