Can one get around this by making a couple assumptions. The first would be that time is quantized (the universe ceases to exist and then exists slightly changed from moment to moment). Now is the changes are causal, then you would have the problem of trying to have an infinity of causal changes, also not permitted, but if some of the changes are random, these would be new and not “counted” as part of any sort of infinite sequence that we can’t have. Am I being at all clear?
The posts on this thread have become pretty unwieldy - I think it would be a good time to point out that the experts in the fields, namely mathematicians and theoretical physicists, don’t seem to have any problem at all with time being infinite in the past.
If, for some reason, you think that it couldn’t have been, then you need to re-evaluate your position. That or publish a paper in a relevant journal making your case, because you would instantly become world-famous.
And Frank Merton, I don’t see any problem with a chain of causality being infinite into the past. Why would you think that couldn’t be? I don’t really see the distinction you’re making between caused events and random events here.
You are engaging in an appeal to authority rather than addressing what seem to me valid points made. Most of the “authorities” I have heard seem to avoid the question as one of philosophy not science and I remember Hawkings once when being asked if the Big Bang was the beginning of time his answer was to the effect that something had to be the beginning.
That’s true, but Half Man Half Wit and Wendell Wagner were substantively addressing the questions, and it seemed not to be having an effect. Some of the people on one side of the question were (it seems to me) taking the position of “I"m right” instead of “this is how it looks to me and can you help me understand where I went wrong.”
Sorry for the late reply, here goes…
[Quote=HalfManHalfWit]
The open interval (0,1) contains infinitely many points … It also contains infinitely many intervals; indeed, it contains exactly as many intervals as the line of natural numbers.
Your argument of pointing to the totality and declaring ‘it’s infinite’ applies to it just as well as to the line of natural numbers. But plainly, we traverse it every day …
Likewise, consider the infinite interval [0, ∞), but with ‘step sizes’ arranged such that the step from 0 to 1 takes 1 second, from 1 to 2 takes 1/2 second, from 2 to 3 takes 1/4 second, and so on. Then, you will traverse the entire interval in 2 seconds, even though its total length is infinite.
[/quote]
I honestly don’t have a response for you with this. This kinda just blindsided me so I want to contemplate it before I give a response. Though, is {0,∞} denoting a point at infinity? I thought that was impossible.(?)
In any case, below is my response pre taking sufficient thought time. Though, I already have written out the below so I figure I’ll post it anyway (took me around 2hrs or more (o_o) ). Forgive me if not everything syncs up with taking what you wrote here into account, although I am pretty sure that is not generally the case.
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The initial infinite distance you are starting with: When you start with a ray or a line (not a segment) you are starting with something that DENOTES an infinite distance. That, as a whole, IS infinite distance. This distance cannot be summed up by saying “all of that distance is ONLY between 2 points.” If the ray or line denotes time, then you are beginning with infinite time.
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You say that there is an infinite amount of natural numbers even if natural numbers never reach a point at ∞. Even if you never have a point at ∞, if you have an infinite amount, that amount will be impassable in sequence and at a constant rate. THERE IS ALWAYS ONE MORE TO GO! Can anyone count “to the end” of all ordinal numbers? If natural numbers were, as a whole PASSABLE, then there would be a point IN that set but OUTSIDE of that set, which is contradictory. Since you have to pass through all seconds in the past which have the same ordinality as natural numbers to get to THIS second, you are saying the same thing and this is a contradiction.
What then is the maximum distance of all natural numbers? You claim that there is only finite distance with natural numbers, so what is THE finite distance of all of them, if its not infinity? (Using the number 1 as a distance of 1, the number 2 as a distance of 2 and so on).
If you use a ray to denote infinite distance in the past, we are no longer dealing with ONLY between two points.
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How did the clock go from you writing (1a,2a, and 3) which says “It can’t (thus doesn’t) exist which proves my argument,” to your conclusion which says: “it doesn’t exist which disproves[u/] my argument”
If the super-task is impossible, how would I be able to show it to “prove” its impossibility?
Didn’t you say there ARE infinite numbers between -4 and -3? (referring to the quote at the very top of this page) Even if there were not, I really don’t get how this relates to my argument.
No, [0,∞) (note the brackets!) is a half-open interval, that is, it does include all point <∞, but not ∞. Otherwise, I’ll happily wait for your answer once you feel you’ve thought about it enough.
But again, this simply does not relate to the problem: as shown above, the mere infinite cardinality of an interval does not preclude its traversability. What would preclude it, once more, would be a distance between two points that is infinite. What you have to show is that there is some process, some sequence of events/moments, that is infinitely long. The simple fact that the totality of all points in the past is infinite does not imply the existence of such a sequence.
OK, we can take this metaphor just as well as that with the clock. A problem would only exist if one had to count to infinity (and finish!) before the present is reached. This is, of course, exacly equivalent to the existence of a clock that has to reach infinity to ‘arrive’ in the present.
Now all you need to realize is that the number to which one can count up to a given point in time is equal to the difference between a point further in the past and the now, if one counts at a constant rate. So, to show that one would have to count ‘to the end’ of all numbers (and nobody’s talking about ordinal numbers, of which there are many, many, many more than natural numbers), you have to show a point in the past from which one starts counting and arrives at infinity in the present. Again, this isn’t possible.
There is none, but every distance between two natural numbers is smaller than infinite. (Otherwise, again, show me two natural numbers whose difference = ∞.)
Only the difference between two points gives the number of moments that have elapsed, the number of ticks a clock shows, the greatest number one could have counted to. Only if one of these equals infinity, is it impossible to reach the present moment. The cardinality of the number of moments in the past is simply a red herring.
The premise (1a) is false if the clock doesn’t exist; but if one of the premises of the argument is false, then the conclusion doesn’t follow. Hence, the argument doesn’t demonstrate (3). Nowhere do I say or imply that the non-existence of the clock proves your argument (as it doesn’t), not sure where you got this from.
The same way I did: by showing an infinite distance on the reordered number line.
…I also say that in the quote you posted? 
Hey HalfManHalfWit, this thread is taking up a lot of energy (takes about 2 hours to give a reply to your posts) .At this point, I think that both of us are pretty entrenched in our position and I don’t think we will get anywhere. (Well, I AM learning, but it is taking quite some energy to do that as well as write the responses, so I should probably spend that time to learn some set-theory first so I can get back to you coming from a better understanding of it)
If/when I do get more of an understanding of set-theory I think I would be able to better talk to you on your wavelength and understand what you are saying better (or at least easier). I am wondering what parts of set theory you think would be the most relevant in terms of grasping your points in the conversation we have been having?
In any case, I have learned some new things in going over this thread with you and everyone, so thank you all for contributing to the conversation.
There’s not really much set theory to this, but if you want to get a better understanding of these issues, Wendell Wagner has provided some very fine literature to dig into. Perhaps start with some of the popular level stuff like the Rudy Rucker book, to see whether the whole thing’s for you. Also, I recently read Everything and More by David Foster Wallace, essentially a sort of intellectual biography of the idea of infinity; I can’t wholeheartedly recommend it, as he sometimes misses in his aim to present stuff at a formal level without formalism, and of course, his style is not for everyone (though I’m a fan, usually), but it’s also not the worst place to start.
You are using the wrong language (math/logic) in an attempt to describe an illusion (Time).
Turns out time is, actually, quite real. I’ll explain later.
Yeah, you’d have to go quite a space to convince anyone that time is an illusion. To begin with, when I ask a friend to meet me at the Rose Garden at one in the afternoon…he does. Time and space have objective reality to that degree, anyway.