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The completed set of natural numbers exists only as a (flawed) concept within our heads; it is no way realisable because it is illogical so cannot exist in the real world.
That set has no well defined end so it is not completely defined and hence it is invalid. Thats why we get all these crazy paradoxes as soon as we go anywhere near actual infinity.
Listen: I'm not going to argue mathematics with you: in mathematics, the set of natural numbers is an actual infinity, not a potential infinity. The contradictions that you think you see come from how you are thinking about constructing sets. We do not construct them the way you described (by counting) for basically that very reason.
/e I mean seriously, how many times have you contradicted yourself (forget mathematics) on the subject of infinity? You have to stop using common sense for that subject if you want to have any consistency. In these subjects: common sense is worse than worthless, it is just plain wrong.
The actual infinite set is defined by the 'axiom of infinity' which just says an actual infinite set exists; it does not prove anything and it's laughably easy to disprove the existence of actual infinity as I just did. Set theory is utter bollocks.
And there we have it folks. BTW set theory unpins probability, classical mechanics, quantum mechanics, and statistics; just to name a few subjects. If you had said that at the start, you could have saved us all a lot of time!
Its fatally flawed. At its heart is a polymorphic definition of a set; as both a well defined, finite object and as the selection criteria for a potentially actually infinite set, which is not a well defined object.
Cantor believed God was infinite; that was the whole reason for introducing actual infinity into set theory: to model God not nature.
Mathematics is the logic of certainty. -Joe Blitzstein
It is not a model of nature.
But the axiom of infinity is just plain wrong... thats where all the paradoxes come from. Honestly, the set of all sets does not exist. Pull the other one. Cantors paradox, Galileo's paradox, Hilbert's Hotel, all due to the error of assuming the actually infinite exists.
Those only carry the label of "paradox" for legacy reasons.
Set theory was patched up with duck tape to hide all the paradoxes.
Space would contract rather like it is expanding at the moment, so the photons would have nowhere to escape; they would be pulled back into the big crunch with everything else.
Sorry guys, I am dropping out. Dan has spewed so WRONG I can never hope of commenting on all of it.
Dan, EVERY DAMNED word you have typed is completely wrong. Go back to school and study theoretical astrophysics and you will discover how wrong that delusion is.
rmfr
You need to open your mind, not everything they taught you at school was right. Science is a succession of two steps forward, one step back. Science makes huge mistakes, for example:
https://en.wikipedia.org/wiki/Phlogiston_theory
We have to remain open minded and question established dogma.
The only dogma I have ever seen that needs questioning is religion and its cousin pseudoscience.
You have yet to spew nothing else but religion and pseudoscience.
rmfr
I note you are not addressing my actual arguments but are instead resorting to vague generalities.
Dan, the problem is people are providing you with answers that have the preponderance of evidence to support it...
I.e. acceleration of the universe and dark energy being repulsive... thus supporting big rip/entropy death.
And you simply swipe it away saying "No I don't buy it" etc... Well sorry, the universe doesn't care what you like/dislike.
The best we can do is be good Bayesians and follow the data.
Furthermore, it's great to be sceptical and yes mistakes are made in the past in science but surely if you are holding science to that level, then you should do likewise with religion!
Is it possible they made massive mistakes 2000 years ago!
I'm not religious. The expansion rate of the universe has changed in the past; there is no reason to not expect it to change again in the future.
The big rip/heat death scenarios do not work because there is an end of time and everything has to come back to the state at the start of time; IE Big Crunch. Energy/Matter cannot just disappear into thin air, it has to go somewhere.
The only place in the universe there is enough energy/matter for the Big Bang is the Big Crunch.
Those models don't have an end of time; so your criticism of them doesn't make much sense.
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The expansion rate is a function of the Hubble parameter, which is a function of time.
But if you belief in Eternalism And Finitism then logically there must be an end of time, so those models that do not have an end of time are suspect.
The expansion rate was dramatically higher during the era of Inflation, then it slowed right down, some research says its oscillating right now; who knows what will happen in the future. We could have Cosmic Deflation and a big crunch.
You postulate that time must have an end, then try to use that to argue that other models are wrong? That is one of the most egregious acts of question begging I've ever seen. That is like hall of shame worthy.
Its quite a simple argument; we live in 4d space time and everything is finite. That logically leads to an end of time.
That is not a postulate of Special Relativity. Which makes your statement that SR agrees wildly inaccurate. If you want SR as evidence that your postulates are right, you need to show that SR comes to the same conclusions as you, without using your postulates. You are question begging, again.
SR demonstrates the Eternalism, I've demonstrated the finitism. The two add up to an end of time.
Do you have citations to back your claims?
Well these are new mostly ideas so I do not have many citations... the Special and General Theories of Relativity both agree with my conclusion.
I hope people will look at the arguments with an open mind.
Please tell us exactly how SR agrees with your postulate that time must have an end. Please be explicit.
Well it says that eternalism is right. Then all you need is finitism and you must have logically an end of time.
Please provide a detailed derivation using only SR, that reproduces your postulate of "eternalism".
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What? More question begging. If SR agrees with you (like you said it does) you'll need a SR derivation for "finitism".
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Both of these tasks (even if you are right) are nigh impossible; because to do this you will need to derive a mathematical relation that is interchangeable with your postulate(s); which you haven't even yet expressed as a relation. Good luck!
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/e It is easy to just sit there and claim SR or any other model supports you; it is quite another to demonstrate it. People who have never done this sort of thing don't seem to appreciate how hard it is; even if you already know it is true!
Very well put indeed sir.
And with that, I think we can assert that...
1. You haven't met the burden of proof.
2. And albeit a theoretical possibility, you haven't actually 'proved' your claim.
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