I will illustrate briefly what I mean, that you may perceive how I wish to direct you in the investigation of the question, What is Truth? and how shall it be determined? The science of mathematics is said to be certain and demonstrative. And why is the science of mathematics any more demonstrable than is any other science? Why is it that the truth which it affirms can be any more positively demonstrated than any other truth? Is it because number and quantity are more fixed and certain than are qualities and attributes of being and existence? Why is it that the affirmations of mathematics are more demonstrable than the truths of any other science? I answer, that it is simply owing to the mode of proceeding in our investigations. If we will adopt the same process that we do in mathematics, we can have the same certainty upon all other questions that come within the sphere of man’s perceptions and affections. The mathematician comes down into his own consciousness, and finds certain conscious affirmations pertaining to number and quantity. He puts them down as truths not to be disregarded, and calls them self-evident truths or axioms. They are such affirmations of the consciousness as everybody must, per force, admit to be true; and when he has obtained the affirmations of his consciousness pertaining to number and quantity, he puts them down as truths not to be disregarded. They are always true everywhere, and under all circumstances, where number and quantity are to be investigated. He assumes nothing to be true which conflicts with these conscious affirmations of the soul. “Things equal to the same thing are equal to one another” must be received as true throughout the wide universe, so far as the mathematician investigates; and he allows nothing to controvert that self-evident truth; and so of all other 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.