in the spaces beyond which is not already known in the fringe. This introduction of a eulogistic term into a mathematical question is original. The 'true' and the 'false' infinite are about as appropriate distinctions in a discussion of cognition as the good and the naughty rain would be in a treatise on meteorology. But when we grant that all the worth of the knowledge of distant spaces is due to the knowledge of what they may carry in them, it then appears more than ever absurd to say that the knowledge of the fringe is an equivalent for the infinitude of the distant knowledge. The distant spaces even simpliciter are not yet yielded to our thinking; and if they were yielded simpliciter, would not be yielded secundum aliud, or in respect to their material filling out.
Shylock's bond was an omnipotent instrument compared with this knowledge of the finite, which remains the ignorance it always was, till the infinite by its own act has piece by piece placed itself in our hands.
Here Hegelism cries out: "By the identity of the knowledges of infinite and finite I never meant that one could be a substitute for the other; nor does true philosophy ever mean by identity capacity for substitution." This sounds suspiciously like the good and the naughty infinite, or rather like the mysteries of the Trinity and the Eucharist. To the unsentimental mind there are but two sorts of identity,—total identity and partial identity. Where the identity is total, the things can be substituted wholly for one another. Where substitution is impossible, it must be that the identity is incomplete. It is the duty of the student then to ascertain the exact quid, secundum which it obtains, as we have tried to do above. Even the Catholic will tell you that when he believes in the
