cipally the middle-class journals of opinion on which the circle of London
evolutionists supported themselves. Mathematics, however, was more closely
attached to academic bases; Boole made his first connection here in the early
1840s by publishing, in the Cambridge Mathematical Journal, some elementary
but pioneering work in the computation of algebraic invariants—one of the
alternative algebras which Cayley was to develop (Kline, 1972: 927). Personal
correspondence with De Morgan at the time of the Hamilton controversy
brought Boole recognition and an academic position in Ireland.
Boole takes Peacock and De Morgan a step further. Mathematics is no
longer to be seen as the science of magnitudes, but as a general method for
operations with symbols of whatever content. Boolean algebra redefines arith-
metical operations as unions and intersections of sets. Subsequently Boole’s
ideas were applied in Jevons’s “logical piano” (1869)—a combination of logic
machine and mechanical calculator—and in Venn’s diagrams of 1881 (Kneale
and Kneale, 1984: 420–421; Boyer, 1985: 672).
Most of the action in British algebra-cum-logic took place within the
overlapping branches of a network (see Figure 13.2). One node is Trinity
College, Cambridge, beginning with the mathematical and logical reformers
Peacock, Herschel, Babbage, and Whewell, who produced a chain of pupils
including De Morgan, Cayley, Sylvester, and Jevons, with Boole as an offshoot.
Another lineage descends from the Utilitarian circle of philosophical radicals
around Bentham and James Mill. By midcentury this group had spawned two
successor groups: one at London, the Huxley–Spencer–George Eliot circle of
anti-religious evolutionists; the other branch played back into Trinity College,
where a circle formed in the 1850s around John Grote, younger brother of
George Grote, who had belonged to the original Utilitarians. Among Grote’s
protégés were Venn and Sidgwick; the latter, who wrote the great work of
ethics on modified Utilitarian principles, was the teacher of McTaggart and
G. E. Moore. Together with Cayley, professor of mathematics at Cambridge
from the 1860s down to his death in 1895, this constituted an intergenerational
network leading directly to Whitehead and Russell.
The network was about to become fateful in philosophy. It also stimulated
the creativity of another characteristic British field. British economics was
created by much the same network we have been reviewing in philosophy:
Locke, Hume, and Smith in the core philosophical networks of their time;
Ricardo (1817) and J. S. Mill (1848) in the Utilitarian circles. The earlier
ingredients were a non-academic social movement, combined with the analyti-
cal principles generated by an intellectual network. When the British universi-
ties reformed in the 1860s, economics now became academic, meshing with
the nearest adjacent disciplines, thus intersecting with both philosophy and
mathematics. Jevons, who developed the marginal utility theory in 1871 to
708 •^ Intellectual Communities: Western Paths