Three Types and Traditions of Logic: Syllogistic, Calculus and Predicate Logic

Modern logic grew out of the work of Frege and of the tradition which Boole initiated. However, as the Quine-Putnam exchange illustrates, the relations between the respective camps are far from being well understood. We can get some clues from the way Frege critically discusses the Boole-Schroder tradition. Furthermore Michael Wolff has suggested that there is a close and internal relatedness of all three major types of logic, even declaring syllogistic logic to be the one and only "strictly formal" type of logic. A closer look at the Euler diagrams and their influence on the understanding of logic in the 19th century can highlight something of a silent revolution under way, preparing logicians to accept the non-exclusive alternative as basic, to accept tautologies as the paradigm of truth, and to introduce truth-functionality. The second half of this contribution offers an overview of the three traditions, in giving brief answers to the same series of questions. In addition, Wittgenstein's Tractatus is included in the questionnaire. All of this will may help to view the history of logic as the interaction of the three distinct, yet intrinsically related paradigms of Syllogistic, Calculus and Predicate logic.