affirmations. He allows nothing, in his investigations, to conflict at all; and whatever does conflict, he affirms to be false. Then, before he takes another step, he is very careful to fix upon accurate definitions, so that we may know precisely what he means—may understand exactly the scope of what he says. For instance, speaking of geometry, he will say that it pertains to the measurement of extent, and extent has three dimensions—length, breadth, and thickness. He next goes on to give definitions of that which is necessary to bound space—tells you what is a straight line, what a curved line, what is a plain surface, what is a curved surface, etc. After having ascertained the affirmations of the consciousness of the soul, in respect to number and quantity, and having fixed accurately upon the definition of all terms to be used, he then commences by demonstration, and will not go one step faster than demonstration attends him—does not launch at all into conjecture. He makes the relation between premises and conclusion inevitable; and if there be not an inevitable relation, he does not establish his proposition mathematically.
Now, what is true in respect to mathematics, is true in respect to every other subject that may come before the mind. There are conscious affirmations of the soul lying at the basis of all investigation; and in these conscious affirmations of the soul is to be found the standard by which to try the truth of whatever plane or sphere of thought. The first point to be taken is to ascertain what are the affirmations of the soul upon these points to be investigated. Our next step is to fix upon certain definitions, so that we can always un-
