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
