Proof Infinity is Impossible

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Consul
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Re: Proof Infinity is Impossible

Post by Consul » June 28th, 2020, 12:18 am

devans99 wrote:
June 27th, 2020, 10:17 am
But E=mc^2 - matter and energy are equivalent.
No, they are not, because "m" stands for "mass" rather than for "matter".

Misconceptions about Eo=mc2: https://plato.stanford.edu/entries/equi ... cAbouEoMc2
"We may philosophize well or ill, but we must philosophize." – Wilfrid Sellars

devans99
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Re: Proof Infinity is Impossible

Post by devans99 » June 28th, 2020, 8:21 am

Thomyum2 wrote:
June 27th, 2020, 4:42 pm

An object is simply something that can be observed. A material object, which is what we’re talking about here, is one that occupies space and has mass. There’s no requirement that it cannot be missing an ‘end’ or that it must have a middle. In fact, objects don’t even have a ‘start’ or an ‘end’, which are just terms that refer to those points where we begin and end our observation or measurement of it.

You’ve proposed a 3-dimensional brick which has five boundaries instead of the usual six, with four of the sides extending infinitely in one direction. There’s nothing here that makes this logically impossible – it only seems so because no one has ever recorded encountering such a thing, and because our current conceptual models of the structure of matter and space don't easily accommodate it.

Natural numbers are counts, not measures - these are not the same thing. Discrete entities can be counted, but a single object is a continuous entity and so its dimensions can only be measured. To measure, you have to devise a unit against which you can compare the object to perform the measurement, which you then do by counting the units. Yes, to accomplish this you can arrange numbers linearly on another object (such as a ruler) and space them equally apart (by the amount of your unit), and by doing so create a tool for measuring. But numbers only are used in measurements for purposes of counting the units - you cannot measure anything just with numbers.

The same thing applies to sets: these are conceptual collections of items with a defined set of characteristics. A ‘collection’, in and of itself, has no inherent spatial dimension until you give it one.
I think you are not quite seeing that the topology of something without end is fundamentally impossible - you might like to think further on the nature of a finite brick with a left end and no right end - can you explain how you can conceive of such a thing existing?

Here is a different proof that comes to the same conclusion:

1) Imagine a ruler that has a left end but no right end.
2) It goes on forever so logically it has all the natural numbers inscribed upon it,
3) (incidentally - if that's not a measure, I'm not sure what it? The natural numbers are a kind of measure - you just need to assign an arbitrary scale to them - eg 1 = 1 cm, 2 = 2 cm, etc...)
4) If it has every natural number X inscribed upon it, it must be longer than all natural numbers X
5) But natural numbers increase without bound - its impossible for something to be larger than all natural numbers (because they go on forever)
6) So the ruler cannot be longer than all natural numbers
7) So an infinite ruler is impossible

devans99
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Re: Proof Infinity is Impossible

Post by devans99 » June 28th, 2020, 8:36 am

Sculptor1 wrote:
June 27th, 2020, 5:45 pm
devans99 wrote:
June 27th, 2020, 2:50 pm


Maths explicitly declares there exists a set with a greater than finite number of objects in it.
No. Maths has some abstract ideas, that can exist in people's heads without ANY reference to reality.
Such as the square root of minus one. Or ANY negative number. Or ANY irrational number.
It can have perfection such as circles, and straight lines. None of which can exist in reality.
I think it you read the actual definition, it clearly says 'there exists...':

https://en.wikipedia.org/wiki/Axiom_of_infinity

If then you look at the dictionary definition of 'exists' - 'have objective reality or being'.

That's pretty clear - maths says infinite objects exist in reality.

It is set theory we are talking about here - sets clearly exist in reality - and maths is saying that a set with a greater than finite number of objects exists in reality.

Anyway, infinity is logically impossible - so it cannot even exist in our heads - see the infinite brick example in the OP - it does not make sense even in our minds. In our minds we can imagine all sorts of things, including impossible stuff like talking trees or fairies - infinity is in the same category - illogical.

I'll give you one more example:

1) Maths says a line segment is made up of an uncountably infinite number of zero length points (the Dedekind-Cantor continuum - as taught in school)
2) How many points are there on a line segment length 1?
3) line length / point length = number of points
4) IE 1 / 0 = UNDEFINED
5) So you see if we assume an infinite number of zero length points, we get a nonsense result.
6) So it must actually be line segments are composed of a finite number of non-zero length points

It all comes down to Euclid - he said 'a point is that which has no extent'. But if it has no extent, it cannot exist, so it can't be the subcomponent of other components.

Atla
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Re: Proof Infinity is Impossible

Post by Atla » June 28th, 2020, 9:44 am

Sculptor1 wrote:
June 27th, 2020, 5:42 pm
Atla wrote:
June 27th, 2020, 2:43 pm

Space can be a bigger infinite ffs.
HAHAHA
Or did you really think that there can only be one kind of "actual" infinity

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Re: Proof Infinity is Impossible

Post by Atla » June 28th, 2020, 9:46 am

Consul wrote:
June 28th, 2020, 12:13 am
Atla wrote:
June 27th, 2020, 3:31 pm
You've got to be kidding. Toes are not an actual set of objects, they are physically continuous.
According to the mereological doctrine called the Doctrine of Arbitrary Undetached Parts, your toes needn't be physically discontinuous with or disconnected from your feet in order to be material objects in their own right.

QUOTE>
"Many philosophers accept what I shall call the Doctrine of Arbitrary Undetached Parts (DAUP). Adherents of this doctrine believe in such objects as the northern half of the Eiffel Tower, the middle two-thirds of the cigar Uncle Henry is smoking, and the thousands (at least) of overlapping perfect duplicates of Michelangelo's David that were hidden inside the block of marble from which (as they see it) Michelangelo liberated the David. Moreover , they do not believe in only some 'undetached parts'; they believe, so to speak, in all of them. The following statement of DAUP, though it is imperfect in some respects, at least captures the generality of the doctrine I mean to denote by that name:

For every material object M, if R is the region of space occupied by M at time t, and if sub-R is any occupiable sub-region of R whatever, there exists a material object that occupies the region sub-R at t."

(Van Inwagen, Peter. "The Doctrine of Arbitrary Undetached Parts." In Ontology, Identity, and Modality: Essays in Metaphysics, 75-94. Cambridge: Cambridge University Press, 2001. p. 75)
<QUOTE
You don't have to copy/paste every unhinged nonsense you find.

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Terrapin Station
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Re: Proof Infinity is Impossible

Post by Terrapin Station » June 28th, 2020, 11:40 am

devans99 wrote:
June 28th, 2020, 8:21 am
Still didn't answer. You're claiming that what you're observing on a video is photons?

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Thomyum2
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Re: Proof Infinity is Impossible

Post by Thomyum2 » June 28th, 2020, 12:01 pm

devans99 wrote:
June 28th, 2020, 8:21 am
I think you are not quite seeing that the topology of something without end is fundamentally impossible - you might like to think further on the nature of a finite brick with a left end and no right end - can you explain how you can conceive of such a thing existing?
No, I cannot conceive of such a thing existing. But that I cannot conceive of it does make it 'fundamentally impossible'.
devans99 wrote:
June 28th, 2020, 8:21 am
Here is a different proof that comes to the same conclusion:

1) Imagine a ruler that has a left end but no right end.
2) It goes on forever so logically it has all the natural numbers inscribed upon it,
3) (incidentally - if that's not a measure, I'm not sure what it? The natural numbers are a kind of measure - you just need to assign an arbitrary scale to them - eg 1 = 1 cm, 2 = 2 cm, etc...)
4) If it has every natural number X inscribed upon it, it must be longer than all natural numbers X
5) But natural numbers increase without bound - its impossible for something to be larger than all natural numbers (because they go on forever)
6) So the ruler cannot be longer than all natural numbers
7) So an infinite ruler is impossible
This proof is less convincing than the first one! It is full of nonsensical statements:

2) - It cannot have 'all the natural numbers' on it - there is no such thing as 'all' of an infinite series, by definition.
4) & 5) & 6) - It cannot be 'longer than all natural numbers' because a number has no length. An object can only be longer than another object, not longer than a number. You are comparing measurements to counts again. It wouldn't make sense to say that "this brick is longer than the number of beans in this jar", would it?

I suggest that infinity is fundamentally unknowable, perhaps, or as you said, 'undefined'. But it does not follow that it is impossible. There is no possible or impossible in the empirical sciences of material things - there is only what we have observed, and what we have not observed.

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Thomyum2
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Re: Proof Infinity is Impossible

Post by Thomyum2 » June 28th, 2020, 12:04 pm

Edit to the above post - second sentence should read: "But that I cannot conceive of it does not make it 'fundamentally impossible'."

devans99
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Re: Proof Infinity is Impossible

Post by devans99 » June 28th, 2020, 12:08 pm

Terrapin Station wrote:
June 28th, 2020, 11:40 am
Still didn't answer. You're claiming that what you're observing on a video is photons?
It is clearly something (energy) travelling from a light source (the explosion) to a camera (which detects and records photons).

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Re: Proof Infinity is Impossible

Post by devans99 » June 28th, 2020, 12:12 pm

Thomyum2 wrote:
June 28th, 2020, 12:01 pm
devans99 wrote:
June 28th, 2020, 8:21 am
Here is a different proof that comes to the same conclusion:

1) Imagine a ruler that has a left end but no right end.
2) It goes on forever so logically it has all the natural numbers inscribed upon it,
3) (incidentally - if that's not a measure, I'm not sure what it? The natural numbers are a kind of measure - you just need to assign an arbitrary scale to them - eg 1 = 1 cm, 2 = 2 cm, etc...)
4) If it has every natural number X inscribed upon it, it must be longer than all natural numbers X
5) But natural numbers increase without bound - its impossible for something to be larger than all natural numbers (because they go on forever)
6) So the ruler cannot be longer than all natural numbers
7) So an infinite ruler is impossible
This proof is less convincing than the first one! It is full of nonsensical statements:

2) - It cannot have 'all the natural numbers' on it - there is no such thing as 'all' of an infinite series, by definition.
4) & 5) & 6) - It cannot be 'longer than all natural numbers' because a number has no length. An object can only be longer than another object, not longer than a number. You are comparing measurements to counts again. It wouldn't make sense to say that "this brick is longer than the number of beans in this jar", would it?

I suggest that infinity is fundamentally unknowable, perhaps, or as you said, 'undefined'. But it does not follow that it is impossible. There is no possible or impossible in the empirical sciences of material things - there is only what we have observed, and what we have not observed.
But we are assuming an INFINITE ruler - it goes on forever - so logically, it must have every natural number inscribed upon it.

I am using the natural numbers as a measure of the ruler (the ruler has 1,2,3,4... on it at 1cm intervals). If the ruler goes on forever, then it is longer than any finite natural number, so it must be longer than all natural numbers - but that's impossible (natural numbers go on forever) - so an infinite rule is impossible.

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Re: Proof Infinity is Impossible

Post by Steve3007 » June 28th, 2020, 12:14 pm

There are an infinite number of even numbers. Therefore there are no odd numbers.

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Re: Proof Infinity is Impossible

Post by Terrapin Station » June 28th, 2020, 12:39 pm

devans99 wrote:
June 28th, 2020, 12:08 pm
Terrapin Station wrote:
June 28th, 2020, 11:40 am
Still didn't answer. You're claiming that what you're observing on a video is photons?
It is clearly something (energy) travelling from a light source (the explosion) to a camera (which detects and records photons).
Here's an example of a hydrogen bomb test video:
What do we see there? Super-heated particles (at least some of it in a plasma state), smoke-like, billowing, expanding clouds of particulates, buildings being destroyed, etc. Right?

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Ron Krumpos
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Re: Proof Infinity is Impossible

Post by Ron Krumpos » June 28th, 2020, 12:56 pm

Our biggest 'brick' is our mind. The concept of infinity is suprarational, beyond reason, logic or images.

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Re: Proof Infinity is Impossible

Post by Thomyum2 » June 28th, 2020, 12:58 pm

devans99 wrote:
June 28th, 2020, 12:12 pm
But we are assuming an INFINITE ruler - it goes on forever - so logically, it must have every natural number inscribed upon it.

I am using the natural numbers as a measure of the ruler (the ruler has 1,2,3,4... on it at 1cm intervals). If the ruler goes on forever, then it is longer than any finite natural number, so it must be longer than all natural numbers - but that's impossible (natural numbers go on forever) - so an infinite rule is impossible.
Yes, I follow the thought experiment, but still find it nonsensical (nothing personal - I just find most talk involving infinity to be nonsensical in general :) ). It cannot have 'every number' on it, because by definition, there is no such thing as 'every number'. Terms such as 'every' and 'all' only apply sensibly to finite sets or quantities.

So it also doesn't make sense to say that the infinite ruler is longer than all natural numbers. It could be said that for any given natural number X, that the infinite ruler has a length greater than X units. In other words, for any finite ruler that you could place against the infinite one, you could see that the infinite extended further. But it could not be said that length of the ruler is greater than all numbers, because that is not sensible. (And even if it was, I still don't see how that would prove that the infinite object is impossible.)

Incidentally, I have read that Cantor did make proofs that there are different kinds of infinities and that actually some infinite sets can be shown to be larger than other infinite sets - that there are actually different kinds of infinities - but that's a level of mathematics that's a bit over my head.

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Re: Proof Infinity is Impossible

Post by devans99 » June 28th, 2020, 1:03 pm

Terrapin Station wrote:
June 28th, 2020, 12:39 pm


Here's an example of a hydrogen bomb test video:


What do we see there? Super-heated particles (at least some of it in a plasma state), smoke-like, billowing, expanding clouds of particulates, buildings being destroyed, etc. Right?
Super-heated particles? Guess they must of been heated up by the energy released in the explosion?

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