Appendix 16.

(543) [Logical impossibility in things]

Certain things contain a hidden logical impossibility, not immediately evident. This situation arises when the idea we have of something is defective because too extensive. We do not consider the thing in itself but take it indiscriminately as forming part of a genus or species. In this case, we have to sift it thoroughly by examining both the thing itself and its characteristics. It is not sufficient to consider only its common qualities in order to be sure of its possibility. A mathematical example may be useful here. 'What is the square root of 2, expressed in a finite series of numbers?' The answer to this problem seemed possible before mathematicians started to work on it. They concluded, however, that there could be no answer, and produced a demonstration of the impossibility of expressing the square root of 2 in a finite series of whole numbers or fractions. A similar demonstration is applicable to all recurring numbers. In our example, it was necessary to demonstrate the impossibility of the problem because the impossibility was hidden and not immediately obvious.

The reason for such mental imperfection, which obscures the impossibility of certain things and consequently impedes certainty about their possibility, lies in what we have said about the indetermination of the idea of being. This idea is a tabula rasa, in mere potency relative to determinate beings. The mind cannot form a judgment about them or their possibility: 1. without thinking of determinations; and 2. without confronting the determinations with the idea of being, their supreme norm. In a word, the rule for judging the possibility of things is innate, but the judgment about their possibility, and the matter required for such a judgment, is not innate. The judgment has to be made, and often not without considerable difficulty

Kant, who had not noted that in itself possibility is simply a negative concept meaning 'the thing under discussion does not contradict the laws of thought and existence', also confused possibility with the danger we sometimes experience of judging it wrongly. This led him to deny that a thing can be judged possible provided we show that in it (in its idea) there is no repugnance, and made him require something more for the concept of possibility, as he does in his Critique of Pure Reason. This requirement distanced him even further from grasping the truth (cf. Part 1, bk. 2, c. 2, sect. 3, art. 4). However, there is some truth in what he says: the positive foundation of possibility is indeed in ideal being itself. In fact, everything we conceive has this proper characteristic: we conceive it as possible. Conceiving something, therefore, is the same as conceiving it as possible.