_Probability_ has a similar position in the sciences. The scholar who has discovered a new thought, a new order, explanation or solution, etc., will find it indifferent whether he has made it only highly probable or certain. He is concerned only with the idea, and a scholar who is dealing with the idea for its own sake will perhaps prefer to bring it to a great probability rather than to indubitable certainty, for where conclusive proof is presented there is no longer much interest in further research, while probability permits and requires further study. But our aim is certainty and proof only, and even a high degree of probability is no better than untruth and can not count. In passing judgment and for the purpose of judgment a high degree of probability can have only corroborative weight, and then it is probability only when taken in itself, and proof when taken with regard to the thing it corroborates. If, for example, it is most probable that X was recognized at the place of a crime, and if at the same time his evidence of alibi has failed, his footmarks are corroborative; so are the stolen goods which have been seen in his possession, and something he had lost at the place of the crime which is recognized as his property, etc. In short, when all these indices are in themselves established only as highly probable, they give under certain circumstances, when taken together, complete certainty, because the coincidence of so many high probabilities must be declared impossible if X were not the criminal. In all other cases, as we have already pointed out, _assumption_ and probability have only a heuristic value for us lawyers. With the assumption, we must of course count; many cases can not be begun without the assistance of assumption. Every only half-confused case, the process of which is unknown, requires first of all and as early as possible the application of some assumption to its material. As soon as the account is inconsistent the assumption must be abandoned and a fresh one and yet again a fresh one assumed, until finally one holds its own and may be established as probable. It then remains the center of operation, until it becomes of itself a proof or, as we have explained, until so many high probabilities in various directions have been gathered, that, taken in their order, they serve evidentially. A very high degree of probability is sufficient in making complaints; but sentencing requires “certainty,” and in most cases the struggle between the prosecution and the defense, and the doubt of the judge, turns upon the question of probability as against proof.[143]