Let the probability of a conclusion, as derived from the premises (that is on the supposition that it was never imagined to be possible till the argument was heard), be called the _intrinsic probability_ of the argument. This is found by multiplying together the probabilities of all the assertions which are necessary to the argument. Thus, suppose that a conclusion was held to be impossible until an argument of a single syllogism was produced, the premises of which have severally five to one and eight to one in their favour. Then ⅚ × ⁸⁄₉, or ⁴⁰⁄₅₄, is the intrinsic probability of the argument, and the odds in its favour are 40 to 14, or 20 to 7. But this intrinsic probability is not always that of the conclusion; the latter, of course, depending in some degree on the likelihood which the conclusion was supposed to have before the argument was produced. A syllogism of 20 to 7 in its favour, advanced in favour of a conclusion which was beforehand as likely as not, produces a much more probable result than if the conclusion had been thought absolutely false until the argument produced a certain belief in the possibility of its being true. The change made in the probability of a conclusion by the introduction of an argument (or of a new argument, if some have already preceded) is found by the following rule. From the sum of the existing probability of the conclusion and the intrinsic probability of the new argument, take their product; the remainder is the probability of the conclusion, as reinforced by the argument. Thus, _a + b − ab_ is the probability of the truth of a conclusion after the introduction of an argument of the intrinsic probability _b_, the previous probability of the said conclusion having been _a_. Thus, a conclusion which has at present the chance ⅔ in its favour, when reinforced by an argument whose intrinsic probability is ¾, acquires the probability ⅔ + ¾ − ⅔ × ¾ or, ⅔ + ¾ − ½, or ¹¹⁄₁₂; or, having 2 to 1 in its favour before, it has 11 to 1 in its favour after, the argument. When the conclusion was neither likely nor unlikely beforehand (or had the probability ½), the shortest way of applying the preceding rule (in which _a + b − ab_ becomes ½ + ½_b_) is to divide the sum of the numerator and denominator of the intrinsic probability of the argument by twice the denominator. Thus, an argument of which the intrinsic probability is ¾, gives to a conclusion on which no bias previously existed, the probability ⅞ or (3 + 4)/(2 × 4). THE END. LONDON:—PRINTED BY JAMES MOYES, Castle Street, Leicester Square. ------------------------------------------------------------------------ TRANSCRIBER’S NOTES 1. Silently corrected obvious typographical errors and variations in spelling. 2. Retained archaic, non-standard, and uncertain spellings as printed. 3. Enclosed italics font in _underscores_.