A History of The Connectives

Contemporary students of logic tend to think of the logic of the connectives as the most basic area of the subject, which can then be extended with a logic of quantifiers. Historically, however, the logic of the quantifiers, in the form of the Aristotelian theory of the syllogism, came first. Truth conditions for negation, conjunction, and disjunction were well understood in ancient times, though not until Leibniz did anyone appreciate the algebraic features of these connectives. Approaches to the conditional, meanwhile, depended on drawing an analogy between conditionals and universal affirmative propositions. That remained true throughout the ancient, medieval, and early modern periods, and extended well into the nineteenth century, when Boole constructed an algebraic theory designed to handle sentential and quantificational phenomena in one go. The strength of the analogy, moreover, undercuts a common and otherwise appealing picture of the history of logic, according to which sentential and quantificational threads developed largely independently and, sometimes, in opposition to each other, until Frege wove them together in what we now consider classical logic. Frege did contribute greatly to our understanding of the connectives as well as the quantifiers. But his contribution consists in something other than unifying them into a single theory.