But it is particularly to be noticed that the probability thus calculated is not the whole probability of the conclusion, but that only which it derives from the premises in question. Whately’s[117] remarks on this subject might mislead the reader into supposing that the calculation is completed by multiplying together the probabilities of the premises. But it has been fully explained by De Morgan[118] that we must take into account the antecedent probability of the conclusion; A may be C for other reasons besides its being B, and as he remarks, “It is difficult, if not impossible, to produce a chain of argument of which the reasoner can rest the result on those arguments only.” The failure of one argument does not, except under special circumstances, disprove the truth of the conclusion it is intended to uphold, otherwise there are few truths which could survive the ill-considered arguments adduced in their favour. As a rope does not necessarily break because one or two strands in it fail, so a conclusion may depend upon an endless number of considerations besides those immediately in view. Even when we have no other information we must not consider a statement as devoid of all probability. The true expression of complete doubt is a ratio of equality between the chances in favour of and against it, and this ratio is expressed in the probability 1/2. [117] *Elements of Logic*, Book III. sections 11 and 18. [118] *Encyclopædia Metropolitana*, art. *Probabilities*, p. 400. Now if A and C are wholly unknown things, we have no reason to believe that A is C rather than A is not C. The antecedent probability is then 1/2. If we also have the probabilities that A is B, 1/2 and that B is C, 1/2 we have no right to suppose that the probability of A being C is reduced by the argument in its favour. If the conclusion is true on its own grounds, the failure of the argument does not affect it; thus its total probability is its antecedent probability, added to the probability that this failing, the new argument in question establishes it. There is a probability 1/2 that we shall not require the special argument; a probability 1/2 that we shall, and a probability 1/4 that the argument does in that case establish it. Thus the complete result is 1/2 + 1/2 × 1/4, or 5/8. In general language, if *a* be the probability founded on a particular argument, and *c* the antecedent probability of the event, the general result is 1 - (1 - *a*)(1 - *c*), or *a* + *c* - *ac*.