Stoic Logic and Natural Term Logic

Abstract

In this paper we propose a reconstruction of the theory of multiple generality in Stoic Logic using the Natural Term Logic (NTL) developped by the author in \cite{ntl}. Contrary to a frequent misconception, it can be shown conclusively, based on the available evidence, that Stoic logic was far more than a mere propositional logic (we further argue that even identifying the Stoic conditional with any type of propositional connective is misleading). Its more general and complex logical theory - and notable the treatment of multiple generality - was rather patterned after the logico-syntactic mechanisms of natural language (subject to a regimentation which recalls Polish notation) rather than the variable-based quantifier logic of the modern Fregean tradition. NTL is likewise is a variable-free formal framework which captures the core syntactic and logic mechanisms of natural language (and notably a large array of features involving intensionality and anaphoric constructions). Bobzien and Shogry \cite{bobzienshogry} have presented abundant evidence and arguments for the case that quantified conditionals and multiple generality were treated by the Stoics through a disambiguifying regimentation of syntax using indefinite pronouns and anaphoric constructions involving such pronouns. There are however some patent difficulties involving how exactly the equivalent of universal quantification was treated. In this paper we explore some possible building blocks for a formal reconstruction of the Stoic logic of multiple generality based on a variant of NTL. We focus on formalizing the more general form of Stoic modus ponens involving quantified conditions which was clearly attested by ancient authors. We also sketch, as a preliminary study for formalizing the grammatical theory deployed in Stoic logic, how NTL can be used to formalize adjectival and adverbial constructions.