Things do not move through time at all. Space-time is a coordinate system
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Second. Things do not move through time at all. Time is defined by correlating between different kinds of change of state of physical systems.
I already already refuted your claim that your description of time doesn't have problems with an infinite number of past state changes being impossible.
You ignored what I said which refuted your claim and merely repeated your original claim, which is a fallacy of repetition.
Can you find a mathematical contradiction with a past infinite universe? If not then it's not contradictory. Mathematical relations are necessarily logically valid.
You don't understand that the nature of abstract mathematics allows for the construction of mathematically valid concepts that have no possible relationship to concrete reality.
Although there can be an infinite number of abstract objects in a mathematical formulation, in reality there are many reasons this doesn't work.
One example I already gave, which you ignored, is that if there were an infinite number of state changes and you started at the beginning then you could never arrive at the present state. You have not attempted to refute that. Therefore my conclusion remains standing against your claim.
To that I can add another example that helps demonstrate why this can't work in reality; The grim reaper paradox.
Starting at 8am, at 9am a grim reaper will activate to kill a particular individual if they are still alive.
But at every halfway point prior to that another grim reaper will activate to kill the target if they are still alive. Ie. One at 8:30am, another at 8:15, etc.
It's impossible for the target to survive until 9am, yet no specific grim reaper is capable of actually killing the target because it divides infinitely without ever coming to an end.
Mathematically you could probably write this out as a valid abstract formula. But it doesn't translate into something that works in concrete reality.
It is physically impossible to traverse an infinite series of events or states to any given point.
Other examples that show the absurdity of an actual number of concrete objects in the universe:
Let's say you had an infinite number of actual objects lined up in the universe.
You have an infinite number of objects lined up in front of you. You double the number of objects lined up in front of you. How many do you have now? Infinity. The same number as you started with. et there are twice as many objects. But math says you have the same number of objects.
What if you take an infinite number of objects in a line and you cut every even numbered one out. How many would you have?
So infinity - infinity = infinity.
What if you removed all the objects?
Infinity - infinity = zero.
What if you removed all objects but 10 of them?
Infinity - infinity = 10.
How long will it take man A to count to infinity? Infinity.
How long will it take man B to counter to infinity if he counts 100,000 times faster? Infinity.
Mathematically the same answer, but in terms of reality we know one should be faster than the other.
So the exact same equation gives you different answers. A logical absurdity and an impossibility in reality.
This is a case where math is telling you things that wouldn't line up with reality.
But we can take that example further and show why the task itself cannot be physically undertaken:
You would never be able to arrive at the end of the equation because you would spend an infinite amount of time trying to add and subject infinity from the equation.
Infinity as an actual number of things also cannot exist because you could never arrive at the point where you could create an infinite number of objects to add to the equation. You'd never arrive at the point at which you had achieved creating an infinite number of objects. It would take you an infinite mount of time - which could never be reached.
We can take this further and say that true infinity, with regards to sets of objects (such as sequential numbers), doesn't even exist in math. Which refutes your claim that infinity is consistent with math. You might represent the concept of infinity with a symbol - but you can't actually calculate using an infinite number of objects. You'd never be able to arrive at the end point in order to complete your equation because there is no end point. Not that I am referring to math with regards to an infinite set of numbers/objects, not math with regards to an equation that cycles around repeating itself infinitely (such as an equation that generates fractals patterns).
This is similar to the grim reaper paradox whereby the equation is stuck in a loop where it can't be solved because it's waiting for an infinite number to reach an end point but it never can.
If a consistent mathematical theory exists for a past eternal universe (and it does... see loop quantum cosmology), then there cannot be any logical contradiction with a past eternal universe regardless of what someone like Craig says.
There are two problems with your claim:
1. You are operating from the fallacy that mathematically proven ideas are proven to exist in reality. The examples I gave above should be sufficient to demonstrate that is not always the case.
Another example that comes to mind is Hawking could use imaginary numbers to remove the troublesome singularity behind the creation of the universe from his equations, but then his equations no longer reflected reality so therefore wasn't useful to describe anything. When his equations were converted back to real numbers to reflect reality the singularity reappeared.
You can use math tricks to prove all manner of absurd things that don't conform to physical reality.
2. Loop quantum cosmology can't be past eternal because you can't solve the entropy problem of the second law of thermodynamics. You can't explain why the whole system wouldn't eventually break down over an infinite amount of time to rest at an entropy equilibrium. It would have had an infinite amount of time to do that. So our current universe should already be at such a state if the hypothesis were true.
And if it isn't past eternal then Craig's arguments all still apply.
Cosmologists do not care about infinite regress at all, as it has no mathematical contradiction.
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Frankly these ancient so called classical logical contradictions have no relevance to physics and reality as quantum theory has shown.
You didn't answer the questions which refute your claim:
If what you claim is true, then why did Vilenkin in the video you posted explicitly say his theory operates a certain way to avoid an infinite regress?
Why do you think he sees this as something to be avoided?
Why do you think neither Krauss nor Carroll try to dispute Craig's claim that an infinite regress is logically impossible?
If they could then Craig's entire argument would be undermined.
Your claim that cosmologists don't care about the paradoxes caused by actual infinity in reality is disproven by looking at the theories they actually develop.
String theorist decided that one dimensional strings must have minimum planck distance so as to avoid the inherent problems of there being an infinite number of actual strings occupying a given space.
Loop quantum gravity, maintains a minimum distance between objects as well to avoid the problems associated with an infinite regress of smaller objects.
Why do you think they are avoiding this if it supposedly isn't a problem?
Here us yet another mathematical consistent cyclic univese model just to demonstrate.
Big Bounce Simulations Challenge the Big Bang
I already addressed big bounce models in a previous post. You did not attempt to refute any of my arguments but you just ignored them.
My conclusions remain standing as you have failed to challenge my arguments for those conclusions.
By ignoring my arguments and merely repeating your claim that the big bounce solves the problem, you are committing the fallacy of argument by repetition.
You do not refute my arguments against the big bounce by simply ignoring them and repeating your claim that the big bounce refutes my position.