II. On the other hand, a statement in a document as to an objective fact is never enough to establish that fact. The chances of falsehood or error are so many, the conditions which gave rise to the statement are so little known, that we cannot be sure that none of these chances has taken effect. The critical examination provides no definitive solution; it is indispensable if we are to avoid error, but it is insufficient to conduct us to truth.

Criticism can prove no fact; it only yields probabilities. Its end and result is to decompose documents into statements, each labelled with an estimate of its value—worthless statement, statement open to suspicion (strong or weak), statement probably (or, very probably) true, statement of unknown value.

Of all these different kinds of results one only is definitive—the statement of an author who can have had no information on the fact he states is null and void; it is to be rejected as we reject an apocryphal document.[169] But criticism here merely destroys illusory sources of information; it supplies nothing certain to take their place. The only sure results of criticism are negative. All the positive results are subject to doubt; they reduce to propositions of the form: "There are chances for or against the truth of such and such a statement." Chances only. A statement open to suspicion may turn out to be true; a statement whose truth is probable may, after all, be false. Instances occur continually, and we are never sufficiently well acquainted with the conditions under which the observation was made to know whether it was made ill or well.

In order to obtain a definitive result we require a final operation. After passing through the ordeal of criticism, statements present themselves as probable or improbable. But even the most probable of them, taken by themselves, remain mere probabilities: to pass from them to categorical propositions in scientific form is a step we have no right to take; a proposition in a science is an assertion not open to debate, and that is what the statements we have before us are not. It is a principle common to all sciences of observation not to base a scientific conclusion on a single observation; the fact must have been corroborated by several independent observations before it is affirmed categorically. History, with its imperfect modes of acquiring information, has less right than any other science to claim exemption from this principle. An historical statement is, in the most favourable case, but an indifferently made observation, and needs other observations to corroborate it.

It is by combining observations that every science is built up: a scientific fact is a centre on which several different observations converge.[170] Each observation is subject to chances of error which cannot be entirely eliminated; but if several observations agree, this can hardly be in virtue of a common error: the more probable explanation of the agreement is that the observers have all seen the same reality and have all described it correctly. Errors are personal and tend to diverge; it is the correct observations that agree.

Applied to history, this principle leads to a last series of operations, intermediate between purely analytical criticism and the synthetic operations—the comparison of statements.

We begin by classifying the results yielded by critical analysis in such a way as to bring together those statements which relate to the same fact. The operation is facilitated mechanically by the method of slips. Either each statement has been entered on a separate slip, or else a single slip has been assigned for each fact, and the different statements relating to it entered upon the slip as met with in the course of reading. By bringing the statements together we learn the extent of our information on the fact; the definitive conclusion depends on the relation between the statements. We have, then, to study separately the different cases which may occur.

III. Most frequently, except in contemporary history, the documents only supply a single statement on a given fact. In such a case all the other sciences follow an invariable rule: an isolated observation is not admitted into science; it is quoted (with the observer's name), but no conclusions are drawn from it. Historians have no avowable motive for proceeding otherwise. When a fact is supported by no more than the statement of a single man, however honest he may be, historians ought not to assert it, but to do as men of science do—give the reference (Thucydides states, Cæsar says that ...); this is all they have a right to affirm. In reality they all retain the habit of stating facts, as was done in the middle ages, on the authority of Thucydides or of Cæsar; many are simple enough to do so in express terms. Thus, allowing themselves to be guided by natural credulity, unchecked by science, historians end by admitting, on the insufficient presumption afforded by a unique document, any statement which does not happen to be contradicted by another document. Hence the absurd consequence that history is more positive, and seems better established in regard to those little known periods which are represented by a single writer than in regard to facts known from thousands of documents which contradict each other. The wars of the Medes known to Herodotus alone, the adventures of Fredegonda related by none but Gregory of Tours, are less subject to discussion than the events of the French Revolution, which have been described by hundreds of contemporaries. This is a discreditable state of things which cannot be ended except by a revolution in the minds of historians.

IV. When we have several statements relating to the same fact, they may contradict each other or they may agree. In order to be certain that they really do contradict each other, we have to make sure that they do actually relate to the same fact. Two apparently contradictory statements may be merely parallel; they may not relate exactly to the same moment, the same place, the same persons, the same episodes of an event, and they may be both correct.[171] We must not, however, infer that they confirm each other; each comes under the category of unique statements.

If the contradiction is real, at least one of the statements is false. In such cases it is a natural tendency to seek to reconcile them by a compromise—to split the difference. This peace-making spirit is the reverse of scientific. A says two and two make four; B says they make five. We are not to conclude that two and two make four and a half; we must examine and see which is right. This examination is the work of criticism. Of two contradictory statements, it nearly always happens that one is open to suspicion; this should be rejected if the competing statement has been judged very probably true. If both are open to suspicion, we abstain from drawing any conclusion. We do the same if several statements open to suspicion agree together as against a single statement which is not suspected.[172]