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 - were 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) and includes as a particular case Quine's reformulation of predicate logic in \cite{quine}. 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 propose, in light of the above considerations, a formal reconstruction of the Stoic logic of multiple generality based on a variant of NTL.