In their monumental work, The Development of Logic, Martha Kneale and William Kneale maintain that during the seventeenth century logic was “in decline as a branch of philosophy.” But an era that included Leibniz, who according to the Kneales “deserves to be ranked among the greatest of all logicians,” as well as Locke, who dismisses formal logic as “learned Ignorance” while writing “the first modern treatise devoted specifically to philosophy of language,” suggests drama and excitement, not decline. While traditional logic was indeed in decline, logic itself was being transformed into modern mathematical logic. Moreover, the turn away from formal logic was also a dramatic turn to natural language for insight and solutions to the problems of philosophy. These two turns, the mathematical and linguistic turns of early modern philosophy, are defining features of seventeenth-century European philosophy.

EARLY MODERN LOGIC

In 1626, the Dutch logician Franco Burgesdijk maintained that there were three kinds of logicians: Aristotelians, Ramists, and Semi-Ramists. While Aristotelians continued to develop Aristotle’s logic of categorical syllogisms and immediate inferences, Ramists sought alternative logics that captured reasoning that traditional Aristotelian logic ignored. Semi-Ramists, also called “Philippo- Ramists” after Luther’s collaborator Philipp Melanchthon, sought a synthesis of traditional and alternative logics, which included the search for formal methods to capture nonsyllogistic reasoning.