To understand these principles and the proof of them, we must notice certain preliminary considerations. In the _first_ place, the very problem of distinguishing the possible, the actual, and the necessary presupposes the existence of distinctions which may prove open to question. It presupposes that something may be possible without being actual, and again that something may be actual without being necessary. In the _second_ place, Kant's mode of approaching the problem assumes that we can begin with a conception of an object, e. g. of a man with six toes, and then ask whether the object of it is possible, whether, if possible, it is also actual, and whether, if actual, it is also necessary. In other words, it assumes the possibility of separating what is conceived from what is possible, and therefore _a fortiori_ from what is actual,[4] and from what is necessary. _Thirdly_, in this context, as in most others, Kant in speaking of a conception is thinking, to use Locke's phraseology, not of a 'simple' conception, such as that of equality or of redness, but of a 'complex' conception, such as that of a centaur, or of a triangle in the sense of a three-sided three-angled figure. It is the apprehension of a 'complex' of elements.[5] _Fourthly_, what is said to be possible, real, or necessary is not the conception but the corresponding object. The question is not, for instance, whether the conception of a triangle or of a centaur is possible, actual, or necessary, but whether a triangle or a centaur is possible, actual, or necessary. Kant sometimes speaks loosely of conceptions as possible,[6] but the terms which he normally and, from the point of view of his theory, rightly applies to conceptions are 'objectively real' and 'fictitious'.[7] _Lastly_, Kant distinguishes 'objectively real' and 'fictitious' conceptions in two ways. He speaks of establishing the objective reality of a conception as consisting in establishing the possibility of a corresponding object,[8] implying therefore that a fictitious conception is a conception of which the corresponding object is not known to be possible. Again, he describes as fictitious new conceptions of substances, powers, and interactions, which we might form from the material offered to us by perception without borrowing from experience itself the example of their connexions, e. g. the conception of a power of the mind to perceive the future; and he says that the possibility of these conceptions (i. e. the possibility of corresponding objects) cannot, like that of the categories, be acquired _a priori_ through their being conditions on which all experience depends, but must be discovered empirically or not at all. Of such conceptions he says that, without being based upon experience and its known laws, they are arbitrary syntheses which, although they contain no contradiction, have no claim to objective reality, and therefore to the possibility of corresponding objects.[9]