The Grim Reaper Paradox

Notes on my position: I am defending 2 potential positions that will refute Pro's contention that an actual infinite in time cannot exist. These 2 positions may well be mutually exclusive, or coherent and concede some of Pro's points but the thesis of the arguments are to negate the general themes of Pro. Time might well be quantised (I.e. A certain length if time cannot be infinitely divided), which seems to be a contention that Pro is pushing, but my argument continued that that alone, even if true, does not prove Pro's assertion time is not infinite. I will defend this further later in this rebuttal. I only aim to caste enough doubt on each of Pro's premises to make the conclusion dubious and therefore unsubstantiated. I hope that clarifies my position, which is not as Pro asserts 'An admission of defeat'. General Rebuttal: Unfortunately, Pro makes the argument that there must have been a Grim Reaper, which was the first Grim Reaper, in order for the victim to die. This is attested to in everyday experience, we all travel from A to B, even though we, theoretically, need to traverse an infinite number of increasingly small increments to reach B. (See Zeno's paradoxes for such examples). We can agree that the time the victim dies is 1.00pm + 1/2^n minutes. Now, since pro has made the argument such that the first Grim Reaper, must be the n=infinity Grim Reaper, then it follows that 1/2^infinity = zero exactly. I provided two such mathematical proofs that this must equal zero. Unless Pro can rebut this then the argument stands that the victim dies at 1.00 pm. Of course mathematicians are going to wince at my deliberate depiction of infinity as a number rather than a concept, it serves it's purpose to show what would happen if I accept the assumptions Pro makes. I made the argument that simultaneous causality/effect may be an issue here, and explained why it's not a case because by my same line of reasoning, an infinite number of Grim Reapers will come at exactly 1.00pm, and simultaneously issue the death warrant, which is compatible. This also negates Pro's other point that for every nth reaper, there will be a n+1 reaper before it. Since 1/n^2 is zero, then 1/(n+1)^2 must also equal zero. Therefore, an infinite number of Grim Reapers can/must appear at exactly 1.00 pm. Infinite Past Rebuttal: Pro has not substantiated his claim that expansion and thermodynamics require that time has a beginning. While some theories do posit the singularity of the Big Bang to be an absolute beginning, it is not required in others, for there are multiple explanations for both of these. There are a number explanations compatible with an eternal universe of the 2nd Law of Thermodynamics and Inflation. One such example is eternal inflation (Or the Multiverse), where baby universes break off from the eternally inflation (http://en.wikipedia.org...), where out universe is one of an infinite number of sub-universes that broke off from the main expansion, which itself has no beginning. The only objection I have seen from Pro regarding this is what is space expanding into. However he needs to substantiate his presupposition that space needs something to expand into at all. Until then his argument holds no weight. Pro has an interesting point regarding thermodynamics and the arrow of time. Without entropy, does time mean anything? I would argue no, it is impossible to tell which state is the past or future states without an understanding of the entropy of both systems. If the entropy of two 'snapshots' in time are identical, then it follows it's impossible to tell which is the past. The Eternal Inflation depictions of an eternal universe, depict just that. An every increasing number of universes, with ever increasing entropy. Notes on Causality: All of the descriptions of time so far assume classical notions of causality. Such notions are not well preserved in the smallest of scales (very small divisions of time, space). One example includes a number of derivations of Wheeler"Feynman absorber theory (http://www.hydrogen2oxygen.net...). These examples are valid here since Pro has not defined any of the Grim Reaper's attributes in time, space and other physical processes (necessary to make his argument work). Therefore in ever decreasing increments of time and space, effects on the quantum scale become very important, and the implications of causality at such scales is likely subject of our current understanding of such in quantum physics. Conclusion: The argument has gone rather off track (my doing), but is necessary I rebut Pro's blanket argument that time cannot be infinite. Since Pro's central thesis only attacks the divisibility of a unit of time, rather the number of possible actual units, it does not prove his main point, even if there was a true contradiction in the statement, which I have defended independently.