ii. _Ab experientia vaga_: from general experience: for instance, all facts or phenomena which come to us through our senses as phenomena, but of the causes of which we are ignorant. 2. We know a thing as we have correctly conceived the laws of its phenomena, and see them following in their sequence in the order of nature. 3. Finally, we know a thing, _ex scientia intuitiva_, which alone is absolutely clear and certain. To illustrate these divisions, suppose it be required to find a fourth proportional which shall stand to the third of three numbers as the second does to the first. The merchant's clerk knows his rule; he multiplies the second into the third and divides by the first. He neither knows nor cares to know why the result is the number which he seeks, but he has learnt the fact that it is so, and he remembers it. A person a little wiser has tried the experiment in a variety of simple cases; he has discovered the rule by induction, but still does not understand it. A third has mastered the laws of proportion mathematically, as he has found them in Euclid or other geometrical treatise. A fourth, with the plain numbers of 1, 2, and 3, sees for himself by simple intuitive force that 1:2=3:6. Of these several kinds of knowledge the third and fourth alone deserve to be called knowledge, the others being no more than opinions more or less justly founded. The last is the only real insight, although the third, being exact in its form, may be depended upon as a basis of certainty. Under this last, as Spinoza allows, nothing except the very simplest truths, _non nisi simplicissimae veritates_, can be perceived; but, such as they are, they are the foundation of all after-science; and the true ideas, the _verae ideae_, which are apprehended by this faculty of intuition, are the primitive instruments with which nature has furnished us. If we ask for a test by which to distinguish them, he has none to give us. 'Veritas,' he says to his friends, in answer to their question, 'veritas index sui est et falsi. Veritas se ipsam patefacit.' All original truths are of such a kind that they cannot without absurdity even be conceived to be false; the opposites of them are contradictions in terms.--'Ut sciam me scire, necessario debeo prius scire. Hinc patet quod certitudo nihil est praeter ipsam essentiam objectivam.... Cum itaque veritas nullo egeat signo, sed sufficiat habere essentiam rerum objectivam, aut quod idem est ideas, ut omne tollatur dubium; hinc sequitur quod vera non est methodus, signum veritatis quaerere post acquisitionem idearum; sed quod vera methodus est via, ut ipsa veritas, aut essentiae objectivae rerum, aut ideae (omnia illa idem significant) debito ordine quaerantur.' (_De Emend. Intell._)