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I actually support the concept of time as the Fourth Dimension, not Space-Time.
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Let me see if I interpret this the way you intended.
You say that time as the fourth dimension is acceptable. However, say that the space-time paradigm is not acceptable?
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example: they happened in the past, are in the same form that gives us the paradoxes described above.(pot of gold, achilles/tortoise)
Do you understand what I'm saying?
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I understand what you are saying. To elaborate, I find that you are stating the questions cosmology ask are based on incomplete logic, such that, the questions is missing a valuable piece of information, the answer follows that same pattern. The consequences of which, in those two particular cases are a paradox.
Therefore, if what I interpret is accurate to your suggestion, you claim cosmology is missing a valuable piece of information (whether it produces a paradoxical answer or not, at this point in my post is ignored, mainly because I don't know what paradox you suggest exists in cosmology as it is).
Now, I am going to respond based on my interpretations and assuming they are correct.
In the tortoise and achilles race, the important peice of information that was missing in the context of how story is told is the "t" factor. Because the tortoise and achilles (the characters expressing the logic) ignores the fact that time is being devided smaller and smaller, as each measurement is taken, they arrive at the odd conclusion that achilles can't pass the tortoise. If they were to take account the time factor, they would realize that, each consecutive distance they refer to is also covered by a shorter amount of time compared to the previous distance, and should realize their mistake when they have eventually hit pause on both of their actual motion, and should recognize that if each unit of time remained equal, then so would each unit of distance, given they continued at a constant velocity.
You suggest that the investigation into the cosmology is forgetting a valuable piece of information. Although I may have stated this above, I ask, what is that piece of information?
(back to me lecturing my thoughts)
It has been acknowledged that there is a unique logic in how observations can be made. They take into account that if we do not follow this specific (known) logic we will trek down the path of logic in those paradoxes you provided, and as a result, acquire results that do not apply to what actually occurs in experiments.
The logic that is acknowledged when making observations is that, the location of the observer is = to the center of their field of view.
If for example, I get up and walk outside in a clear night, everywhere I look, information is traveling towards me, and can be represented as a sphere of incoming information. Furthermore, a location of an object in this sphere, has a distance factor and also a time factor. That is, the object can be measured to be "x" distance from my point of observation as well as it takes a given amount of "t" for information(light etc) to travel that distance.
This implies that for every point of observation, there is a center, and a surrounding sphere that has both a space and time factor attributed to it.
With that said, and hopefully understood, we can now remove the sphere concept, knowing we have the impression of data coming at us from all directions, which can create the imagery of a sphere, when we encapsulate that incoming information by an equal distance in all directions.
What we have now in place of this sphere concept is a space and time concept. With this space-time concept, the logic that follows is that the only center that can exist is the one which we determine is the observer, making an observation of which to determine the logic of reality.
This implies that there is no true center to the universe, there is as follows, as many centers of the universe as there is points to express.
This logic further explains that regardless of where you position an observer in the universe; on the furthest imagined edge, or somewhere half way between earth and that edge, they will never be located anywhere other than the center of the universe, more accurately, the relative center of the universe. Furthermore, the distance that expands outwards from this particular observer, will always be considered as also, events of the universe with a specific "t" factor attributed to it. Said more simply, that what an observer observes, regardless of the position they are located, and regardless of the object being referred to (in observation) is always going to be acknowledged as an observation of a event in a previous time.
To continue what this logic also implies, is that the present moment, in all of the universe exists in all locations, and unfolds equally for all locations(that is considered to have an observer).
For example: If you were to plot a graph on the entire observed universe, and on this graph position 1,000,000 points of observation, every single one of those points of observation would be experiencing a present "time" of the universe, as in we imagine jumping to those points instantaneously, as to subject ourselves to their view, and thus finding that the present moment exists in each one of those points (we would not appear at some ancient point of time in the earlier stages of the universe). When we observe from any of these points, we will always observe the universe as we do now here on earth. That is, looking out and observing the past state of the universe, where the furthest observable point would be the beginning, and we seem to be located right at around the center, in the present moment.
One way to look at this is that, all observations declare that the future, in respect to what we are going to observe, is coming from distance "x" from us, inwardly from all directions. That is, our future is unknown in the sense, it has not reached us yet, and it will take time to reach us as it travels distance to get here. (this is strictly to the future of observation).
When we reflect on this, and apply the inquiry of the universe having an edge, as you brought forward, we can consider that, if we were to be located on that edge, we would find ourselves in the exact same circumstance (excluding variables like relativistic velocities).
And therefore, the universe can have no edge that is more special than any other observed edge, or no center that is more special than any other observed center.
Does this make sense to you? Are you familiar with these thoughts?
We can't put a boundary on the universe using this logic. If we tried, we would be saying that the boundary existed billions of years ago(the furthest things we can see). The boundary we imagine doesn't exist anymore, and what we think we see as a boundary is energy that contains information that is billions of years old, and yet, our future is formed by this information that is billions of years old. And this occurs the same way anywhere you imagine yourself to be.
