Regarded, however, as a logical division, Kant's arrangement seems to me of very little service. For such logical purposes indeed, as we are now concerned with, it really seems to resolve itself into a _two_-fold division. The distinction between the apodeictic and the assertory will be admitted, I presume, even by those who accept the metaphysical or psychological theory upon which it rests, to be a difference which concerns, not the quantity of belief with which the judgments are entertained, but rather the violence which would have to be done to the mind by the attempt to upset them. Each is fully believed, but the one can, and the other cannot, be controverted. The belief with which an assertory judgment is entertained is full belief, else it would not differ from the problematic; and therefore in regard to the quantity of belief, as distinguished from the quality or character of it, there is no difference between it and the apodeictic. It is as though, to offer an illustration, the index had been already moved to the top of the scale in the assertory judgment, and all that was done to convert this into an apodeictic one, was to _clamp_ it there. The only logical difference which then remains is that between problematic and assertory, the former comprehending all the judgments as to the truth of which we have any degree of doubt, and the latter those of which we have no doubt. The whole range of the former, therefore, with which Probability is appropriately occupied, is thrown undivided into a single compartment. We can hardly speak of a 'division' where one class includes everything up to the boundary line, and the other is confined to that boundary line. Practically, therefore, on this view, modality, as the mathematical student of Probability would expect to find it, as completely disappears as if it were intended to reject it. 19. By less consistent and systematic thinkers, and by those in whom ingenuity was an over prominent feature, a variety of other arrangements have been accepted or proposed. There is, of course, some justification for such attempts in the laudable desire to bring our logical forms into better harmony with ordinary thought and language. In practice, as was pointed out in an earlier chapter, every one recognizes a great variety of modal forms, such as 'likely,' 'very likely,' 'almost certainly,' and so on almost without limit in each direction. It was doubtless supposed that, by neglecting to make use of technical equivalents for some of these forms, we should lose our logical control over certain possible kinds of inference, and so far fall short even of the precision of ordinary thought.