form thus included attempts to replace Aristotelean syllogistic logic with a new
logic of empirical inquiry. This was the subject of Whewell’s work at Trinity,
Cambridge, in the 1830s and of John Stuart Mill’s first book, the source of his
early fame, his Logic in 1843. On the side of the algebraists, De Morgan in
the 1840s extended his axiomatization into logic. This brought him into a
public dispute over priority with Sir William Hamilton (not to be confused
with the physicist W. R. Hamilton) in 1847. Conflicts typically lead to widen-
ing the network of allies; in the same year Boole’s first book, The Mathematical
Analysis of Logic, was prompted by Boole’s intervening in the dispute on De
Morgan’s side.
De Morgan and Boole were reformers, mathematical imperialists on the
turf of logic. Sir William Hamilton was a philosophical conservative. An
Edinburgh law professor, Hamilton had acquired the chair of logic and meta-
physics in 1836 for his defense of traditional religion after the manner of the
Scottish common-sense philosophy. Reid and Stewart had rebutted Humean
skepticism by a classification of innate human faculties, including a faculty of
common sense. In 1829—just the time when Carlyle was popularizing German
philosophy at Edinburgh—Hamilton updated the position against the growing
influence of Kant. Hamilton denied Kant’s antinomies; by the law of contra-
diction, either space is infinite or it is not, although we cannot know which.
There is direct knowledge through the senses of the existence of objects,
although what they are must be inferred through logic. In conflicts conserva-
tism cannot stay static; Hamilton too overthrows syllogistic logic as making
inadequate distinctions. His doctrine holds that the quantities “all,” “some,”
and “none” apply to the predicate as well as the subject. “All men are mortal”
is ambiguous; it could mean “all men are all mortals” (i.e., only men are
mortal) or “all men are some (of the) mortals.” Hamilton’s quantification of
the predicate was buried in his better-known philosophical system and became
known only in the 1840s, when Hamilton raised a priority dispute with De
Morgan.^14 Since Hamilton by now was the most famous British philosopher
of his day, he made an excellent sounding board for De Morgan’s logic.^15
Boole’s Laws of Thought (1854) generalized this controversy over the most
elementary parts of arithmetic. Boole was an autodidact, a mathematics teacher
at an elementary school, seemingly an unlikely person to contribute to the
frontiers of mathematics. But Boole looks less like an anomaly when we see
that individuals with limited formal education dominated the philosophy net-
work in the British midcentury generation, unlike at most other times: Spencer,
Huxley, Lewes, George Eliot, Buckle all are similar to Boole in this respect.
Non-academic creativity in philosophy peaked in the 1840s through the 1860s.
This was the period when the traditional university system was most under
criticism and alternative bases for intellectual networks were expanding—prin-
The Post-revolutionary Condition^ •^707