Leibniz's comments are again brief. The primitive truths which are known by intuition are to be divided into two classes,--truths of reason and of fact. The primitive truths of reason are necessary, and may be called identical, because they seem only to repeat the same thing, without teaching us anything. A is A. A is not non-A. Such propositions are not frivolous or useless, because the conclusions of logic are demonstrated by means of identical propositions, and many of those of geometry by the principle of contradiction. All the intuitive truths of reason may be said to be made known through the "immediation" of ideas. The intuitive truths of fact, on the other hand, are contingent and are made known through the "immediation" of feeling. In this latter class come such truths as the Cartesian, "I think, therefore I am." Neither class can be proved by anything more certain. Demonstration is defined by Leibniz as by Locke. The former recognizes, however, two sorts,--analytic and synthetic. Synthesis goes from the simple to the complex. There are many cases, however, where this is not applicable; where it would be a task "equal to drinking up the sea to attempt to make all the necessary combinations. Here the method of exclusions should be employed, cutting off many of the useless combinations." If this cannot be done, then it is analysis which gives the clew into the labyrinth. He is also of the opinion that besides demonstration, giving certainty, there should be admitted an art of calculating probabilities,--the lack of which is, he says, a great defect in our present logic, and which would be more useful than a large part of our demonstrative sciences. As to sensitive knowledge, he agrees with Locke that there is such a thing as real knowledge of objects without us, and that this variety does not have the same metaphysical certainty as the other two; but he disagrees regarding its criterion. According to Locke, the criterion is simply the greater degree of vividness and force that sensations have as compared with imaginations, and the actual pleasures or pains which accompany them. Leibniz points out that this criterion, which in reality is purely emotional, is of no great value, and states the principle of the reality of sensible phenomena which we have already given, repeating that it is found in the _connection_ of phenomena, and that "this connection is verified by means of the truths of reason, just as the phenomena of optics are explained by geometry."