Page:Mind (New Series) Volume 9.djvu/90

 76 HUGH MACCOLL : nary speech without being forcibly reminded of a certain nursery composition, whose ever-increasing accumulation of thats affords such pleasure to the infantine mind ; I allude, of course, to "The House that Jack Built". But trivial matters in appearance often supply excellent illustrations of important general principles. There is a story that Sir Isaac Newton was once thought to be in his second child- hood because he was seen one summer day at his open window gravely engaged in blowing soap-bubbles, which he appeared to regard with intense interest, as, one after another, they slowly floated away in the sunlight. It was however no case of second childhood : the great philosopher was really engaged in studying the laws of reflexion, re- fraction and colour; and soap-bubbles happened to afford the most suitable data for a particularly promising line of investigation. Prof, de Morgan's remark 1 that Probability was "the unknown God whom the schoolmen ignorantly worshipped " when, in their logical dissertations, they discussed the subject of modality, was as true as it was witty ; and the remark might beextended to their treatment of other logical questions besides those of modality. Undoubtedly there is an intimate con- nexion which Boole was, I believe, the first to point out, between the mathematical theory of chances and all problems of formal logic. Boole did not succeed in clearly explaining this connexion, mainly because of his erroneous conception as to the real meaning (in dealing with such problems) of the word independent. This meaning I will define presently ; I now proceed to give a concrete illustration of the preceding symbolic statement A 1 "", and of the exact value (in certain circumstances) of the chance of its being true. As in my sixth and seventh papers in the Proceedings of the A Mathematical Society, I use the fractional symbol ^ to denote the chance that A is true on the assumption that B is true ; B being some hypothesis consistent with, but not necessarily A implied in, the data of the problem. Hence must denote the chance that A is true on the assumption that e is true ; that is to say, denotes the chance that A is true on no assumption beyond the data of the problem. Thus, when we simply speak of the chance that A is true, we must be under- 1 See Dr. Venn's Logic of Chance, p. 299.