Dogmatic theology, or the science of positive belief, resembles pure mathematics. Its ideas and formularies can not be too strictly, or too simply, defined; nor, where it admits of demonstration, can its proofs be carried out with too rigorous and mathematical a precision. For in these matters it is impossible to give the least room or influence to individual caprice without hazarding the loss of all that is most essential in the positive articles of faith. Philosophy, on the other hand, in treating of such subjects--or, at least, that part of it which is occupied with these matters--resembles rather mixed geometry in its several applications, such as practical mensuration, or the science of fortification and the art of war. For philosophy is, if we may so speak, an applied theology. Adopting the universal ideas of the one living God and his overruling Providence, and, what is so closely connected therewith, of the soul’s immortality and man’s free will, it adapts them, in many valuable practical applications, to the whole and almost boundless field of historical knowledge and the development of the human race, as well as to all physical and experimental sciences, and even to the wide domain of scientific disputes and merely human opinion, with its several conflicting systems. In this course of practical application philosophy needs not, in its expressions and formularies, scrupulously to confine itself to the terminology of its sister science, or to repeat its words with a careful exactness. On the contrary, its best and wisest course is to move with freedom, changing and varying its expressions at pleasure. For inasmuch as it is not itself so rigorously tied up as theology is to authority, so it can not appeal to it with equal justice in order to enforce assent to its own teaching. In the same way, too, that in algebraic equations a mere hypothetical calculation is oftentimes introduced, which, moreover, afterward suggests many a valuable practical application, so, also, a similar hypothetical use of the theological magnitudes or axioms, if we may so speak, is quite open and allowable to philosophy in the pursuit of its merely scientific ends. It is only the most general articles of the faith that philosophy makes use of. At least, the minuter and sharply-defined determinations of a positive creed are not immediately and indispensably necessary for its object. Now, an overruling Providence, the soul’s immortality, and the freedom of the will, are articles of universal belief, which, although, perhaps, not couched in express words and definite notions, yet still as germs and vague feelings exist, however deeply they may slumber, in every human breast that is as yet pure and uncontaminated by that captious skepticism which frets and corrodes itself with its seeming perplexities. These, philosophy may safely take for granted. Nay, it is its duty so to do; and where it does so in the right way,