The Mathematical Origins of 19 th Century Algebra of Logic ∗

Most 19th century scholars would have agreed to the opinion that philosophers are responsible for research on logic. On the other hand, the history of late 19th century logic clearly indicates a very dynamic development instigated not by philosophers, but by mathematicians. A central outcome of this development was the emergence of what has been called the “new logic”, “mathematical logic”, “symbolic logic”, or, from 1904 on, “logistics”. This new logic came from Great Britain, and was created by mathematicians in the second half of the 19th century, finally becoming a mathematical subdiscipline in the early 20th century. Charles L. Dodgson, better known under his pen name Lewis Carroll (1832–1898), published two well-known books on logic, The Game of Logic of 1887 and Symbolic Logic of 1896 of which a fourth edition appeared already in 1897. These books were written “to be of real service to the young, and to be taken up, in High Schools and in private families, as a valuable addition of their stock of healthful mental recreations” (Carroll 1896 , xiv). They were meant “to popularize this fascinating subject,” as Carroll wrote in the preface of the fourth edition of Symbolic Logic (ibid.). But, astonishingly enough, in both books there is no definition of the term “logic”. Given the broad scope of these books the title “Symbolic Logic” of the second book should at least have been explained.