jectural or hypothetical construction, a tentative idea, which may to a large extent prove not to correspond with the fully developed purpose which the result of the inquiry, when reached, presents to consciousness in as determinate form as is humanly possible. So far as our narrow human consciousness does permit this result of mathematical inquiry ever to appear to us in its complete expression, it is finally observed, however, as a fact of experience, or complex of facts of experience, as a series of properties and relations, embodied in diagrams, symbols, and systems of symbols. This expression, as far as it goes, fulfils the purpose defined from the start, the very outset of the mathematical inquiry. In this case one says, “Yes, I see this to be true, and I see that this is what the initial definitions meant.” Such a result of mathematical inquiry, just in so far as it is satisfactory, is a result that sends us no farther, or that defines no object lying yet beyond itself. This then is the answer to the mathematician’s initial query.
In just as far as we pause satisfied, we observe that there “is no other” mathematical fact to be sought in the direction of the particular inquiry in hand. Satisfaction of purpose by means of presented fact, and such determinate satisfaction as sends us to no other experience for further light and fulfilment, precisely this outcome is itself the Other that is sought when we begin our inquiry. This Other, this outcome, is at once uniquely determined by the true meaning already imperfectly present at the outset, and it is also not consciously present in the narrow instant’s experience with which we begin. A vaguely indeterminate act of will thus begins
