Chapter 40

THE GROUNDS OF DISBELIEF.

The result of examining evidence is not always belief, or even suspension of judgment, but is sometimes positive disbelief. This can ensue only when the affirmative evidence does not amount to full proof, but is based on some approximate generalisation. In such cases, if the negative evidence consist of a stronger, though still only an approximate, generalisation, we think the fact improbable, and disbelieve it provisionally; but if of a complete generalisation based on a rigorous induction, it is disbelieved by us totally, and thought impossible. Hence, Hume declared miracles incredible, as being, he considered, contrary to a complete induction. Now, it is true that _in the absence of any adequate counteracting cause_, a fact contrary to a complete induction is incredible, whatever evidence it may be grounded on; unless, indeed, the evidence go to prove the supposed law inconsistent with some better established one. But when a miracle is asserted, the presence of an adequate counteracting cause _is_ asserted, viz. a direct interposition of an act of the will of a Being having power over nature. Therefore, all that Hume proved is, that we cannot believe in a miracle unless we believe in the power, and _the will_, of the Deity to interfere with existing causes by introducing new ones; and that, in default of such belief, not the most satisfactory evidence of our senses or of testimony can hinder us from holding a seeming miracle to be merely the result of some unknown natural cause. The argument of Dr. Campbell and others against Hume, however, is untenable, viz. that, as we do not disbelieve an alleged fact (which may be something conforming to the uniform course of experience) merely because the chances are against it, therefore we need never disbelieve any fact supported by credible testimony (even if contrary to the uniform course of experience). But this is to confound _improbability before the fact_, which is _not_ always a ground for disbelief, with _improbability after the fact_, which always is.

Facts which conflict with special laws of causation are only improbable before the fact; that is, our disbelief depends on the improbability that there could have been present, without our knowledge, at the time and place of the event, an adequate counteracting cause. So, too, with facts which conflict with the properties of _kinds_ (which are uniformities of mere coexistence not proved to be dependent on causation), that is, facts which assert the existence of a new _kind_; such facts we disbelieve only if, the generalisation being sufficiently comprehensive, some properties are said to have been found in the supposed new _kind_ disjoined from others which always have been known to accompany them. When the assertion would amount, if admitted, only to the existence of an unknown cause or an anomalous _kind_, _unconformable_, but, as Hume puts it, _not contrary_ to experience, in circumstances so little explored, that it is credible hitherto unknown things may there be found, and when prejudice cannot have tempted to the assertion, one ought neither to admit nor to reject the testimony, but to suspend judgment till it be confirmed or disproved from other sources. Only facts, then, which are contradictory to the laws of Number, Extension, and Universal Causation (since these know no counteraction or anomaly), or to laws nearly as general, are improbable after, as well as before the fact, and only these we should term _absolutely impossible_, calling other facts _improbable_ only, or, at most, _impossible in the circumstances of the case_.

Between these two species of improbabilities lie _coincidences_; that is, combinations of chances presenting some unexpected regularity assimilating them in so far to the results of law. It was thought by d'Alembert that, though regular combinations are as probable as others according to the mathematical theory, some physical law prevents them from occurring so often. Now, stronger testimony may indeed be needed to support the assertion of such a combination as, e.g. ten successive throws of sixes at dice, because such a regular series is more likely than an irregular series to be the result of design; and because even the desire to excite wonder is likely to tempt men to assert the occurrence falsely, though this probability must be estimated afresh in every instance. But though such a series _seems_ peculiarly improbable, it is only because the comparison is tacitly made, not between it and any one particular previously fixed series of throws, but between all regular and all irregular successions taken together. The fact is not in itself more improbable; and no stronger evidence is needed to give it credibility, apart from the reasons above mentioned, than in the case of ordinary events.