If you could have a finite period of time, it would be impossible to have an infinite number of states in that time because it would require time to change from one state to the nex — Metaphysician Undercover
I don't believe that you can model a continuum in this way, because you are assigning ends to it. What principle allows you to put a beginning and an end to a continuum? — Metaphysician Undercover
This is contradiction. You are saying that the continuum is made up of discrete units, "1 second", "1 year". To say that is to deny that it is a continuum — Metaphysician Undercover
Right, if you could model time as discrete units you would not run into these problems. The problem though, is that we experience time as continuous, and we've found no natural divisions to form the basis for the finite N, the number of discrete units per second. I don't think the Planck unit provides us with this. — Metaphysician Undercover
It is possible because of the nature of continuous: to move from point 0 to point 1, you first have to travel through point 0.1, then 0.01, then 0.001, then 0.0001 and so on to infinity. Each distinct point represents a different state with different distinct time and space co-ordinates. — Devans99
Any given finite distance we can represent by the reals between 0 and 1. For instance the distance of 2 miles maps like this:
0 mile -> 0.0
1 mile -> 0.5
2 miles -> 1.0 — Devans99
I mean that we can use arbitrary units to sub-divide the continuum (but it is not actually made of discrete units). — Devans99
That's how it is when someone has a Belief about something — SteveKlinko
The traditional Christian view of God is that he is eternal and infinite. I wonder if some people are still religiously invested in infinity? I suspect some atheists might likewise be 'religiously' invested in infinity as a mechanism to explain the apparent fine tuning of the universe for life?
Every time you really work out a problem or analyze a little Deeper it is always found that Infinity is a big problem — SteveKlinko
Wikipedia lists a few (but there are more):
https://en.wikipedia.org/wiki/List_of_paradoxes#Infinity_and_infinitesimals
In cosmology they have this paradox:
https://en.wikipedia.org/wiki/Measure_problem_(cosmology)
The solution is a finite universe but cosmologists press on regardless... — Devans99
Watching a sunset means to observe a sun from one event being not below horizon to is one. Remember that is comparing and observation is a phenomenon therefore you are part of the event as well as thoughts that you think of. It's just comparing a prior to the now. — BB100
Also when I mean points I meant if you were to describe a ball at the top of your house and than it was on your porch, it would be referring to the events that happened in between those two like being at certain relative distances at certain events. This also goes to my point of not infinite past for there can not be an infinite events inverween the ball at the top and to the prch for addition synthesis from a point never leads to infinity. — BB100
So you're just restating Zeno's paradox — Metaphysician Undercover
Clearly, your sets as written do not indicate that the right is a subset of the left. The left contains 4 and 6, which are not contained in the right. It is not a subset. — Metaphysician Undercover
If you buy 4D space-time, then information is not transitory, it has permanent residence in a region of space-time, so I would expect information density to apply over a time period as well as a volume of space. — Devans99
Say we have a system composed of 1 particle that travels 1 meter in 1 second. If space is continuous, how many different states does the system go through? IE If the particle is travelling along the X-axis, the states are just the different positions it occupies x=0 x=0.1 etc... — Devans99
You have got to be kidding me. Both the left and right contained 4 and 6, your just had to continue the mapping a few more spots. — MindForged
(4 & 6 appeared on the right side earlier because the right side was only even numbers, so obviously the natural numbers take longer to get to the even numbers since it also has the odd numbers). — MindForged
What is the meaning of actual infinity?
Do you mean physically manifest? If so, space may be infinite. — TheMadFool
Actually I don't buy 4D space-time — Metaphysician Undercover
And you haven't really explained what you mean by "information density" so I'm sort of lost here. — Metaphysician Undercover
This is why Aristotle concluded that there is a categorical difference between being and becoming, which cannot be reconciled: the two are in compatible. If change is represented as two distinct states of being (the ball on the roof, and the ball on the porch for example), then to account for the change between these two states we need to introduce a third state which is neither the one nor the other. Now we have an intermediate state, and we need to account for the change between the first and the intermediate, as well as the intermediate and the other, so we introduce two more states. This would result in an infinite regress of states. There appears to be an infinite number of states between any two states, if change is represented as different states. So he proposed that "becoming" (active change) is categorically different from "being" (states of existence), and activity cannot be represented by states. — Metaphysician Undercover
Aristotle handled the topic of infinity in Physics and in Metaphysics. He distinguished between actual and potential infinity. Actual infinity is completed and definite, and consists of infinitely many elements. Potential infinity is never complete: elements can be always added, but never infinitely many — Wikipedia
Can you explain the last bit? "elements can always be added, but never infinitely many"? — TheMadFool
Do you buy special relativity? He only has two axioms and both sound very reasonable: — Devans99
1. Something can’t come from nothing
2. So base reality must have always existed
3. If base reality is permanent it must be timeless (to avoid actual infinity)
4. Time was created and exists within this permanent, timeless, base reality
5. So time must be real, permanent and finite — Devans99
The amount of information you can get into a volume of space-time by regarding the spacial co-ordinates of particles as information:
- So in discrete space, I could represent a particle's position with (0.35, 0.60, 0.90); terminating decimals / rational numbers - a finite amount of information.
- But in continuous space, the particle's position is represented by (0.353534..., 0.604836..., 0.903742...); non-terminating real numbers - an infinite amount of information.
An infinite amount of information in a finite volume of space-time is nonsense and leads to paradoxes... — Devans99
I don't think that it's reasonable to believe the speed of light to be constant. — Metaphysician Undercover
I see a logical flaw here. You have a base reality which is permanent and timeless. You have a time which is created, comes into existence, within this permanent, timeless base reality. But then you conclude that time is permanent. That is contrary to your premise, that time is created. — Metaphysician Undercover
I agree with you on this matter. Now look at what happens if we separate space from time, and postulate a discrete space with a continuous time. The particle has an infinite number of possible locations because the time between t1 and t2 is infinitely divisible. However, the discrete space limits these possibilities to a finite number. So within the immaterial realm, which is represented conceptually as the realm of time passing, there are infinite possibilities, the information is infinite. But in actuality, the possibilities (and therefore information) are limited by the true nature of space. — Metaphysician Undercover
don't think an axiom is right or wrong. By definition it is accepted as true. If course we can reject it but that doesn't invalidate the theorems that derive from the axiom. — TheMadFool
By the way I still don't understand the difference between actual and potential infinity — TheMadFool
A universal speed limit makes sense for any universe; if you allow objects to be accelerated upto an infinite velocity (as in Newtonian mechanics), then you get bizarre paradoxes like objects suddenly disappearing from the universe. — Devans99
If you doubt the speed of light is constant you are also dismissing much of modern science: — Devans99
How would time be created/made real in such a base reality? Each moment in our time must have been mapped to a co-ordinate in timeless, permanent, base reality. Hence past, present, and future are equally real. — Devans99
The problem is if you assume time is immaterial, you get eternal existence then you get all the paradoxes listed in this OP: — Devans99
It's not that there is a universal speed limit which I doubt, it is that there is something (light) which has the same speed in every frame of reference. I think that it is quite plausible that there is a universal speed limit, but we do not know enough about the universe to be able to determine it. — Metaphysician Undercover
Yes, and if you've read my earlier posts I've dismissed a lot of modern mathematics as well as contradictory. — Metaphysician Undercover
Can you imagine a point in time when there was a future with no past? — Metaphysician Undercover
How is "eternal existence" different from your assumption of a permanent base reality? — Metaphysician Undercover
Maths should not reflect whats impossible. — Devans99
don't know if infinity has practical applications but surely it is interesting to realize we can analyze it in an understandable way through set theory or whatever else it is. — TheMadFool
The start of time. Time is finite and permanent. Has a start and end. Its possible the start and end are joined to form a circle. — Devans99
The difference is:
- Eternal existence implies everything has existed for ever within time. Implies time has no start. Implies Actual Infinity. Implies all the paradoxes I listed in the other OP.
- Permanent existence outside of time does not require Actual Infinity. — Devans99
Mathematicians create universes with different axioms and then study them logically. If such a creation finds practical application in the world then well and good but this isn't a necessity.
Strangely, it's more a rule than an exception that mathematical theories have actual real world applications. I don't know if infinity has practical applications but surely it is interesting to realize we can analyze it in an understandable way through set theory or whatever else it is. — TheMadFool
s contradictory, to say that something has a start and end and also that it is permanent. If it's circular there is no start or end. — Metaphysician Undercover
You're using a different definition of "eternal" again. We were talking about "eternal" in the sense of outside of time. This is clear from you assumption of a "timeless" base reality. So your argument here for a difference is just equivocation. — Metaphysician Undercover
we have a problem with your stated claim that time co-exists with this eternal existence. Unless you allow for a dualist separation, or some such thing, you have the contradictory properties of "timeless", and also "time", referring to one and the same reality. — Metaphysician Undercover
Not if you are thinking 4D space-time; you have to imagine the universe as a static object in 4D space-time. — Devans99
What I mean is time exists inside the timeless base reality. So time is a finite 'thing' existing within a timeless, permanent, finite base reality. — Devans99
If I continue the mapping a few more spots, the even numbers go to 8, 10. But these numbers will be outside of the set of natural numbers, on the left. Don't you see that with this type of mapping, the set of even numbers will always contain numbers outside the set of natural numbers which it is mapped to, so it is impossible for it to be a subset? — Metaphysician Undercover
Right, so no matter how you lay it out, if you maintain equal cardinality the set on the right side will always contain numbers which are not contained in the set on the left side. Surely you can acknowledge this. So do you agree with me that it is impossible that the set on the right side is a subset of the set on the left side? If not, why not? — Metaphysician Undercover
When you say "the natural mumbers" you're ready conceding the issue because you're tacitly acknowledging that there's some common property or rule which makes some numbers "natural numbers". — MindForged
The even numbers are necessarily part of the natural numbers, it's literally just the naturals without the odd numbers, that's a proper subset. — MindForged
No because no matter what even number shows us we will always get it in the naturals just a few spots down. I've already explained why not. Speaking of the natural numbers and the even numbers is not me creating said sets by extensionally writing out small parts of the set. That's simply to illustrate the pattern. Unless you seriously think understanding a mathematical relationship requires writing out a entire pattern, this response of yours isn't sensible. It's not a real objection. — MindForged
This is why we need good ontology, metaphysics, to separate the principles, or axioms which are consistent with the true actual reality, from those which simply appear to be such because they are useful. — Metaphysician Undercover
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