Is the scientist, however, to allow no presumption at all? That would be impossible. When making his calculations the mathematician presupposes the correctness of the multiplication table. Or is he first to prove that twice three are six? He could not do it, because it is immediately self-evident. In his optical experiments in the laboratory, in drawing inferences as to the nature of light from different indications, the physicist presupposes that senses are able to observe the facts correctly, that everything has its respective reason, that nothing can be and not be, at the same time, under the same conditions. Can he or must he try first to prove it? He must presume it because it is beyond a doubt, and because it cannot be proved at all, at least all of it cannot. The astronomer, too, makes unhesitating use of the formulas of mathematics without examining them anew; every natural scientist calmly presupposes the correctness of the results established by his predecessors and goes on building upon those results: he may do so because he cannot with reason doubt them. Hence presumptions are common; they may be made when we are convinced of their truth; they must be made because not everything can be proved. Much cannot be proved because it is immediately self-evident, as, for instance, the ability to recognize the true or the elementary principles of reasoning; many other things cannot always be proved minutely, because not every scientist cares to begin with the egg of Leda. He that wants to build a house builds upon a given base; if he will not accept it, if he desires to dig up the fundament to the very bottom, in order to lay it anew, he will be digging forever, but the house will never be built. Hence to say that science must be unprepossessed cannot mean that it must not make any presupposition. What, therefore, does it mean? Simply this: _Science must not presume anything to be true which is false, nor anything as proved which is still uncertain and unproved_. Whatever the scientist knows to be certain he may take as such, presuming it as the foundation and direction of further work; and what he knows to be probable he may suppose to be probable. In so doing he in no way offends against the ideal that should be ever-present to his mind—the truth, because he merely allows himself to be guided by the truth, recognized as such. And the sequence of truth cannot but be truth, the sequence of certainty cannot but be certainty. But should he presuppose to be true what is false and unproved, and the uncertain to be certain, then he would offend against truth, against the aim of every science.