After all this we hope there will be no doubt that the evidence of mathematics, which has become the pattern and symbol of all evidence, rests essentially not upon demonstration, but upon immediate perception, which is thus here, as everywhere else, the ultimate ground and source of truth. Yet the perception which lies at the basis of mathematics has a great advantage over all other perception, and therefore over empirical perception. It is _a priori_, and therefore independent of experience, which is always given only in successive parts; therefore everything is equally near to it, and we can start either from the reason or from the consequent, as we please. Now this makes it absolutely reliable, for in it the consequent is known from the reason, and this is the only kind of knowledge that has necessity; for example, the equality of the sides is known as established by the equality of the angles. All empirical perception, on the other hand, and the greater part of experience, proceeds conversely from the consequent to the reason, and this kind of knowledge is not infallible, for necessity only attaches to the consequent on account of the reason being given, and no necessity attaches to the knowledge of the reason from the consequent, for the same consequent may follow from different reasons. The latter kind of knowledge is simply induction, _i.e._, from many consequents which point to one reason, the reason is accepted as certain; but as the cases can never be all before us, the truth here is not unconditionally certain. But all knowledge through sense-perception, and the great bulk of experience, has only this kind of truth. The affection of one of the senses induces the understanding to infer a cause of the effect, but, as a conclusion from the consequent to the reason is never certain, illusion, which is deception of the senses, is possible, and indeed often occurs, as was pointed out above. Only when several of the senses, or it may be all the five, receive impressions which point to the same cause, the possibility of illusion is reduced to a minimum; but yet it still exists, for there are cases, for example, the case of counterfeit money, in which all the senses are deceived. All empirical knowledge, and consequently the whole of natural science, is in the same position, except only the pure, or as Kant calls it, metaphysical part of it. Here also the causes are known from the effects, consequently all natural philosophy rests upon hypotheses, which are often false, and must then gradually give place to more correct ones. Only in the case of purposely arranged experiments, knowledge proceeds from the cause to the effect, that is, it follows the method that affords certainty; but these experiments themselves are undertaken in consequence of hypotheses. Therefore, no branch of natural science, such as physics, or astronomy, or physiology could be discovered all at once, as was the case with mathematics and logic, but required and