The notion of Gedankending concerns objects about which we can possess no knowledge since they transcend the limits of our experience. Nonetheless, we are compelled to refer to such objects on account of the irreducible finitude of our experience. We cannot know them, but we must think them: "As sensible intuition does not extend to all things without distinction, a place remains open for other and different objects" (CPR, A 288). In other words, all our (finite) thought can do is to draw a certain limit, restrict the field of our knowledge, without making any positive statements about its Beyond; the "Thing-in-itself" is given only as pure absence, in the guise of a certain place which, on account of the finitude of our experience, must forever remain empty. And it is here that we encounter the difference between negative and indefinite / limiting judgment: noumena are objects of indefinite-limiting judgment. By saying "the Thing is non-phenomenal," we do not say the same as "the Thing is not phenomenal"; we do not make any positive claim about it, we only draw a certain limit and locate the Thing in the wholly nonspecified void beyond it.
Along this line of thought, Kant introduces in the second edition of the Critique of Pure Reason the distinction between positive and negative meanings of "noumenon": in the positive meaning of the term, noumenon is "an object of a nonsensible intuition," whereas in the negative meaning, it is "a thing insofar as it is not an object of our sensible intuition" (CPR, B 307). The grammatical form should not mislead us here: the positive meaning is expressed by the negative judgment and the negative meaning by the indefinite judgment. In other words, when one determines the Thing as "an object of a nonsensible intuition," one immediately negates the positive judgment which determines the Thing as "an object of a sensible intuition": one accepts intuition as the unquestioned base or genus; against this background, one opposes its two species, sensible and nonsensible intuition. Negative judgment is thus not only limiting, it also delineates a domain beyond phenomena where it locates the Thing -- the domain of the nonsensible intuition -- whereas in the case of the negative determination, the Thing is excluded from the domain of our sensible intuition, without being posited in an implicit way as the object of a nonsensible intuition; by leaving in suspense the positive status of the Thing, negative determination saps the very genus common to affirmation and negation of the predicate.
Herein lies also the difference between "is not mortal" and "is notmortal": what we have in the first case is a simple negation, whereas in the second case, a non-predicate is affirmed. The only "legitimate" definition of the noumenon is that it is "not an object of our sensible intuition," i.e., a wholly negative definition which excludes it from the phenomenal domain; this judgment is "infinite" since it does not imply any conclusions as to where, in the infinite space of what remains outside the phenomenal domain, the noumenon is located. What Kant calls "transcendental illusion" ultimately consists in the very (mis)reading of infinite judgment as negative judgment: when we conceive the noumenon as an "object of a nonsensible intuition," the subject of the judgment remains the same (the "object of an intuition"); what changes is only the character (nonsensible instead of sensible) of this intuition, so that a minimal "commensurability" between the subject and the predicate (i.e., in this case, between the noumenon and its phenomenal determinations) is still maintained.
A Hegelian corollary to Kant is that limitation is to be conceived of as prior to what lies "beyond" it, so that ultimately Kant's own notion of the Thing-in-itself remains too "reified." Hegel's position on this point is subtle: what he claims by stating that the Suprasensible is "appearance qua appearance" is precisely that the Thing-in-itself is the limitation of the phenomena as such. "Suprasensible objects (objects of suprasensible intuition)" belong to the chimerical "topsy-turvy world"; they are nothing but an inverted presentation, projection, of the very content of sensible intuition in the form of another, nonsensible intuition -- or, to recall Marx's ironic critique of Proudhon in The Poverty of Philosophy: "Instead of the ordinary individual with his ordinary manner of speaking and thinking, we have nothing but this ordinary manner purely and simply -- without the individual." (The double irony of it, of course, is that Marx intended these lines as a mocking rejection of Proudhon's Hegelianism, i.e., of his effort to supply economic theory with the form of speculative dialectics!) This is what the chimera of "nonsensible intuition" is about: instead of ordinary objects of sensible intuition, we get the same ordinary objects of intuition, without their sensible character.
This subtle difference between negative and indefinite judgment figures in a certain type of witticism where the second part does not immediately invert the first part by negating its predicate but repeats it with the negation displaced onto the subject. The judgment "He is an individual full of idiotic features," for example, can be negated in a standard mirror way, i.e., replaced by its contrary "He is an individual with no idiotic features"; yet its negation can also be given the form of "He is full of idiotic features without being an individual." This displacement of the negation from the predicate onto the subject provides the logical matrix of what is often the unforeseen result of our educational efforts to liberate the pupil from the constraint of prejudices and chchés the result is not a person capable of expressing himself or herself in a relaxed, unconstrained way, but an automatized bundle of (new) clichés behind which we no longer sense the presence of a "real person." Let us just recall the usual outcome of psychological training intended to deliver the individual from the constraints of his or her everyday frame of mind and to set free his or her "true self," with all its authentic creative potentials (transcendental meditation, etc.): once the individual gets rid of the old clichés which were still able to sustain the dialectical tension between themselves and the "personality" behind them, what take their place are new clichés which abrogate the very "depth" of personality behind them. In short, the individual becomes a true monster, a kind of "living dead." Samuel Goldwyn, the old Hollywood mogul, was right: what we need are indeed some new, original clichés.
Invoking the "living dead" is no accident here: in our ordinary language, we resort to indefinite judgments precisely when we endeavor to comprehend those borderline phenomena which undermine established differences, such as those between living and being dead. In the texts of popular culture, the uncanny creatures which are neither alive nor dead, the "living dead" (vampires, etc.), are referred to as "the undead"; although they are not dead, they are clearly not alive like us, ordinary mortals. The judgment "he is undead" is therefore an indefinite-limiting judgment in the precise sense of a purely negative gesture of excluding vampires from the domain of the dead, without for that reason locating them in the domain of the living (as in the case of the simple negation "he is not dead"). The fact that vampires and other "living dead" are usually referred to as "things" has to be rendered with its full Kantian meaning: a vampire is a Thing which looks and acts like us, yet it is not one of us. In short, the difference between the vampire and the living person is the difference between indefinite and negative judgment: a dead person loses the predicates of a living being, yet he or she remains the same person; an undead, on the contrary, retains all the predicates of a living being without being one. As in the above-quoted Marxian joke, what we get with the vampire is "the ordinary manner of speaking and thinking purely and simply -- without the individual."
One is tempted to affirm that this logic of infinite judgment contains in nuce Kant's entire philosophical revolution: it delineates transcendentally constituted reality from the uncanny, prohibited / impossible, real domain of the Thing which had to remain unthought since in it Good overlaps with radical Evil. In short, Kant replaced the traditional philosophical opposition of appearance and essence with the opposition of phenomenal reality and the nournenal Thing which follows a radically different logic: what appears as "essential" (moral law in ourselves) is possible and thinkable only within the horizon of our finitude, of our limitation to the domain of phenomenal reality; if it were possible for us to trespass this limitation and to gain a direct insight into nournenal Thing, we would lose the very capacity which enables us to transcend the limits of sensible experience (moral dignity and freedom).
