A brief review of the main features of Stoic logic by Phillip de Lacy

 "The whole of ethics, then, is included in the rational use of appearances. What makes this use rational? The next four discourses, 5--8, answer this question by showing how the operations of logic are employed in ethics" (116).

"Before the examination of these discourses, however, it is necessary to review briefly the main features of Stoic Logic. The Stoics maintained that philosophy is based on absolute certainty. They recognized no theory of probability and they rejected skepticism in all of its forms. The Stoic wise man assents only to those propositions which are necessarily true. He never holds a mere opinion, as opposed to knowledge, for he never assents to anything false. Of course, complete infallibility is not within the reach of the ordinary man, but every soul naturally assents to the true, rejects the false and withholds judgment about the obscure. In order to avoid assenting to anything false, the Stoic uses certain criteria of certainty. There are two forms of knowledge, mediate and immediate. The latter of these is derived from appearances. The criteria of the truth of an appearance is _katalepsis_. An appearance is _kataleptike_ when it expresses accurately the underlying object it reveals, in such a way that the appearance would not be possible if that object did not exist. Mediate knowledge, or inference, is valid when there is a necessary connection between the premise and the inference to be made from it. All inference is of the form: "If _p_, then _q_," or equivalent hypothetical, disjunctive, and conjunctive forms; e.g., "Either not _p_ or _q_," "Not both _p_ and not _q_," "If not _p_, then not _q_." The hypothetical form of inference (_sunemmenon_), which is regarded as the fundamental form, is valid only when there is a necessary connection between the hypothesis, or sign, and the conclusion, or the thing signified. This necessary connection is called "consequence" (_akolouthia_). It is tested by contraposition (_anaskeue_), i.e., the inference: "If _p_, then _q_," is valid if it is true that, "If not _q_, then not _p_." The favorite Stoic example of inference is: "If it is day, it is light." We may prove the validity of this by contaposition: "If it is not light, it is not day." Or, as Diogenes states it, the hypothetical inference is valid if the opposite of the conclusion contradicts the hypothesis. For example, the proposition, "It is not light," contradicts the proposition., "It is day." Therefore, the hypothetical inference, "If it is day, it is light," is valid. The tests of both mediate and immediate knowledge are based on the principle of contradiction. A thing is true if its denial results in contradiction or impossibility. Hence all tested truth for the Stoics is necessary truth. A set of terms preserved by Diogenes emphasizes this fact. Dialectic, he says, is characterized as avoidance of rash assent (_aproptosia_), resistance to mere probability (_aneikaiotes_), irrefutability (_anelenxia_), correct reference of appearances to reason (_amataiotes_), and science (_epistime_) is sure (_asphales_) and unchangeable (_amataptotos_)" (116)."

The Logical Structure of the Ethics of Epictetus by Phillip de Lacy