When the relation of things is not thus obvious, that is, when the proposition involves the _determination_ of the relation between two or more things whose relations are not intuitively perceived, the mind may sometimes come to a certainty, concerning the relation, by the interposition of a chain of axioms; that is, of propositions where the relations are intuitively perceived. This is called demonstration. In all such cases, the mind would perceive the relation, and come to a certainty intuitively, if adequately cultivated and enlarged; or, in other words, all propositions that now, to us, require demonstration, would, to such a cultivation, become mere axioms: consequently, now, where one man sees a mere axiom, another requires demonstration. But the great mass of our ideas are too imperfect or too complicated to admit of intuitive conclusions; consequently, as to them, we can never arrive at demonstration. Here we substitute facts; and reason, that, as heretofore one certain fact has accompanied another certain fact, so it will be hereafter. This is what the philosophers call analogy. Analogy is thus founded on experience, and is, therefore, far less perfect than intuition or demonstration. That gravitation will always continue is analogical; we do not know it intuitively; nor can we demonstrate it. Analogical propositions are, therefore, to us mere probabilities. But our knowledge has cognizance of ideas only. These ideas we substitute for the things they represent, in which there is a liability to err. Thus a compound idea is an assemblage of the properties of a thing, and may be incomplete and inadequate; wholly different from any quality in the thing itself. What is our idea of spirit, colour, joy? Yet we may conceive an intelligence so extended as to admit that even analogical problems should become intuitive: with God every thing is intuitively known. But even intuitive propositions sometimes reach beyond our comprehension. Example—a line of infinite length can have no end: therefore, the half of an infinite line would be a line also of infinite length. But all lines of infinite length are of equal length; therefore, the half of an infinite line is equal to the whole. Such fallacies prove that human reason is quite limited and liable to err: and hence the importance of faith in God, in the steadfastness of his laws, and the certainty of their operations. “And Jesus answering said unto them, have faith in God.” _Mark_ xi. 22. “And when they were come, and had gathered the church together, they rehearsed all that God had done with them, and how he had opened the door of faith unto the Gentiles.” _Acts_ xiv. 27. “So, then, faith cometh by hearing, and hearing by the word of God.” _Romans_ x. 17. That is, by revelation. “Now faith is the substance of things hoped for, the evidence of things not seen.” _Heb._ xi. 1. “But without faith it is impossible to please God; for he that cometh to God must believe that he is, and that he is