[To continue: I have been discussing whether Bayes’ 1763 essay was devised as a challenge to the work of David Hume and I have been tracing the history of induction as a method of acquiring scientific knowledge. Induction begins with Aristotle (and Socrates) and is introduced in Aristotle’s Posterior Analytics.]
Aristotle’s essays on logic (or Organon) consists of six books: Categories, On Interpretation, Prior Analytics, Posterior Analytics, Topics, and On Sophistical Refutations. Although I am primarily interested in his Posterior Analytics due to its focus on induction, Aristotle’s Prior and Posterior Analytics are often considered together. The importance of Aristotle’s Prior Analytics lies in its system of logic — a system that influenced Western thought for millennia. Because no formal logic preexisted Aristotle (at least, to the best of Aristotle’s knowledge), Aristotle was faced with the task of building this system from its first principles.
The Prior Analytics contains 73 chapters in total. However, the basic structure of Aristotle’s logic rests largely in his introductory chapters. Aristotle’s logic focused on how to determine whether a conclusion could be deemed true (or, more specifically, valid) given a set of specific premises. In his Prior Analytics, Aristotle was less concerned with how one arrives at these initial premises (or what exactly can be said to be initially true or self-evident and what that thing is) but more on how to logically deduce a valid conclusion from this starting point.
The centerpiece of Aristotle’s Prior Analytics is the syllogism. In terms of entomology, syllogism stems from syllogismos (inference, conclusion, or calculation). Translation of Aristotle’s work has traditionally reserved the word syllogism to identify the specific form of Aristotle’s logic. Modern translation, however, has chosen a more literal interpretation of syllogism to mean, simply, deduction. For example, below are two translations of the first chapter of Prior Analytics. The first is from Owen (1853) and the second from Smith (1989) [italics added]:
- We must first state the subject of our inquiry and the faculty to which it belongs: its subject is demonstration and the faculty that carries it out demonstrative science. We must next define a premiss, a term, and a syllogism, and the nature of a perfect and of an imperfect syllogism; and after that, the inclusion or noninclusion of one term in another as in a whole, and what we mean by predicating one term of all, or none, of another.
- We must first state what our inquiry is about and what its object is, saying that it is about demonstration and that its object is demonstrative science. Next, we must determine what a premise is, what a term is, and what a deduction is, and what sort of deduction is complete and what sort is incomplete; and after these things, what it is for something to be or not be in something as a whole, and what we mean by ‘to be predicated of every’ or ‘predicated by none.’
By the 20th century, Aristotle’s system of logic had been largely superseded by the analytic approach of Frege, Russell, and Wittgenstein. However, a renewed interest in Aristotle’s Analytics was prompted by Lukasiewicz in the 1950s. (If you have ever used a calculator, you are paying silent homage to Lukasiewicz and a variation of his system of mathematical notation.) Following Lukasiewicz, a coordinated body of work on Aristotle’s Prior Analytics was conducted at the Department of Philosophy at the University of Buffalo. That work has now spanned over 40 years. The purpose of the Buffalo group was to reclaim and rejuvenate Aristotle’s Prior Analytics and its system of syllogistic logic. Smith’s translation, that was quoted above, is part of that work.
Despite over two millennia of study, Aristotle’s work on syllogisms remains a source of study and discovery.
In the next post of this series, I will begin a walk-through the basic structure of a syllogistic argument. (I think I might actually work my way through the whole Analytics – there seems to be an absence of that on the internet.)
- Corcoran, J. (2009). Aristotle’s logic at the University of Buffalo’s Department of Philosophy. Ideas y Valores, 140, 99-117.