The world is an idea the object of which is transcendent. It can't be seen all at once but is defined by its relation to some or another experience of being in it. Kant describes it in his first Critique as one of the three Ideas of Reason, the use of which is justified by their service in organizing diverse groups of things which are understood but not brought together into a systematic whole; (the other two being God and the Soul). And because without such organizational principles diverse experience could not be coherently brought together by a singular thinking subject, the three Ideas are transcendental as necessary for the possibility of experience itself, even if its objects can form no part of that experience.

The puzzle which the topic description provided by the program page above invites the reader to consider is not whether or not a world can exist which is not possible, since by definition nothing impossible exists, but rather whether a world can exist which plays no organizational role in the acquisition of comprehensive experience. For this a transcendental argument can be given, just as it can with the other two ideas considered below:

1) For the soul, If one can ask one's self whether one has a soul or not, it must exist, since a soul is self-reflective by definition, and therefore if this occurs it exists.
2) As for God, the traditional "ontological proof" can suffice, which states, at least in one version found in Descartes' seventh Meditation, that because the idea of God contains the predicate of perfection, and something more perfect can not arise from something less perfect, the idea could not have come from the imperfect thinking subject, and therefore must have come from its object which accordingly must exist.

These arguments are of course rejected by classical Criticism, since their use is not justified by the existence of their objects to which unverifiable predicates apply, (to wit, immortality and omniscience), but by their necessity for the possibility of comprehensive experience. To ask about impossible worlds then is intelligible only as asking about whether worlds exist which condition no experience whatsoever. Rather than asking about impossible worlds, the question should be translated as seeking a way to conceptualize a world which can't have anybody in it, the parts of which could never constitute parts of any experience. The transcendental argument for the world, that if it can be thought then it exists, on account of the fact that no thought can occur without a world to occur in, won't work in this case because the question concerns precisely the possibility of worlds which don't need thinkers in them.

The question therefore can be reduced to this: Are there unthinkable worlds? If so, how could they be known? If not, how could such worlds be imagined so that the question is intelligible? Deploying the noun as a verb (following one famous philosopher), --are there worlds which don't world? What kind of world would one be which just sits there with nothing responding to it?

After considering the issue which is brought up by the program-page statement above, admission here of concession following reflection ought to be made that the post above fails to approach it with sufficient appropriateness. Rather than existence of impossible (= unthinkable) worlds, the issue brought up seems closer to existence of what makes a world impossible, rather than how to go about being in one. Because any world must be made up of parts, which is to say there are no part-less worlds, any preclusion of combination sets a limit to positive ontological claims. In grammar for example both an informative inference from a tautology and a positive reference of a contradiction would belong to impossible worlds. Similarly by logical implication, two false sentences can imply a true one, but by material implication, no such consequence is possible, as this latter requires the specification of contents which are not transitive across logical divisions. In the example of the conditional form, a true antecedent and a false consequent yield a false subsequent (or conclusion) in both cases, because truth in both cases requires an existence operator. For material implication this is unproblematic, e.g. black swans don't exist because no one's seen one yet. But the same holds for logical implication on the basis that although nothing can be false without something first asserted to be true, something can be true without ever having to be asserted at all. Classical logic therefore contains a pre-assertoric claim which concerns the world's existence which is constituted by contents of a belief unconditioned by particular experience. As this belief is presupposed by the use of universal rules in cognition, it can be described as "pre-logical".

So if belief in the existence of the world, which must be understood in every case as a particular one with specified material characteristics, is presupposed in both spontaneous and comprehensive use of rules of division and combination which are assumed to be universally shared, --are the contents of this belief generated according to the rules the use of which assumes them? If so, how could it be verified? If not, ought one to start doing it? Can one grasp the notion of an impossible world by simple analysis of pre-logical existence claims? Or could one provide a positive reference to world-impossibility by indicating that some aspects of existence are too close to ever be reached? For this latter would place an impossible world within the foundations of an actual one which, accordingly, could not sufficiently be characterized as "one's own".