Page:Mind (New Series) Volume 6.djvu/521

 SYMBOLIC REASONING. 505 I express my opinion that the work is weakest where it is generally supposed to be strongest, namely, in the power and originality of its logical calculus, and that what Boole him- self, and others after him, considered his greatest achievement and " the crowning triumph of his method," namely, the application of his calculus to probability, is precisely that portion of his work in which his failure has been complete and absolute. Boole may not inaptly be compared to Shakespeare. Both authors possessed a remarkable analyt- ical insight into the workings of the human mind ; the one of its secret motives and passions ; the other of the subtle laws of its intellectual operations ; yet both the one judged by his plays, the other by his Laws of Thought showed but little constructive ability. Just as Shakespeare limited himself to skilful adaptations to his purpose of the dramatic plots of preceding playwrights or of the accepted facts of history, so Boole limited himself to skilful adaptations to new uses of the rules and formulae which he found ready to his hand in mathematics. Boole undoubtedly showed great originality and ability in his application of these rules and formulae, and an unfortunate thing I believe it has been for symbolic logic that he did show this originality and ability. I cannot help thinking that the seeming success which at- tended his efforts to squeeze all reasoning into the old cast- iron formulae constructed specially for numbers and quantities has tempted many other able logicians to waste their energies in the like futile endeavours ; when those energies might have been employed with far greater chances of success in inventing new and independent formulae, more elastic and more suitable for the highly general and widely varying kinds of problems which are destined to enter more and more largely into the ever-expanding subject of Symbolic Logic. As regards the introduction of absolutely new symbols, such as Schroder's = and Pierce's <, I think it should be avoided as much as possible. Generally speaking, it is better to put to fresh uses the familiar symbols of old acquaintance than have recourse to strangers. This may be a conservative prejudice on my part, but it is a fact that I have myself introduced no new symbol, though I have freely exercised my right of definition and interpretation as regards some of the symbols and combinations of symbols already in common use among mathematicians. The symbols +, =,:,::, with subscripts, indices, and commas, are all old friends ; while the symbol !, though a more recent arrival on mathematical territory, has been there long enough to have acquired the rights of naturalisation.