Arianna Castelli

Was the greatest grammarian of antiquity truly a second-rate Stoic philosopher in disguise? For decades, scholars have seemed to believe so. This book shatters that consensus. By analyzing Apollonius Dyscolus’ core concepts—from proper names to conditionals—this book reveals a thinker far more eclectic and original than previously believed. Apollonius synthesized Stoic, Aristotelian, and Alexandrian ideas to create a unique grammatical project, allowing us to appreciate ancient Greek grammar as a sophisticated semantic theory in its own right—one that pragmatically deploys the philosophical lingua franca of the post-Hellenistic period to solve practical problems of language. This book is an essential reading for anyone seeking to understand how Western linguistic theory truly began.

In addition to Chrysippean syllogistic analysis, the ancient sources attest to and provide examples of an unorthodox analysis conducted with a different logical principle, namely the Synthetic Principle (SP), from the canonical themata. This alternative analysis is structurally distinct from the standard one: (i) it uses indemonstrables as inference rules rather than as zero-ary rules/axioms; (ii) it is based on assumptions rather than axioms; (iii) the directionality of the proof goes from the leaves (initial sequents) to the root (sequent to be proven). A formalization of SP is here presented, and its deductive equivalence with the three themata of standard Chrysippean analysis demonstrated. Additionally, by comparing it with Gentzen’s Cut Rule and Mix Rule, it is shown that SP is, in fact, a stronger principle (at least within the Stoic system). Finally, as for the origin of this principle, it is conjectured for it to be Peripatetic, subsequent to Aristotle, based on the lexicon and the similarities between its two formulations (Sextus Empiricus and Alexander of Aphrodisias). Moreover, a debated passage from Galen suggests that the subsequent introduction of SP into Stoic logic, and thus the invention of a method of syllogistic reduction different from that of Chrysippus, is due to Antipater of Tarsus.