If now it be asked how, if triangles, squares, square roots, genera, and the like, are but improvised human ‘artefacts,’ their properties and relations can be so promptly known to be ‘eternal,’ the humanistic answer is easy.  If triangles and genera are of our own production we can keep them invariant.  We can make them ‘timeless’ by expressly decreeing that on the things we mean time shall exert no altering effect, that they are intentionally and it may be fictitiously abstracted from every corrupting real associate and condition.  But relations between invariant objects will themselves be invariant.  Such relations cannot be happenings, for by hypothesis nothing shall happen to the objects.  I have tried to show in the last chapter of my Principles of Psychology [Footnote:  Vol. ii, pp. 641 ff.] that they can only be relations of comparison.  No one so far seems to have noticed my suggestion, and I am too ignorant of the development of mathematics to feel very confident of my own view.  But if it were correct it would solve the difficulty perfectly.  Relations of comparison are matters of direct inspection.  As soon as mental objects are mentally compared, they are perceived to be either like or unlike.  But once the same, always the same, once different, always different, under these timeless conditions.  Which is as much as to say that truths concerning these man-made objects are necessary and eternal.  We can change our conclusions only by changing our data first.

The whole fabric of the a priori sciences can thus be treated as a man-made product.  As Locke long ago pointed out, these sciences have no immediate connection with fact.  Only if a fact can be humanized by being identified with any of these ideal objects, is what was true of the objects now true also of the facts.  The truth itself meanwhile was originally a copy of nothing; it was only a relation directly perceived to obtain between two artificial mental things. [Footnote:  Mental things which are realities of course within the mental world.]

We may now glance at some special types of knowing, so as to see better whether the humanistic account fits.  On the mathematical and logical types we need not enlarge further, nor need we return at much length to the case of our descriptive knowledge of the course of nature.  So far as this involves anticipation, tho that may mean copying, it need, as we saw, mean little more than ‘getting ready’ in advance.  But with many distant and future objects, our practical relations are to the last degree potential and remote.  In no sense can we now get ready for the arrest of the earth’s revolution by the tidal brake, for instance; and with the past, tho we suppose ourselves to know it truly, we have no practical relations at all.  It is obvious that, altho interests strictly practical have been the original starting-point of our search for true phenomenal descriptions, yet an intrinsic interest in the bare describing function