With the aid of the theory of probabilities, we may extend the sphere of deductive argument. Hitherto we have treated propositions as certain, and on the hypothesis of certainty have deduced conclusions equally certain. But the information on which we reason in ordinary life is seldom or never certain, and almost all reasoning is really a question of probability. We ought therefore to be fully aware of the mode and degree in which deductive reasoning is affected by the theory of probability, and many persons may be surprised at the results which must be admitted. Some controversial writers appear to consider, as De Morgan remarked,[116] that an inference from several equally probable premises is itself as probable as any of them, but the true result is very different. If an argument involves many propositions, and each of them is uncertain, the conclusion will be of very little force. [116] *Encyclopædia Metropolitana*, art. *Probabilities*, p. 396. The validity of a conclusion may be regarded as a compound event, depending upon the premises happening to be true; thus, to obtain the probability of the conclusion, we must multiply together the fractions expressing the probabilities of the premises. If the probability is 1/2 that A is B, and also 1/2 that B is C, the conclusion that A is C, on the ground of these premises, is 1/2 × 1/2 or 1/4. Similarly if there be any number of premises requisite to the establishment of a conclusion and their probabilities be *p*, *q*, *r*, &c., the probability of the conclusion on the ground of these premises is *p* × *q* × *r* × ... This product has but a small value, unless each of the quantities *p*, *q*, &c., be nearly unity.