On the Difference between the Two Barbaras

[full article, abstract in English; only abstract in Lithuanian] The paper deals with the problem of the “two Barbaras” in the Aristotelian modal syllogistic. The problem consists in Aristotle’s differing views on two at a first sight similar in nature syllogisms of mixed assertoric (X) and necessary (L) premises: Barbara LXL and Barbara XLL. The fact that Aristotle believed the first syllogism to be valid and the second one – not, has been received either 1) negatively, because both Barbaras have been held to be invalid, or 2) negatively, because both Barbaras have been held to be valid, or 3) positively, by giving a reason why the two Barbaras differ. We commit ourselves to the position (3) by proving that modal propositions for Aristotle have their modalities de dicto and that Aristotelian modal operators act according to their own separate rules where only the type of the modality of a major premise is relevant for the modal status of the conclusion.

6. Logic

‘Logic’ explains that logic has a broad and a narrow sense in Stoic theory and deals with a subset of sayables and meanings. Their logic is close to what we would call propositional logic. Chrysippus was the pioneer and genius of Stoic logic. He seems to have held that in simple assertoric logic all valid inference forms could be reduced to combinations of five basic and indemonstrable argument forms, with the assistance of several other logical and metalogical principles. The Stoics also worked extensively on modal syllogistic and other areas of research in logic with a sophistication not paralleled in some cases until the 20th century.

Kātibī (d. 1277), Taḥtānī (d. 1365), and the

The Epistle for Shams al-Din on the Rules of Logic is a much-studied textbook written by Najm al-Din al-Kātibī (d. 1277). It is a compact and difficult treatment of logic that concentrates above all on modal syllogistic, though it touches on all the major topics covered in the Arabic logical tradition. It reflects the results of the further development of Avicenna’s project of modifying Aristotelian logic, a project that attracted enormous attention through the thirteenth century. The Shamsiyya, as the epistle is commonly referred to, was initially received with some hostility, but came to be accorded a central place in the madrasa curriculum in the fourteenth century, in large part because of the commentary on it written by Qutb al-Din al-Razi (d. 1365).