One difficulty in interpreting the Kantian distinction between negative and infinite judgements is to determine when and why a negative judgement does not imply the corresponding infinite one. This has to be reconciled with the principle of complete determination. My aim in this paper is to point out that the principle says that every thing (so perhaps not every object) is completely determined in terms of a predicate and its opposite, and to argue that certain objects (such as objects of pure intuition) cannot stand under the principle. I try to argue that by ‘thing’ we should understand objects that can be said to exist (or not exist). They stand, as to their possibility, under the principle, insofar as to conceive a thing is to conceive it as a single thing, distinct from all other possible things. Since the world cannot be conceived as one thing among others, the negative judgement ‘the world is not infinite’ would not imply ‘the world is not infinite (finite)’.