240 THE PRINCIPLES OF SCIENCE. 



the establishment of a conclusion and their probabilities 

 be m, n, p, q, r, &c., the probability of the conclusion on 



the ground of these premises is mxnxpxqxr* 



This product has but a small value, unless each of the 

 quanties m, n, &c., be nearly unity. 



But it is particularly to be noticed that the probability 

 thus calculated is not the whole probability of the con- 

 clusion, but that only which it derives from the premises 

 in question. Whately's 1 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 111 

 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.' 

 We must also bear in mind that the failure of one argu- 

 ment does not, except under special circumstances, disprove 

 the truth of the conclusion it is intended to uphold, other- 

 wise there are few truths which could survive the ill 

 considered arguments adduced in their favour. But as 

 a rope does not necessarily break because one strand in it 

 is weak, 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 ^. 



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 ^. If we also have the 



1 ' Elements of Logic,' Book III, sections, n and 18. 

 m ' Encyclopaedia Metrop.' art. Probabilities, p. 400. 



