  In this paper we argue and present evidence for the use of the natural
deduction rules for universal and existential quantifiers in ancient
philosophy. More specifically, we present evidence for the use and
understanding of such rules for multiple quantification over non-necessarily
monadic predicates and nested quantifiers over non-necessarily monadic
predicates - all which amounts to the possession of mechanisms for dealing with
multiple generality. This work aims to complement the paper by Bobzien and
Shogry\cite{mult} which argues that Stoic logicians had already all the
elements necessary to deal with multiple generality. While we also draw some
evidence from Sextus Empiricus (a common source for Stoic logic) our focus is
not on the Stoics but on logical aspects of Aristotle, Euclid, Galen and
Proclus. Bobzien and Shogry argued for the ability of Stoic logic to express
multiple generality through regimentation and anaphora - universal
quantification is expressed by the tis + ekeinos construction on conditionals -
but say relatively little about deduction rules. Our focus is on the quantifier
rules themselves, specifically from the point of view of natural deduction with
some incursions into dependent-type theory. This paper shares with Bobzien and
Shogry the general aim of arguing for a 'somehwhat more gradual development' of
the the logic of multiple generality from Aristotle to Frege.
