The Grim Reaper Paradox

I thank Con for entertaining the merit of this argument with me. I also thank the reviewers and referees for their respective opinion and engagement on the matter irrespective of the outcome. The contentions stated above by Con are indeed what the Grim Reaper Paradox seeks to show, and so those of course will be my contentions. The Grim Reaper Paradox A Proof by Contradiction or Indirect Proof for the Finitude of the Past The Set Up Let us say that there were an infinite number of Grim Reapers each of whom had two tasks: 1) to check whether Con is still alive at the Grim Reaper’s appointed time 2) if he is still alive, to kill him instantaneously The last Reaper (Reaper 1) performs this dual task at exactly 1:01pm. The next-to-last Reaper (Reaper 2) performs the task at exactly 1:00:30 (a half minute after 1pm) ... and so on; such that each Reaper n, is assigned the moment 1/2^n minute after 1pm. Necessary Consequences There is no first Reaper because for each Reaper n, there are infinitely many Reapers who are assigned moments of time earlier than Reaper n’s appointment. It is certain that Con does not survive because in order to live he must still be alive at one minute after one. But we have said that if he survives up until 1:01pm then Reaper 1 will strike. But Con will also not survive until 1:01pm because in order to do so he must be alive at 30 seconds after 1pm, in which case Reaper 2 will have killed him. Likewise, Con can't survive until 1/2^n minutes after 1pm, for every n. The Result Hence no Grim Reaper can have the opportunity to kill Con. So it's impossible that he survive, and also impossible that any Reaper kill him! However, it seems also to be impossible for Con to die with certainty and yet to do so without any cause. An Alternative Set Up Sans Causality But now let's do away with causal notions, welcome to Grim Space: where a Grim Reaper can both issue and fail to issue a death warrant, which is a contradiction. Consequently, the Grim place assumes that an actual infinite amount of time can exist. Say the high ranking Grim Reaper known as Vernich issues a death warrant by placing a particle the size of a point in a predetermined position, exactly the distance = d/2^n meters from a plane. (That is, arbitrarily close to the plane). But suppose there is also a Grim Mover (Vernich's servant) that checks to see if any earlier Reaper has issued a warrant by seeing if a particle is already at a distance of d/2^i meters from the plane for some i greater than n. (That is, closer to the plane than what would otherwise allow Vernich issue a death warrant). [as the exponent i in the denominator increases, the distance between the point particle and the place ultimately get infinitely close] If a particle has already been placed in the predetermined position, Vernich does nothing. But if there is no particle in an appropriate location, then Vernich issues his warrant, placing a particle exactly d/2^n meters from the plane. Necessary Consequences At 1:01pm some particle is at d meters of the plane and no particle is located there. If there is no particle at any location d/2^i meters from the plane, for any i, and there were no particle d/4 meters from the plane, then Reaper 1 would place a particle in d/2 meters. The Result Therefore a contradiction occurs. For there must be, at 1:01pm, some particle in an appropriate position, but if the particle is located at that time in position d/2^n meters from the plane, then every Grim Reaper whose number is greater than n did nothing, contrary to our hypothesis. Thus we have an impossibility associated with temporal infinity, and so time is finite in its existence. [1] Sources 1. RobKoons.net/media/83c9b25c56d629ffffff810fffffd524.pdf