method of quaternions to inventing multiple algebras and investigating their
properties. Modern higher mathematics was just becoming conscious that
symbol systems need not be taken for granted as neutral tools of the trade;
results of this awareness included not only quaternions but also the non-Euclid-
ean geometries discovered in the 1820s and systematized by Riemann in 1854.
New symbol systems could be posited and new realms of discovery opened up
by examining their consequences.^52 Young Peirce had an even grander vision:
mathematics is the key to all symbol systems and therefore all knowledge; the
method of positing symbols and exploring their consequences is the very stuff
of the universe.
In the 1880s Peirce developed his combination of higher mathematics and
Idealism into an evolutionary cosmology. Because he identified the working of
logic in the mind with reality itself, Peirce anthropomorphized the universe.
Borrowing a concept from the new experimental psychology, he argued that
the unconscious habits from one sign to another, which constitute inference,
exist throughout reality. Nature is an endless string of signs, each pointing
beyond itself: “Even plants make their living... by uttering signs.” There is
nothing beyond signs: “Reals are signs. To try to peel off signs and get down
to the real thing is like trying to peel an onion and get down to [the] onion
itself.” Peirce called his position “synechism,” the doctrine that the external
referent of any true proposition is a real continuum in the mathematical sense,
“something whose possibilities of determination no multitude of individuals
can exhaust.” The same holds in epistemology and in ontology: “Our knowl-
edge is never absolute but always swims, as it were, in a continuum of
uncertainty and of indeterminacy. Now the doctrine of continuity is that all
things swim in continua.”^53 The technical basis comes from Cantor’s work on
higher orders of infinite sets, which Peirce followed up during his years in the
Hopkins mathematics department. Pushing mathematics onto the terrain of
philosophy, Peirce posited a collection beyond all trans-finite sets, an ultimate
ground of reality in which there is nothing discrete and everything is welded
into a continuum. There are no isolated sense impressions nor any logical
particulars; only universals are real.
By the 1890s, as Peirce’s career was cut adrift from scientific institutions,
his philosophy increasingly took the form of a scientific-religious system from
which he planned to make a fortune in mass-marketed promotions. These
business ventures came to nothing, but Peirce sketched out his principles of
popularized Idealism in the guise of evolution as a principle of self-sacrificing
love, manifested in periodic laws of history analogous to those of chemistry.
Alternatively, scientific laws themselves are the result of evolution. Matter is
“effete mind.” The universe is evolving from “a chaos of unpersonalized
feeling,” in which chance plays a decreasingly lesser part as habits emerge
Intellectuals Take Control: The University Revolution^ •^677