The Development of Modus Ponens in Antiquity: From Aristotle to the 2nd Century AD Author(s):

'Aristotelian logic', as it was taught from late antiquity until the 20th century, commonly included a short presentation of the argument forms modus (ponendo) ponens, modus (tollendo) tollens, modus ponendo tollens, and modus tollendo ponens. In late antiquity, arguments of these forms were generally classified as 'hypothetical syllogisms'. However, Aristotle did not discuss such arguments, nor did he call any arguments 'hypothetical syllogisms'. The Stoic indemonstrables resemble the modus ponensltollens arguments. But the Stoics never called them 'hypothetical syllogisms'; nor did they describe them as ponendo ponens, etc. The tradition of the four argument forms and the classification of the arguments as hypothetical syllogisms hence need some explaining. In this paper, I offer some explanations by tracing the development of certain elements of Aristotle's logic via the early Peripatetics to the logic of later antiquity. I consider the questions: How did the four argument forms arise? Why were there four of them? Why were arguments of these forms called 'hypothetical syllogisms'? On what grounds were they considered valid? I argue that such arguments were neither part of Aristotle's dialectic, nor simply the result of an adoption of elements of Stoic logic, but the outcome of a long, gradual development that begins with Aristotle's logic as preserved in his Topics and Prior Analytics; and that, as a result, we have a Peripatetic logic of hypothetical inferences which is a far cry both from Stoic logic and from classical propositional logic, but which sports a number of interesting characteristics, some of which bear a cunning resemblance to some 20th century theories. 'Aristotelian logic', as it was taught from late antiquity onwards and as it can be found in logic compendia up until the 20th century,2 commonly Accepted January 2002 'The basic idea of this paper was presented as one half of my lecture 'Ipotesi e argomento ipotetico nella logica stoica e peripatetica' given as part of the Erasmus scheme in Padua, April 1994. After a period in a drawer it was recycled into a paper of its own, versions of which in German and English have been presented at Beme (1998), Oxford (1998), and Yale (1999). 1 am grateful to my audiences for their constructive criticism, in particular to Mario Mignucci, Helmut Linneweber Lammerskitten, and Tobias Reinhardt, and wish to thank the British Academy for its support. 2 E.g. J.N. Keynes, Studies and Exercises in Formal Logic, London 1924 (4th ed.), 3524, 360-2. ? Koninklijke Brill NV, Leiden, 2002 Phronesis XLVIl14 Also available online www.brill.nl