Saturday, July 5, 2008

A Foot Note To Schopenhauer

Schopenhauer had no interest in Mathematics and knew nothing about the tremendous developments that were occurring under his nose. It did not occur to him therefore, as it had not to Kant or any of his other followers, that mathematics is the true synthetic a priori.

In 1831, Evariste Galois used a hint from Newton about symmetries in relations between the coefficients and roots of algebric equations to prove that equations of the fifth degree had no general or algorithmic solution (like the algorithm that everyone learns for quadratic equations) and invented group theory in order to complete his proof. Mathematics had become by that time a European enterprise, building on the work of Euler and Gauss and many others in the 18th century. Lagrange, Cauchy, Abel, Dedekind, Dirichlet, Helmholtz, Kronecker, Kummer, Riemann, Sylow are just a few of the names that a man like Schopenhauer who claimed to be up to date in all the sciences, ought to have known about.

When Schopenhauer died in 1867, history had passed him by. The Communist Manifesto was published in 1848. The purpose of philosophy, said Marx, is not to understand the world but change it. Schopenhauer's message of esthetic contemplation or Buddhist self control and denial was of no use to people who were under the tiger's or Capitalist paw. Henceforth the romantic will would take new directions. Marxism, without any of the checks and balances that 18th century liberalism had devised, proved to be wonderfully useful--as the world would learn at horrendous cost--to the will to power, which as Schopenhauer had shown, is what makes the world go round.

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