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We admit the perplexity which a portion of our faculties, whose action we are most familiar with, and from which we are accustomed to receive most of our conclusions, experience in handling, or rather in striving to handle, the infinite. This fact presents to us no difficulty; we see the reason why these faculties are not adequate to the labor laid upon them. Indeed, our belief in the infinite would be overthrown by a successful presentation of it, either by the imagination or by the judgment under its own forms, and is established by this very failure on their part. The objection of our adversary is proof with us.

On the other hand, the opposite view, that the notion is wholly illusory, is involved in difficulties that it cannot evade. How can Spencer insist that any presentation of the infinite is not adequate, when he has no notion of what the infinite is? How can a notion be shown to be illusory, except by a growing intuition? How can Hamilton require us to accept by faith that which is unintelligible, absolutely and completely so. Here are real contradictions. There can be no general denial of the applicability of any and all conceptions of the infinite, without postulating thereby some notion of the infinite with which these are compared, and, as falling short, are pronounced wanting. One notion of an utterly unknown thing is as good and as adequate as another. Neither can faith make that an object of belief which is utterly unknown to the mind. The faith of Hamilton, and the vanishing conception of Spencer, are both self-contradictory, as being alone able to arise under the furtive, but real light of an idea present and ruling in the mind. No false conception of the Deity can be set aside except by one which is better, or is deemed better; no faith can be expressed except toward a Being thought to be. These perplexities find no removal. To escape, therefore, difficulties whose reason is forthcoming by difficulties that