Paolo Crivelli

Aristotle created logic and developed it to a level of great sophistication. There was nothing there before; and it took more than two millennia for something better to come around. The astonishment experienced by readers of the Prior Analytics, the most important of Aristotle's works that present the discipline, is comparable to that of an explorer discovering a cathedral in a desert. This article explains and evaluates some of Aristotle's views about propositions and syllogisms. The most important omission is the difficult subject of syllogisms involving modalities. Aristotle distinguishes two relations of opposition that can obtain between propositions with the same subject- and predicate-expressions: contrariety and contradiction. In every canonical syllogism, one term is common to the two premises: it is called “middle term,” or simply “middle.” The remaining two terms of the premises are the only ones occurring in the conclusion: they are called “extreme terms,” or simply “extremes.”

It has often been claimed that Aristotle’s expression ‘protasis’ means ‘premiss’ in syllogistic contexts and cannot refer to the conclusion of a syllogism in the Prior Analytics. In this essay we produce and defend a counter-example to these two claims. We argue that the basic meaning of the expression is ‘proposition’ and while it is often used to refer to the premisses of a syllogism, in Prior Analytics 1.29, 45b4-8 it is used to refer to the conclusion of a syllogism. In our view, the best explanation of Aristotle’s use of the expression ‘protasis’ is that it means proposition throughout but is frequently used without change of meaning to refer to the premisses from which a conclusion follows. In Prior Analytics 1.29, 45b4-8 he uses ‘protasis’ to refer to the conclusion when he needs a single expression to refer to both the conclusion and one of the premisses of the syllogism that constitutes the core of a syllogism through the impossible. If we are correct, we have shown that the view that the expression ‘the final protasis’ in EN 7.3, 1147b9ff must mean ‘the final premiss’ and so cannot refer to the conclusion of the relevant syllogism is mistaken.