The Deductive Stystem of Stoic Logic

The Stoics believed that valid arguments are reduced to “undemonstrated’s’’ through “thema’s”. This interpretation, implied by ancient authors, considers Stoic logic as an axiomatic system with argumental rules. On the basis of this view on Stoic logic, undemonstrated’s are used as axioms and Themas as transmission rules. Yet, SextusEmpiricus in his book, Against the Logicians, introduced two examples of Stoic reduction of valid arguments to undemonstrated’s in which he used undemonstrated’s as sentential rules. In this approach, undemonstrated’s are used as inference rules and Themas don’t play any different reasonable role than undemonstrated’ss; on the other words, undemonstrated’s and Themas are used as inference rules. Mates and Bochenski didn’t attention to this conflict and analyzed these two examples like Empiricus. This paper brings up this conflict and suggests two solutions for it. Based on first solution, Stoic logic has two various surfaces and in each surface, it includes one of argumental or sentential rules; Therefore argumental rules and sentential rules can be used simultaneously. In second solution, based on the historical development of Stoic logic, two mentioned interpretations are attributed to Stoics in different historical periods.