Saturday, September 4, 2010

Newton, Leibniz, Wolff, Mathematics, Leibniz' Reputation and Epistemology

I often think about epistemological subjects: What do we know? What can we know? Why do we think we know what we think we know? In particular, I wonder why some people seem so sure that they know the thoughts, feelings and motivations of others, without believing in telepathy, the notion of which I also reject, pending much stronger evidence than anything I've seen so far. I think about this when I hear about jury verdicts being overturned by things like DNA evidence. I think about it when I hear scientists talking about Newtonhaving invented calculus, and rarely mentioning Leibniz,who claimed that he had invented calculus independently of Newton. During his lifetime and since, this claim of Leibniz' has often been called a lie.

In this earlier Wrong Monkey post, as I waited for this volume of letters between Leibniz and Wolffto arrive from Amazon, I speculated on Christian von Wolff'spossible role in the decline of Latin as an academic vernacular. When the book arrived and I read its introduction by C.I. Gerhardt, it became plain that Gerhardt blamed Wolff for damaging Leibniz' reputation. Indeed, it seems Gerhardt may have gathered these particular letters and published this book for no other reason than to expose Wolff's bad behavior and rehabilitate Leibniz' reputation -- his unjustly tarnished reputation, in Gerhardt's opinion. It is Gerhardt's thesis that Wolff, early in his academic career, was weak in mathematics, too weak to justify the academic positions in mathematics and philosophy which he occupied, and that he basically used Leibniz during this period as an unpaid math tutor, and that after Leibniz' death he claimed many of Leibniz' mathematical achievements as his own and downplayed the help he had received from Leibniz. Gerhardt maintains that this misrepresentation of the facts not only helped Wolff acquire and hold academic posts for which he was gravely underqualified, but that it also gave ammunition to those who maintained that Newton alone had invented calculus and that Leibniz had been lying when he claimed otherwise. Gerhardt maintains that the letters between Wolff and Leibniz which he presents on this volume clearly demonstrate all of this.

Do they? I don't know, in large part because my knowledge of math is not extensive enough to allow me to follow all of the math contained in the letters written in Latin bewteen Wolff and Leibniz and collected in Gerhardt's book. My knowledge of math would've been nowhere near cutting-edge 300 years ago when those letters were new, much less is it cutting-edge now, when all these world-class mathematicians and physicists seem quite dismissive of any notion that anyone but Newton had any part in inventing calculus. Then again, those physicists and mathematicians have almost all been American or British. I haven't heard any present-day German experts weigh in on the Newton-Leibniz controversy. And Gerhardt, who published his volume in 1860 with a thesis of Leibniz having been wronged, by Wolff and also by those who praised Newton at his expense, was German. National sentiments were and are widespread, pervasive and often subtle, much more widespread than the obvious hatreds of extremists fringes. And Newton seems to me to have been the sort apt to fight a bitter feud with or without significant cause, like the one he fought against Leibniz until Leibniz died in 1716, and Leibniz seems like the sort who would not feud without cause, who would be reluctant to fight even with cause, and who would cheerfully admit it when and if some laurels had been bestowed upon him which he had not earned.

But how on Earth do I think I know so much about Newton's and Leibniz' personalities and motivations and about their respective characters? Could it not well be that I am predisposed to like Leibniz and dislike Newton because of some other things each of them wrote which have nothing to do with calculus, so that in this quarrel I am judging Newton too harshly and Leibniz too well? Could it not well be that I too am much too hasty to think that I know this or that? that for instance I am completely unjustified in claiming that national sentiment may have tipped the scales in favor of Newton in the judgment of all those expert mathematicians and physicists?

It could be. Of course I still think I'm right and that I am unusually free of prejudice and unusually attuned to the prejudices of others. But I know I haven't proven anything of the sort. I don't think this essay will change many minds about Newton or Leibniz, or Wolff, or Gerhardt, or math in general. But perhaps it will persuade some readers to ponder more often the nature of things like knowledge and certainty. I think that would be a good thing, although I don't think I can prove that either.

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