Deduction through the Ages: A History of Truth

Abstract

The historical roots behind the modern truth table for an implication (an “if-then” statement) in propositional logic are examined from antiquity to the twentieth century.  Beginning with five verbal argument forms attributed to Chrysippus in the third century BCE, the project examines the possible equivalence of these forms to a standard “if-then” statement.  Progress towards this goal is studied from the original writings (sometimes in translation) of George Boole and Gottlob Frege in the nineteenth century, and from the early twentieth-century collaboration, Principia Mathematica, by Bertrand Russell and Alfred Whitehead.  A final resolution to these equivalences is given by the tabular evaluation of propositions developed independently by Ludwig Wittgenstein and Emil Post, who coined the term “truth table,”  in respective works that both appeared in 1921.  The project is designed for a beginning course in undergraduate discrete mathematics.