But matters of fact are not our only stock in trade.  Relations among purely mental ideas form another sphere where true and false beliefs obtain, and here the beliefs are absolute, or unconditional.  When they are true they bear the name either of definitions or of principles.  It is either a principle or a definition that 1 and 1 make 2, that 2 and 1 make 3, and so on; that white differs less from gray than it does from black; that when the cause begins to act the effect also commences.  Such propositions hold of all possible ‘ones,’ of all conceivable ‘whites’ and ‘grays’ and ‘causes.’  The objects here are mental objects.  Their relations are perceptually obvious at a glance, and no sense-verification is necessary.  Moreover, once true, always true, of those same mental objects.  Truth here has an ‘eternal’ character.  If you can find a concrete thing anywhere that is ‘one’ or ‘white’ or ‘gray,’ or an ‘effect,’ then your principles will everlastingly apply to it.  It is but a case of ascertaining the kind, and then applying the law of its kind to the particular object.  You are sure to get truth if you can but name the kind rightly, for your mental relations hold good of everything of that kind without exception.  If you then, nevertheless, failed to get truth concretely, you would say that you had classed your real objects wrongly.

In this realm of mental relations, truth again is an affair of leading.  We relate one abstract idea with another, framing in the end great systems of logical and mathematical truth, under the respective terms of which the sensible facts of experience eventually arrange themselves, so that our eternal truths hold good of realities also.  This marriage of fact and theory is endlessly fertile.  What we say is here already true in advance of special verification, if we have subsumed our objects rightly.  Our ready-made ideal framework for all sorts of possible objects follows from the very structure of our thinking.  We can no more play fast and loose with these abstract relations than we can do so with our sense-experiences.  They coerce us; we must treat them consistently, whether or not we like the results.  The rules of addition apply to our debts as rigorously as to our assets.  The hundredth decimal of pi, the ratio of the circumference to its diameter, is predetermined ideally now, tho no one may have computed it.  If we should ever need the figure in our dealings with an actual circle we should need to have it given rightly, calculated by the usual rules; for it is the same kind of truth that those rules elsewhere calculate.

Between the coercions of the sensible order and those of the ideal order, our mind is thus wedged tightly.  Our ideas must agree with realities, be such realities concrete or abstract, be they facts or be they principles, under penalty of endless inconsistency and frustration.  So far, intellectualists can raise no protest.  They can only say that we have barely touched the skin of the matter.