Actual Infinity in Reality?

[RoadRunner79]

I appreciate all the effort you are putting in, but it seems like you are trying to over complicate things, and answer a number of other question that where not being posed.   It doesn't matter what time the train will arrive in Boston, and the dispute is not that you can reach the end.  

We have a line with a start and an end point.  We will assume that there are an infinite number of points between these two positions.
We progress through this line towards the end point, passing through each point in succession along the way.
From any given point, along that line we will always have more points between the current position and the end position.
All prior points must be reached, in order to reach the end position
If there is always another point, that is not the end, and which precedes the end, then end cannot be reached.
Therefore the end position is not reachable if there is an infinite number of points which must be traveled.  

The disagreement is not that you cannot reach the end position (I believe that motion is fairly well evidenced).  There is not a problem with the logic here.   The problem is that if you have to complete something that never ends, then you will never complete.  To say that it is infinite and that it ends, is contradictory.  Something cannot be both A and !A at the same time.

The two statements in bold are false. The failure of the first bold statement invalidates the second. The rest of the statements are all correct.

And, in fact, if you look at my description, you see why the bold statements are false.

Remember, to go through all those points means that there is a time corresponding to each point. And that is true.

So, yes, if you have not reached the end, there is always another point to go through (in fact, an infinite number of points to go through) and you do reach the end.

Your assumption that we cannot go through an infinite number of points is invalidated.

Those statements follow logically from those that proceeded it.
Here they are again

We have a line with a start and an end point.  We will assume that there are an infinite number of points between these two positions.
We progress through this line towards the end point, passing through each point in succession along the way.
From any given point, along that line we will always have more points between the current position and the end position.
All prior points must be reached, in order to reach the end position
[b]If there is always another point, that is not the end, and which precedes the end, then end cannot be reached.
Therefore the end position is not reachable if there is an infinite number of points which must be traveled. 

If all points prior to the destination must be passed through sequentially, before reaching the destination; and there is an infinite number of points prior to destination so that the next point is always not the destination.  Then the end position will not be reachable.

It cannot be without end, and end at the same time... this is the contradiction.   Now perhaps you assume that your model is infinite, and you can calculate any infinitely small point and corresponding time.  However, this is why I asked numerous times previously, what exactly your points represent, in a real world motion.  If your model is only conceptual, then I suppose you can have whatever you want.   You don't actually traverse an infinite number of points in your model, you just assume that you do.  And if you actually follow the same math that shows that it is infinite, it also shows you that it cannot be completed.    Your model appears to be logically incoherent.

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Was time a factor in what I said at all?

Now if you are arguing against motion from a different perspective or something, then make your case.   Otherwise I don't' see how this fits it.

If you are discussing motion, then time is a factor.

Sure, so are accelerations and deceleration, and if your dealing with actual motion, then it's likely not going to be perfectly consistent all the way through.

However what I was saying didn't involve time, and I don't see where adding time in, effects it.  So while it is assumed that there is motion, that one is traversing the path of the line in some manner; the amount of time, or the even constant motion is not a factor.

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Was time a factor in what I said at all?

Now if you are arguing against motion from a different perspective or something, then make your case.   Otherwise I don't' see how this fits it.

Of course time is a factor.

Heres the article which I linked to a few pages back, and which addresses Zenos motion paradoxes from a physics standpoint.

http://www.mathpages.com/rr/s3-07/3-07.htm

Read the second last paragraph at least, if you dont want to read the whole thing. Though the whole thing is an interesting read.

What do you think in that addresses the logical contradiction being presented in Zeno's paradox?