Prior Analytics, Book I (review)

The interpretation of Aristotle's syllogistic is a bellwether of the logical concerns of the interpreter's time. Aristotle's syllogistic is, in part, a two-tiered classification of syllogisms. Aristotle takes just a few syllogistic forms to be perfect or obviously acceptable and establishes the acceptability of the other imperfect syllogistic forms through a process of perfection—most often, by conversion of the premises of the imperfect syllogism into the premise-set of a perfect syllogism.

The representation of the syllogistic as a modern logical system has, over the last fifty years, taken one of at least two approaches. Lukasiewicz in the 1950s interpreted the syllogistic as an axiomatic theory: the perfect syllogisms are axioms; the imperfect syllogisms are theorems, implications derived from the axioms by means of an underlying system of inferential reasoning; perfection establishes the truth of the imperfect syllogisms. By contrast, Corcoran and Smiley in the early 1970s independently represented the syllogistic as a Fitch-style natural deduction system: the perfect syllogisms and conversion rules are intuitively valid inference rules; the imperfect syllogisms are deductions with more than two premises providing step-wise derivation of a conclusion; perfection establishes the validity of an imperfect argument form. In my view, the syllogistic is a hybrid: as is now well recognized, syllogisms are arguments; but perfection is carried out by non-syllogistic reasoning; as such, neither an axiomatic theory nor a Fitch-style natural deduction logic is an entirely satisfactory representation of the syllogistic. Indeed, although the syllogistic is systematic insofar as it attempts an exhaustive classification of arguments satisfying certain restrictions, it is not a system. Aristotle uses a variety of methods for establishing validity and invalidity, without a concern for proving the consistency of these methods. Some, but not all, perfection techniques resemble a sequent calculus, but I doubt that any representation of the whole syllogistic as a modern system will be entirely satisfactory.

A virtue of Gisela Striker's excellent translation of, and commentary on, the Prior Analytics Book I is its neutrality on these interpretative controversies. Such neutrality comes at a cost. To give a single illustration, Striker translates syllogismos not with 'deduction', as in Smith's 1989 Hackett translation, but with the transliteration 'syllogism'. This translation has the advantage of not favoring any one interpretation or logical representation, but the disadvantage of lending some of Aristotle's claims the appearance of triviality. So, for example, when Aristotle claims that all syllogismoi proceed through one of the syllogistic forms, the claim in Striker's translation appears to be a vacuous truth and not the substantive claim that any suitably constrained argument can be reformulated as a string of one or more of the syllogistic forms. Striker discusses this and similar decisions in the commentary. As such, the translation is most useful in connection with the commentary. For this reason, and also since Striker's translation is inconsistent with Barnes's use of 'deduction' in his translation of the Posterior Analytics and Smith's use of 'deduction' in his translation of Topics Book I, both also in the Clarendon Series, it is unlikely that the translation will supplant Smith's translation of the Prior Analytics.

There are other virtues and concomitant costs. First, the abstraction of Book I from the rest of the Analytics provides a complete and self-contained study of the syllogistic, but arguably fails to locate the syllogistic in its broader context. The Prior Analytics includes a formal study of the syllogistic, but is largely concerned with heuristics, the choice of appropriate premises for desired conclusions, and analytics, the reformulation of given arguments into syllogistic form. And second, in eschewing formalization, the commentary is accessible to the logical novice, but, as a result, the commentary is not the last word on the technical issues.

Striker's commentary ought to be the first port of call for the student, philosopher, or historian of logic interested in broaching the interpretative issues of the syllogistic. The commentary...