great movements of the early 1900s, movements that would grow up into the
divide between logical positivism and phenomenology.
Advantages of Provinciality:
The British Route from Algebra to Philosophy
Modern logical philosophy comes from the convergence of two lines, German
and British. Russell, who brought them together, was the product of a British
network going back several generations. As in Germany, British logic was
produced largely by mathematicians. It is not obvious why British mathematics
should have become creative in the 1830s, for it had been stagnant since the
death of Newton. The social conditions which supported the advance of
mathematics on the Continent were lacking: Britain had neither the educational
reforms of the German universities or the École Polytechnique nor the virtuoso
mathematics of the academies. British mathematics had been largely in the
hands of the universities on the old unreformed model, where the Newtonian
calculus of fluxions had become a scholastic tradition to be upheld against the
Leibnizian rival.
When British mathematics came alive, it was in connection with the move-
ment for university modernization on Continental lines. The Cambridge Ana-
lytical Society was founded in 1813 at Trinity College to introduce Continental
developments in analysis; its youthful members, later to become famous in
various fields, included Herschel (the future astronomer), Babbage, Whewell,
and Peacock. In 1817 Peacock substituted differential for Newtonian fluxional
notation in the mathematics tripos; he remained active lifelong in the move-
ment for university reform. The network of reformers flowing from this group
carried on a long struggle, to a considerable extent by exodus and detour from
the traditional universities. Peacock’s student De Morgan refused a university
position because of the religious test, going instead to the reforming University
College at London; for similar reasons Cayley (another Trinity pupil) and
Sylvester (De Morgan’s pupil, debarred as a Jew) spent long years in private
life, at minor technicals schools, or in America, until positions opened for them
at Cambridge and Oxford after the university reforms. Jevons, another of De
Morgan’s pupils, got his position at Owens College, the reform-oriented prede-
cessor of Manchester University.
British mathematics owes its distinctive orientation to the advantages of
comparative backwardness. Whereas Continental mathematics was concerned
with the complexities of higher analysis, geometry, number theory, and the
solvability of equations, British mathematics dug into the relatively elementary
features of algebra (Richards, 1988; Kline, 1972: 773–776, 797, 805; Boyer,
1985: 621–626; Enros, 1981; Cannon, 1978: chap. 3). Ever since Berkeley in
The Post-revolutionary Condition^ •^705