Formal Logic: Or, the Calculus of Inference, Necessary and Probable

London: Taylor & Walton, 1847. First Printing. Hardcover. Good. 8vo, ex-libris Bryn Mawr with their bookplate and withdrawn stamp, in blue library buckram, with white label on spine, book good with title page having perforated blindstamp and release stamp, bar code on rear flyleaf, ink stamp on pastedown, contents otherwise very good, light foxing. Unfortunately bound without ads, so impossible to know exactly what issue this is, but 1847 on title page. One of the most important contributions to logic in its time, alongside Boole's works. Britannica: "De Morgan introduced the enormously influential notion of a possibly arbitrary and stipulated "universe of discourse" that was used by later Booleans. (Boole's original universe referred simply to "all things.") This view influenced 20th-century logical semantics. De Morgan contrasted uppercase and lowercase letters: a capital letter represented a class of individuals, while a lowercase letter represented its complement relative to the universe of discourse, a convention Boole might have expressed by writing "x = (1 X)"; this stipulation results in the general principle: xX = 0. A period indicated a (propositional) negation, and the parentheses "(" and ")" indicated, respectively, distributed (if the parenthesis faces toward the nearby term) and undistributed terms. Thus De Morgan would write "All A's are B's" as "A) )B" and "Some A's are B's" as "A ( )B." These distinctions parallel Boole's account of distribution (quantification) in "A = vB" (where A is distributed but B is not) and "vA = B" (where both terms are distributed). Although his entire system was developed with wit, consistency, and brilliance, it is remarkable that De Morgan never saw the inferiority of his notation to almost all available symbolisms.