What if an other were other than an other: Derrida, Lacan, Heidegger

What if the other were not one, single other, but more than one other? This is the question Derrida puts to Lacanians.
More precisely, he asks, what if the other were not one, single other, the other, but other than an other? We have to be more precise here because we are not moving between the terms of singularity and multiplicity but between the terms of singularity and alterity, identity and difference. That is, if we were just to ask if the other were not one but more than one, we would be asking if the other were multiple in its singularity, and not about the alterity of this other. When Derrida talks about "other(s)," with the "s" in parentheses, he is not indicating multiplicity: he is not saying that the other is always multiple. Badiou, in his effort to make a Lacanianism complicit with some Derridian notions, precisely interprets it this way--which is only wishful thinking. This is an important distinction: if we were to ask about whether the other were multiple, we would still be thinking of the other itself, of alterity, as singular, as a singular site where multiple others resided.
We now can see that Derrida's question is more radical. What if an other were other than an other? That is, what if alterity was already othered? What if alterity was other to itself? What if, when one tried to specify the place of alterity, of what is not here or with one in their singularity, one never could find it, because it was always in another place than this other place? What if, looking at Pakistan, the other of India, Indians could not find Pakistan--what if Pakistan were elsewhere? Or Israel, with respect to Palestine? Or "terrorism" (to duplicate the way we here raise concepts to otherness to assert superiority--one cannot point to a nation we are the other of, there are too few or too many--and in doing so only reveal an abysmal lack of understanding and respect for national otherness that exceeds every other nation's) with respect to the US? This is what Derrida is getting at. Indeed, it perhaps implies that the other is multiple, but this is not the thrust of the question, for the multiple could only be accounted for if it were viewed as whole, as singular, that is, as other that was not also other to itself.
An other is other than an other. This is what Derrida means when he says, in The Gift of Death, tout autre est tout autre. But this is not a formula that is localizable to only the "late" Derrida, the "ethical" Derrida. This is prevalent in his earliest work. To see how this is so, lets only substitute "difference" for "alterity." What is identical to itself has its other in difference, in what makes identity different in some way from others. We can translate what Derrida says, then, as this: difference is different than difference. Difference is different from itself. Difference has no identity. In other words, this radical difference, a difference that cannot be commensurable with any system or economy of identity, differs the moment where and displaces the location when it would be merely a singular difference and not already different from this difference. Derrida names this difference that is different than difference, différance.
Why is this a question posed to Lacanian psychoanalysis? Because Lacan merely conceives of difference and alterity as different and other. It does not consider it as different and other from itself. It is in this way that Lacan can speak of the Other, even if this Other does not exist or is nothing. As Derrida puts it in "Envoi" (in Psyche, volume 1) the other conceived this way "would disappear like the wholly other" (127). In other words, any alterity that came on the scene as alterity conceived in this way, would merely disappear into what just gets opposed wholly to what is singular. "Wholly" is used because what is other for Lacan is indeed totally other, but is only other as a whole, as a singular otherness, that is, as an otherness that is identical to itself, even if (as Lacan says) it doesn't exist. To put it in a different way, Lacan's Other is not other, because it is merely a singularity opposed to a singularity. To pass off this Other as otherness, like Zizek or Badiou or any other Lacanian, would need some justification in Derrida's view.
This should further illuminate my other writings below on the difference between Derrida and Lacan, especially with respect to their approaches to Freud. I think I'm getting a grip on it now! With this comes a heavy qualification on my first post, which sought to locate them in relationship to Heidegger's question of being. This can't be done, since for neither of the thinkers being is the real question. The real question is alterity, otherness, and how to be responsible for it. In other words, Heidegger's question only becomes interesting when being engages alterity--and for Heidegger this is when being is as itself, opened up or split open in its essence as ek-sistence, or in presence. Let's just sketch out Heidegger's position quickly in relation to the above. Being in presence is for Heidegger being in otherness to itself, and, as this otherness, precisely itself in its ownmost possibility. Presence, then, is otherness in the sense of the wholly other. In other words, being is the otherness of Lacan. Derrida's critique of presence, then, is not a war waged against presence just because presence is bad for Derrida (as many people and even Derridians think), but because presence does not adequately get at the otherness, the ek-sistence of being, like Lacan's otherness. Derrida thus makes presence encounter différance, an othering of an other, a differing of difference. To put it a different way, Heidegger goes beyond the present to presence, and then Derrida makes him go out of presence back into the present that is other than itself, that differs from itself in its presence as present, that re-presents itself. Lacan, for Derrida, cannot do this just as much as Heidegger.