level of international leadership. Their work generally lost out in priority to
De Morgan, Cantor, Dedekind and others. Charles’s mathematics was some-
times erroneous, and not well received by cutting-edge algebraists such as
Sylvester, his Hopkins department chief (EP, 1967: 6:76; DSB, 1981: 10:483–
486). Peirce settled on logic as his preferred path to success because this was
where his early resources best panned out. On European trips in 1870 and
1875, armed with introductions from his father, he met Boole, Jevons, and
Clifford, and impressed them with his developments of mathematical logic, a
new field in which his work was most clearly original.
Peirce’s semiotic originated in the intersection of Idealism and mathematics
(Murphey, 1961; Eisele, 1979; Brent, 1993). Peirce began in the 1860s as a
Kantian and Platonic Idealist, a mixture typical of the Transcendentalists who
frequented his father’s house. He began with a triad of ontological categories:
(a) abstract Ideas in (b) the mind of God, plus (c) the sensory world which
appears as matter. What was original was that Peirce reformulated ontology
through the lens of the logical propositions: matter, mind, and Ideas are
equivalent to subjects, predicates, plus the intervening connection via an “in-
terpretant” mind. Put another way, the copula is a sign relation, and the mind
is nothing more than the user of signs. Peirce absorbed metaphysics into logic,
producing his own semiotic Idealism.
Like the other Idealists, Peirce attacked the empiricist philosophy which
derives knowledge from the association of ideas with sensory objects. Whereas
Green argued that the mind provides relations not given in sensation, Peirce
pointed to the missing ingredient as the sign intervening between object and
mind (or “interpretant”). Signs are never isolated atoms, but part of infinite
series of signs flowing off in several dimensions; the interpretant is itself a sign,
and so is every part of a subject-predicate expression. The connectedness of
meanings with one another had been a stock-in-trade of the Idealists since
Hegel, and Idealist arguments through the turn of the century pointed to the
cultural realms of art and science as evidence of a spiritual reality transcending
the individual. Peirce, who had worked in Agassiz’s laboratory classifying
biological specimens, taxonomized his newly discovered array of semiotic
forms into a vast Linnaean project that he expected would give rise to a science
of all the sciences.
A Kant-like architectonic of categories appealed to Peirce because he rec-
ognized this as territory on which new discoveries could be made. Contempo-
rary mathematics pointed the direction. In 1843 William Rowan Hamilton
(not to be confused with the philosopher Sir William Hamilton) had created
quaternions, an alternative algebra without the commutative law of multipli-
cation. In the 1860s Benjamin Peirce had moved into this area; at the urging
of his son, he developed a linear associative algebra which generalizes the
676 •^ Intellectual Communities: Western Paths