Laurence Goldstein

(1947 - 2014)

Wittgenstein's Tractatus is widely regarded as a masterpiece, a brilliant, if flawed attempt to achieve an ‘unassailable and definitive … final solution’ to a wide range of philosophical problems. Yet, in a 1931 notebook, Wittgenstein confesses: ‘I think there is some truth in my idea that I am really only reproductive in my thinking. I think I have never invented a line of thinking but that it was always provided for me by someone else’. This disarming self-assessment is, I believe accurate. The Tractatus, despite making significant advances on the logical doctrines of Frege and Russell, is essentially a derivative work—Wittgenstein, as he elsewhere acknowledges, provided a fertile soil in which the original seeds of other peoples' thought grew in a unique way. In a play of mine, published in Philosophy (1999), Wittgenstein fails a tough viva on the Tractatus because he fails to properly support some of the weak arguments in the work and because of his inadequate acknowledgment of sources. The present paper further explores some of the antecedents of Wittgenstein's early views and answers some criticisms of the play.

Letting is a common practice in mathematics. For example, we let x be the sum of the first n integers and, after a short proof, conclude that x = n(n+1)/2; we let J be the point where the bisectors of two of the angles of a triangle intersect and prove that this coincides with H, the point at which another pair of bisectors of the angles of that triangle intersect. Karl Weierstrass's colleagues, in an attempt to solve optimization problems, stipulated that the minimum area for a triangle with a given perimeter be a straight line segment conceived as a triangle with zero altitude. (Weierstrass complained that this obscured the insight that some problems have no solutions.) In mathematics applied to physics, we let x be the temperature in Fahrenheit corresponding to 30° Centigrade; we let v be the velocity of the Earth through the luminiferous ether. Before the error was spotted, the official rules for Little League Baseball made an inconsistent stipulation about the dimensions of home plate (Bradley 1996).