So the astoundingly prolific and altogether perhaps rashly ambitious serial killer kills all and only those who do not kill themselves. Thus, of course, the old family problem emerges, the one he inherits from his grandfather the barber: does he in fact kill himself? He kills all who do not kill themselves and as such in so far as he is--as in exists and is not yet himself dead--has not in fact killed himself. Consequently as having not killed himself the onus falls upon him, as the serial killer who kills all who do not kill themselves. As a result, it is imperative that he must kill himself. Yet just as well, if he does–let's imagine him, knife in hand, about to perform the gesture and just on the verge of lunging into himself: he pauses. To kill himself would be to kill himself and would thusly relieve him, the serial killer who kills all and only those who do not kill themselves, of the necessary responsibility of killing himself. If he does not, he must, and if he does... well he couldn't of. Therefore in our most tortured pause, we find our serial killer in a puzzling predicmate. Is he to stab himself? Is he to not? Is he to be stabbed by the serial killer? And at last and evermore can he whilst this possibility is entangled by the ipseity that binds himself and serial killer?
Now what’s additionally interesting here is that in each and every case of the above exercised the necessary result is death. Anyone who stands in at the instantiation of what our initial sentence [s1] spells out is subject to death as either the result of self act (i.e. killing oneself) or as the result of the serial killer’s essential activity (i.e. being murdered by him). We may clarify this by first concretizing s1 as “There exists a serial killer who kills all who do not kill themselves.” Or expressed differently:
s1: (∃x)(∀y)(Kills(x,y)↔¬Kills(y,y))
That is to say, there exists (∃) an x such that for every y, x kills y iff y does not kill themself. In as much then as anyone may ‘stand in’ for y we denote it with the universal quantifier [∀]. It is clear then, as we aimed to clarify, that per s1 all are killed either by x (the serial killer) or by y (themselves). As s1 stands we may understand to be killed as the fate of all necessarily. And this holds seamlessly true in whatever case we may suppose. As if I [b] as the former succumb to the serial killer [x] whilst you [c] take the preemptive measure of killing yourself as the latter the following holds true:
(Kills(b,y)↔¬Kills(b,c))
(Kills(c,y)↔¬Kills(c,c))
Only yet, as we have begun to intimate, is trouble found when our killer himself stands in for y, which y as universally quantified is duly expected. When such is considered what results is the following:
(Kills(x,x)↔¬Kills(x,x))
Our serial killer kills himself if and only if our serial killer does not kill himself. Contradiction shows itself with utmost clarity and at once we return to our killer knife in hand pausing before the gesture that at one end must be performed and yet on the other cannot be done. But now far more severely than a pause of the hand we are made to ask not merely whether the serial killer may or may not kill himself but whether the serial killer may then exist at all. After all by way of s1 it is implicitly so that the existence of our killer is necessarily predicated upon sufficiently meeting the universality of (∀y). y may only be anyone and all if in fact anyone and all may be applied without the production of such quarrelsome contradictions. For if we must exclude x from y for s1 to function normally then y is no longer the universal set that contains any and all. In other words, we have come up against something strange and different. Something modified and not altogether that with which we began.
Although, this is not to say we have reached a dead end. Or perhaps it is precisely because it is a dead end that there is in fact more is to be said. If it is so that to preserve the sanctity of the universal set y that x must not exist then s1 itself is qualified false [⊥]. Thus in this gesture, the existence of x is crossed-out; he is made not to exist. How banal a conclusion it may be to say x does not exist, to say x could never have existed. And yet let us consider the full meaning of this nonexistence remembering at once where we found ourselves initially. Was it not s1 that promised the submitting to all [y] to nonexistence as killed? How curious it is that nonexistence, that which was promised by s1 but could not be granted to x, is in fact in consequence precisely what x is fated. In other words, x may not exist to be killed (to be made to not exist) per s1 because he in a more originary and essential sense has already been made to not exist as the barring of the possibility of his very existence. While we may, in the clouds of semantic confusion, have at one time held the set of the killed to be but a mere subset of the set of the nonexistent and from this taken it for granted that discussion of x as a part of this latter set may stand in complete ambivalence to his exclusion from the former set this is no longer so clear. It appears now that when we speak of the set of the killed we speak truly of those who have been made to not exist. It is in this way of speaking we find this curious commonality accounted for as it is not that x is essentially different from all the rest of y on the grounds of existence; rather it is in who is at cause for their nonexistence. It was for the rest of y as we saw before at the hands of x or themselves [y]; but for x himself contradiction forbade himself the receiving of death for which s1 promised. It is thusly not through x by which his own nonexistence is received but through contradiction itself which renders s1 false. This is itself most curious. x received not a difference of fate but a difference of cause. Death, which was paradoxically both required for him and yet unable to be had, was if effect received in having never been. x does not so much cheat death, as is often the story told of the existing, but rather it is death that is cheated, or perhaps death that cheats on behalf of x in his admittance.
Yet at very last, at the wake that never finds the moment of x’s exit for which it could be so timely, we find ourselves here. In other words, it is not so that we are not. We do in fact exist. The oblivion of existence for all, by both s1 for you, me, and all the rest of y and by ⊥(s1) for x, was not in fact expressed unilaterally in that way. For if it were, s1 would survive the designation of falsity that begets the fate of x in the first place. It would be for the sanctity of the all of y as ∀y to be violated; to build y again on the conditioned and constitutive exclusion of x. But this cannot be. The contradiction, from which the fate of x is wrung, crosses-out not merely the possibility of the existence of x but the standing of s1 as true. It is as an ultimate result that we do wonder: to what then do we owe the sacrifice of the nonexistence of x?