Sets of objects exist in reality  how many toes have you?
Proof Infinity is Impossible

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Re: Proof Infinity is Impossible
You've got to be kidding. Toes are not an actual set of objects, they are physically continuous.

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Re: Proof Infinity is Impossible
But ultimately, your toes are made of discrete atoms.
So it makes sense to talk about the set of atoms of your toes.
 Terrapin Station
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Re: Proof Infinity is Impossible
So you just see photons, not anything moving, and you're claiming that photons are "just energy," is this correct?devans99 wrote: ↑June 27th, 2020, 3:25 pmYou can see atomic bomb blasts  with your eyes  that's got to be energy  photons.Terrapin Station wrote: ↑June 27th, 2020, 3:18 pm
You've seen video footage of energy that's not matter in motion? lol

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Re: Proof Infinity is Impossible
No, there are no discrete atoms, everything is continuous/interconnected with everything else. And even if we treat atoms as discrete, then we have discrete atoms, not sets. And even if we treat atoms as discrete and as sets, grouping the ones together that are in a toe is a perfectly arbitrary, random grouping and therefore makes no sense. I'm out.

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Re: Proof Infinity is Impossible
Well the photons have to move from the light source to your eyes.Terrapin Station wrote: ↑June 27th, 2020, 3:37 pm
So you just see photons, not anything moving, and you're claiming that photons are "just energy," is this correct?
Photons are the force carriers for the electromagnetic force, so as I understand it they are pure energy.
It gets a bit murky at that point. As far as I can make out science says photons have zero rest mass but nonzero relativistic mass (not sure what that means, never got around to looking at it.
Mass is equivalent to energy so I personally expect photons to have a very tiny mass.
Mass is equivalent to energy. Space has energy, so it has mass. So space is something rather than nothing.

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Re: Proof Infinity is Impossible
Science says there are discrete atoms.Atla wrote: ↑June 27th, 2020, 3:41 pm
No, there are no discrete atoms, everything is continuous/interconnected with everything else. And even if we treat atoms as discrete, then we have discrete atoms, not sets. And even if we treat atoms as discrete and as sets, grouping the ones together that are in a toe is a perfectly arbitrary, random grouping and therefore makes no sense. I'm out.
Ernest Rutherford bounced particles off the nucleus of gold atoms to prove the point around the 1900s. I believe its been extensively verified since then.

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Re: Proof Infinity is Impossible
No, science says no such thing and what Rutherford has shown isn't about (fundamental) discreteness.devans99 wrote: ↑June 27th, 2020, 3:50 pmScience says there are discrete atoms.Atla wrote: ↑June 27th, 2020, 3:41 pm
No, there are no discrete atoms, everything is continuous/interconnected with everything else. And even if we treat atoms as discrete, then we have discrete atoms, not sets. And even if we treat atoms as discrete and as sets, grouping the ones together that are in a toe is a perfectly arbitrary, random grouping and therefore makes no sense. I'm out.
Ernest Rutherford bounced particles off the nucleus of gold atoms to prove the point around the 1900s. I believe its been extensively verified since then.
 Terrapin Station
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Re: Proof Infinity is Impossible
You're overlooking what I'm really asking you. You're claiming that on a video of something like a nuclear blast, you're only observing photons?devans99 wrote: ↑June 27th, 2020, 3:47 pmWell the photons have to move from the light source to your eyes.Terrapin Station wrote: ↑June 27th, 2020, 3:37 pm
So you just see photons, not anything moving, and you're claiming that photons are "just energy," is this correct?
Photons are the force carriers for the electromagnetic force, so as I understand it they are pure energy.
It gets a bit murky at that point. As far as I can make out science says photons have zero rest mass but nonzero relativistic mass (not sure what that means, never got around to looking at it.
Mass is equivalent to energy so I personally expect photons to have a very tiny mass.
Mass is equivalent to energy. Space has energy, so it has mass. So space is something rather than nothing.
 Thomyum2
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Re: Proof Infinity is Impossible
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.devans99 wrote: ↑June 27th, 2020, 2:45 pmI think that the requirement for an object to have a nonzero, positive, length does rule out any/all objects from having a UNDEFINED length:
An UNDEFINED length means the object is missing a start or an end or both. Such objects are invalid topologically. For example, an infinite brick with a leftend but no rightend, if it has no rightend, it cannot have a middle (because the middle would count as the rightend). And if it has no rightend, it cannot have a leftend, because the rightend would count as the leftend.
You’ve proposed a 3dimensional 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.
Sure, I see the analogy, but it's important to keep in mind the distinction between the characteristics numbers have in their own right versus those we give them by the way we choose to arrange them on a physical object for a given purpose. Numbers have a sequence, but don't really have a 'structure'.devans99 wrote: ↑June 27th, 2020, 2:45 pmBy ‘entire structure of the natural numbers’  imagine a ruler with every natural number on it. Its topologically very similar to the brick analogy I'm using.
Natural numbers are measures by themselves and their quantity is equal to their size.
…
Sets can be arrange linearly  then they have a dimension  so they are measurable with the natural numbers .
I hope you can see that set of natural numbers, arranged linearly, is a measure and I hope you see that it is analogous to an infinite ruler or infinite brick.
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 actually happen to think this is likely true. I just don’t think you’ve succeeding in proving it yet.
 Sculptor1
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Re: Proof Infinity is Impossible
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.

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Re: Proof Infinity is Impossible
Okay. If this is what 'it' IS, to you, then that is the way 'it' is. Full stop.devans99 wrote: ↑June 27th, 2020, 9:58 amSpace itself is expanding  distance galaxies recede from us at faster than light speed  that's only possible if space is expanding.evolution wrote: ↑June 27th, 2020, 9:50 amBut, from my perspective, 'space' is NOT something that itself could expand.
What is the 'it' in reference to here?
Does this mean that if numbers can be infinite, then so to can distance?
Did you actually read what I wrote above in regards to a 'brick'?
If yes, then what did you actually get, from what I actually wrote?
So space is something, so space is an object, so space must be finite too.
Numbers can't be infinite. Infinite means larger than finite, but finite numbers go on forever  so its not possible for a number to be larger than finite  so there are no infinite numbers.
Space is just like the brick example I gave in the OP  it has to be finite.
Now, what was your purpose in 'trying to' prove to others that infinity is impossible?
 Consul
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Re: Proof Infinity is Impossible
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 twothirds 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 subR is any occupiable subregion of R whatever, there exists a material object that occupies the region subR at t."
(Van Inwagen, Peter. "The Doctrine of Arbitrary Undetached Parts." In Ontology, Identity, and Modality: Essays in Metaphysics, 7594. Cambridge: Cambridge University Press, 2001. p. 75)
<QUOTE
"We may philosophize well or ill, but we must philosophize." – Wilfrid Sellars
 Consul
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Re: Proof Infinity is Impossible
There needn't be any abstract object which is the set of my toes in order for my statement "I have ten toes" to be true.
"We may philosophize well or ill, but we must philosophize." – Wilfrid Sellars