Dialectic, however, or the vertex of the mathematical sciences, as it is called by Plato in his Republic, is that master discipline which particularly leads us up to an intelligible essence. Of this first of sciences, which is essentially different from vulgar logic, and is the same with what Aristotle calls the first philosophy and wisdom, I have largely spoken in the introduction and notes to the Parmenides. Suffice it therefore to observe in this place, that dialectic differs from mathematical science in this, that the latter flows from, and the former is void of hypothesis. That dialectic has a power of knowing universals; that it ascends to good and the supreme cause of all; and, that it considers good as the end of its elevation; but that the mathematical science, which previously fabricates for itself definite principles, from which it evinces things consequent to such principles, does not tend to the principle, but to the conclusion. Hence Plato does not expel mathematical knowledge from the number of the sciences, but asserts it to be the next in rank to that one science which is the summit of all; nor does he accuse it as ignorant of its own principles, but considers it as receiving these from the master science dialectic, and that possessing them without any demonstration, it demonstrates from these its consequent propositions. Hence Socrates, in the Republic, speaking of the power of dialectic, says that it surrounds all disciplines like a defensive enclosure, and elevates those that use it to the good itself, and the first unities; that it purifies the eye of the soul; establishes itself in true beings, and, the one principle of all things, and ends at last in that which is no longer hypothetical. The power of dialectic, therefore, being thus great, and the ends of this path so mighty, it must by no means be confounded with arguments which are alone conversant with opinion: for the former is the guardian of sciences, and the passage to it is through these, but the latter is perfectly destitute of disciplinative science. To which we may add, that the method of reasoning which is founded in opinion, regards only that which is apparent; but the dialectic method endeavors to arrive at the one itself, always employing for this purpose steps of ascent, and at last beautifully ends in the nature of the good. Very different therefore is it from the merely logical method, which presides over the demonstrative phantasy, is of a secondary nature, and is alone pleased with contentious discussions. For the dialectic of Plato for the most part employs divisions and analyses as primary sciences, and as imitating the progression of beings from the one, and their conversion to it again. It likewise sometimes uses definitions and demonstrations, and prior to these the definitive method, and the divisive prior to this. On the contrary, the merely logical method, which is solely conversant