Page:Mind (New Series) Volume 9.djvu/315

 NECESSITY. 301 called by this one name. It needs, I think, only to be seen in any instance, in order to be recognised. Thus when we say : Here are two chairs, and there are two chairs, and therefore, in all, there are four chairs ; it would commonly be admitted that we presuppose in our conclusion that 2 + 2 = 4. Yet it is plain that many a man may arrive correctly at the number of objects before him, in an enor- mous number of instances, without envisaging the so- called abstract propositions that 2 + 2 = 4, or 3 + 1 = 4, or 1 + 1+1+1=4. These, therefore, are different proposi- tions from those which we commonly make about four objects, and yet they are presupposed in all of them. Similarly, when a man says : This is white, and that is black, and there- fore these are different objects ; we should say he implied that black and white are different. And this in itself is a common enough case. But if we go farther and say : That things which have different properties are different ; this is a principle which is involved in every particular judgment of difference that we make ; and we should be unable to give any reason for our judgment that the things are different, except that this and that property, which belong to them respectively, are different. These then are cases of logical priority, and we can determine whether other supposed cases are also of this nature, by considering whether they are like or unlike these. And by no means all cases of inference are of such a kind. For instance, if one says : There has been a horse here : and we ask why ; his reason may be : See these hoof-prints. But that a horse made them is by no means presupposed in the fact that there are hoof- prints there. And yet the inference may be perfectly valid : both propositions may be true, and the one may follow from the other. All propositions, then, are not connected by way of logical priority ; whereas some propositions are. And what universally marks a prior proposition is that it may be true, even though the particular proposition, to which it is prior, should be false. And thus a logically prior proposi- tion is universally prior both to one false and to one true proposition. And, moreover, what Kant showed is that there are a number of propositions logically prior to almost every true ' empirical ' judgment that we make ; and such empirical judgments form an immense majority of all the true propositions of which we are cognisant. They cannot be true, unless the propositions they involve are true : but these may be true, even if the empirical judgments are false. That there is, then, this class of logically prior proposi-