Séminaire Philmath

What is formal in Aristotle’s syllogistic?
Zoé McConaughey  and Ana María Mora-Márquez 

In the fourth century BCE, Aristotle invented “syllogistic”, a logic he developed in his Prior Analytics, especially in the first seven chapters of the first book. With his syllogistic, Aristotle is often credited as the father of Western formal logic. Two issues immediately arise: first, since logicians have recently pointed out various senses of “formal” in modern logic, which of these meanings, if any, do we recognize in Aristotle’s syllogistic when we call him the founder of modern formal logic? Second, would Aristotle himself have shared such a conception of formality? The first issue requires that we explicit the concepts used in modern
formal logic, and how they are used to describe segments of the history of logic – here, Aristotle’s logic – from a “modern point of view”. The second issue takes as its object this “modern point of view” for describing or studying an ancient logic and looks at its historical groundings: do the modern concepts describe what Aristotle did (or tried to do), or do they rather cover (or distort) his project? These two issues are linked; together, they question the relation modern logic has with the history of logic – whether it is only a backwards understanding of the history of logic from a modern perspective or a back-and-forth understanding in which studying the history of logic enriches the modern conception of logic.
Our paper deals with these two issues regarding formality in Aristotle’s syllogistic, and argues that a historically sensitive approach to Aristotle’s logical project sheds light on our modern concept of formality. Such an approach thus enriches modern logic by better understanding its history. The first issue – in which of the senses of “formal” is Aristotle’s logic considered formal? – stems from two recent attempts at providing a taxonomy of the various senses “formal” is used in modern logic: MacFarlane (2000) and Dutilh Novaes (2011). The second issue builds on the first: provided that we have identified one or more
senses of formal (first issue), would Aristotle himself (second issue) have shared such a conception of formality, and would he have considered his own syllogistic as a “formal” enterprise in that very same sense or senses? Uncritically introducing modern logical concepts can mask distinctions Aristotle did make. This kind of doubt is further nourished by approaches to Aristotle’s logic that adopt a unitary conception of modern logic. The presupposition of “a single discipline of formal logic” is at the core of attempts to study
ancient logics “from a modern point of view”: if there is a single discipline that goes from Aristotle to us, then we can use our conception of logic to understand Aristotle’s conception of logic. The problem is that modern formal logic has now developed in such a variety of ways that it is difficult to speak, today, of “a single discipline of formal logic”. The presupposition at the core of studies of Aristotle’s syllogistic “from a modern point of view” tends to take a certain conception of logic for granted, and uncritically applies this conception to Aristotle. Pointing out the plurality of logics and logical frameworks that have been developed in the past century is thus a way to stress the need to ask what Aristotle
himself was trying to do when developing his syllogistic in the fourth century BCE. Our main contention in this paper is that Aristotle’s logic should not be understood only “from a modern point of view”; it should be approached from Aristotle’s aims in developing his own project, aims which can be gathered from a close study of his texts in their context. From such an approach, we will argue for a pragmatic understanding of syllogistic. This paper explores the
above two problems regarding what is formal in Aristotle’s logic and their connection: what we now recognize as formal (first issue), what Aristotle would have accepted as a characterization of his syllogistic enterprise (second issue), and how these two can be reconciled. First, the two recent taxonomies regarding the various senses of “formal” are presented. Then we ask whether these senses apply to Aristotle’s syllogistic, and whether other senses have been proposed while describing Aristotle’s enterprise. Finally, we propose
a different approach to the problem: it is not just the result that should be examined with our modern logical concepts, but the goal Aristotle himself had, the intention behind his logical enterprise. This approach will give us a key for understanding Aristotle’s logic on the one hand, and the notion of formality embedded in his logic on the other.