"Die Reinheit," and purity

I never noticed that Kant's first and most famous critique, the Critique of Pure Reason, really stresses "purity." Kant in his title (Kritik der reinen Vernunft) and in his terminology uses die Reinheit to specify a type of reason that would grasp the a priori synthetically, that is, via pure intuition, pure apprehension. This reason is reinen Vernunft. One could argue that this would be better translated as "clean reason." Die Reinheit is the weiss, the white, without blemish, just as much as it is the abstract, the absolute, the immediate. In German, one says "reinen" when one is talking about a "clean slate," about a "clear intention." Translating it as "clean" would efface Kant's stress on abstraction, indeed. But it would also bring forth what an absolutely revolutionary task this book undertook, and indeed saw itself as undertaking: it is the destruction of the purity of the mind naively thought as what has access to the absolute; it is the destruction of the innate cleanliness one attributes to the human. Hannah Arendt concretely embodies the unbelievable thrust of such a critique in words when she says that Kant's intentions bring forth a "destruction" of the world as we knew it ("Existenz Philosophy," in The Phenomenology Reader, 349): in other words, the only world we live in after a critique of a reason that is supposed to be clean, will be a destroyed world, a sullied, unclean world. Even in the title of the work, Kant is out to destroy, to render unclean.

"The Concept is the killing of the Thing"

Thinking the thing, the object, means thinking the death of the thing as well as its living relation to you: this is what Kojeve means when he says that the Concept is the killing of the Thing. Thinking, for Hegel, is always therefore a thinking of death. It is a thinking that thinks and indeed enacts the death of the thing thought. This is because, at bottom, the being that is thought is at the same time nothing--at least this is what Hegel says in the Science of Logic. The crucial thing to grasp is that even if we consider the thinking of the thing's nothingness, its death or relationship to you [the thinker, the thinking] as dead--even if we consider this thinking of nothingness a reduction of the abstract, pure nothingness of the thing to a determinate nothingness, one still has to think the death of the thing in this act. In other words, sometimes too much stress is put upon Hegel reducing nothingness to something determinate and something able to be exchanged in an economy of being--Bataille and Derrida are guilty of this--and not enough on the fact that what is indeed interesting about the determinate nothingness is that it is nothingness, that it is the death of the thing, the thinking of its negativity as related to whatever that negativity brings about. The recuperation of negativity into a determinate economy of negativity, the extraction of negativity from its abstractness, its purity, is secondary to this engagement with negativity as the other side of every single thing. Only if one stresses that thinking is a thinking of the death of the thing, a simultaneous lifting it into death and out of abstraction, does one really get what Hegel is talking about when he calls this thinking in the Preface to the Phenomenology of Spirit submitting to the "labor, the patience of the negative."
Quickly, I'll just finish by being clear: thinking is the thinking of the death of each thing because at bottom each thing has its being purely, in pure abstraction--in pure being. Now, this is at bottom the same thing as nothingness. Insofar as a being is a being it is equal to nothing--thus, with any thinking of the being of something, one also has to think its negativity. Even when determinate and not pure, the abstract equality of nothing with being reigns... it is what brings about this determination of being and nothing. Thus, one is thinking at the same time of a being and of its death, its abstract nothingness. It is only by thinking this nothingness as part of the thing that one can say something is at all. Also, it is only by thinking this nothingness that one can lift what is equivalent to nothingness out of its abstraction and into the Concept: the Concept is therefore the thinking that comprehends the nothingness, the death of the thing, giving it its determinacy and its nothing equally as it gives it its being. Thus Hippolyte can also say that Language is the death of the thing, along with Hegel, and be right: associating the Concept with language as he does, Hippolyte equally shows us that language is what accesses the nothingness, the death of the thing.

Contributions to Philosophy, Derrida and the "other beginning"

There is perhaps no better way to characterize Derrida's thought than the way Heidegger characterizes his endeavor in his Contributions to Philosophy: that is, as a "crossing over to the other beginning" (3). The other beginning--that is, of Western thought. This beginning is, as Heidegger says in his lecture on "Hegel and the Greeks" (within his book Holzwege, or Pathmarks), is not a beginning and is a beginning at the same time: it is what has remained unthought and presupposed even in the beginning of the Western tradition of thinking. In other words, crossing over to the other beginning of Western thought means not naively beginning again but rather thinking that "to which we are not sufficient [in our thinking] and never have been" ("Hegel and the Greeks"), the withdrawing-movement of Being that gives Being, Ereignis or enowning. Or, as Heidegger himself puts it: "reverence for the first [i.e. forgotten] beginning... must coincide with the retlentlessness of turning away from this beginning to an other questioning and saying" (5).
I say that this phrase "crossing over to the other beginning" exactly characterizes Derrida's effort because it is really what the phrase "deconstruction" means, primarily through its emphasis on construction. Derrida no doubt used the term because it is similar to what what Heidegger occasionally used to explain his philosophical effort of decentering the tradition of Being as presence--a positive "Destruktion." But what is really meant, as Heidegger shows us, is a thinking of the forgotten: it bringing this forgotten to the fore that will enact the "Destruktion" of metaphysics as the metaphysics of Being as presence. As such, by the link we have already established, it is a return to the origin of the origin, the beginning of the beginning, the non-beginning that is the beginning of beginning, the "other" beginning.
And the otherness of this beginning is primarily Derrida's stress throughout his career. While Heidegger probably focused on it more as a beginning, as a presupposition that the beginning of Western thought left behind and yet brought with it everywhere since Parminides, Derrida wanted to find out, and cross into himself, the otherness of this beginning and to think from it. That is, he not only wanted to think from its standpoint (which would be of necessity a non-metaphysical standpoint) as a beginning, he not only wanted to found the task of thinking on this forgotten beginning, but he wanted to think from its standpoint as other, found philosophy as a thinking within the otherness of this beginning, to the maximum possible extent. Thus Levinas remains crucial for him throughout his career.
But perhaps describing deconstruction as a "crossing over to the other beginning" of philosophy would help us think through Derrida's work in a more honest way, and render ourselves able to concretely demonstrate the positive character of deconstruction--that is, what it does that exceeds powerful critique, namely, establish philosophy in this other beginning.