Calculus Ratiocinator vs. Characteristica Universalis? The Two Traditions in Logic, Revisited

It is a commonplace that in the development of modern logic towards its actual shape at least two directions or traditions have to be distinguished. These traditions may be called, following the model of Ivor Grattan-Guinness (1988 ), the tradition of the algebra of logic and the tradition of mathematical logic. They are represented by the developments going back to the British algebraist George Boole with his The Mathematical Analysis of Logic (1847 ), and, independently, to the German mathematician Gottlob Frege with his Begriffsschrift (1879 ) Closely connected to this distinction is a comparative evaluation of the respective logical systems, culminating in the question who parented modern logic. Some interpreters, among them Boole’s biographer Desmond MacHale (1985, 71–72) or P. L. Heath (in Prior, ed., 1967, 542) have seen Boole as the father of modern logic. Others, like Robert Feys (1957 ) call his work the origin of modern logic. A few, like Bertrand Russell (1951, 74), even regarded him as the discoverer of pure mathematics (i. e., according to Russell’s logicism, mathematical logic). (Those who like Wolfgang Lenzen plead for exchanging Boole with Leibniz (1984, 203) will not concern us here.) Most influential, however, have been those who did not deny that the continuous debate about questions relevant for modern logic started with Boole in the middle of the 19th century, but who questioned the scientific value of the algebraic tradition for the actual shape of logic. Arthur Prior may be named