Note 63 — Chapter IV · DE INTERPRETATIONE.

The diagram or parallelogram of logical antithesis, which is said to have begun with Apuleius, and to have been transmitted through Boethius and the Schoolmen to modern times (Ueberweg, System der Logik, sect. 72, p. 174) is as follows:—

A. Omnis homo est justus. --- E. Nullus homo est justus.

✕

I. Aliquis homo est justus. --- O. Aliquis homo non est justus.

But the parallelogram set out by Aristotle in the treatise De Interpretatione, or at least in the Analytica Priora, is different, and intended for a different purpose. He puts it thus:—

1. Omnis homo est justus … … … … 2. Non omnis homo est justus.

4. Non omnis homo est non justus … … … … 3. Omnis homo est non justus.

Here Proposition (1) is an affirmative, of which (2) is the direct and appropriate negative: also Proposition (3) is an affirmative (Aristotle so considers it), of which (4) is the direct and appropriate negative. The great aim of Aristotle is to mark out clearly what is the appropriate negative or Ἀπόφασις to each Κατάφασις (μία ἀπόφασις μιᾶς καταφάσεως, p. 17, b. 38), making up together the pair which he calls Ἀντίφασις, standing in Contradictory Opposition; and to distinguish this appropriate negative from another proposition which comprises the particle of negation, but which is really a new affirmative.

The true negatives of homo est justus — Omnis homo est justus are, Homo non est justus — Non omnis homo est justus. If you say, Homo est non justus — Omnis homo est non justus, these are not negative propositions, but new affirmatives (ἐκ μεταθέσεως in the language of Theophrastus).