More Wit in PM

Abstract

78 Discussion c:\users\kenneth\documents\type3401\rj 3401 193 red.docx 2014-05-14 8:54 PM MORE WIT IN PM Michael E. Berumen 37155 Dickerson Run Windsor, co 80550, usa opinealot@gmail.com eldom does one find a piece by Bertrand Russell without a morsel of humour or wryness. Sometimes the Russellian wit is obvious. Other times it is more subtle, maybe even requiring a second look just to be sure. Headlong into some of his most technical and difficult works, a delightful bon mot might suddenly punctuate the philosophical solemnity. One doesn’t ordinarily think of Principia Mathematica as a sourcebook for Russellian waggishness , but it is there, to be sure—albeit one will negotiate many pages of symbols and scant prose before finding a specimen. Perhaps the best-known witticism amongst cognoscenti is, after having proved 1 + 1 = 2 (PM ∗110 .643, 2: 83), the authors observe, “The above proposition is occasionally useful .” The most complete directory for these jewels that I know is by Kenneth Blackwell.1 I thought it unlikely another would be found, so imagine my surprise when, after having dusted off my seldom-used Volume 3 to look something up, I came across a droll nugget that (to the best of my knowledge) has not been highlighted before. Something tells me Russell was biting down on his pipe stem and had a twinkle in his eye when he (I assume Russell, but they, anyway) wrote in the summary of Section A of Part vi, “Quantity”: Great difficulties are caused, in this section, by the existence-theorems and the question of types. These difficulties disappear if the axiom of infinity is assumed, but it seems improper to make the theory of (say) 2/3 depend upon the assumption that the number of objects in the universe is not finite. (PM 3: 234; italics mine) “Improper” indeed, the erstwhile Victorian says! By way of explanation, he goes on to say, We have, accordingly, taken pains not to make this assumption, except where, as in the theory of real numbers, it is really essential, and not merely convenient. Even that has a bit of Russellian sarcasm. So, accept the challenge and find another. In the meantime, take comfort in the knowledge that the sometimes controversial Axiom of Infinity is an unnecessary assumption in mixing one part soda and two parts Red Hackle. 1 “The Wit and Humour of Principia Mathematica”, Russell 31 (2011): 151–60. S ...