As regards logic in a stricter sense, Aristotle   was the founder, and his proudest claim was to have invented the syllogism. But the Stoics challenged his claim and supplied a version of syllogism much closer to modern logic. Each side maintained that the other could not accommodate important examples of argumentation. These debates are reflected in Alexander. We see developments in modal logic, also invented by Aristotle, and Neo-platonist contributions on the problem of induction and the nature of mathematics. Also significant is the treatment of language and the appeal to the efficacy of divine names in religious ritual to represent some names, contrary to Aristotle, as natural rather than conventional. It was here that Ammonius   reverted to Porphyry  ’s view of names as conventional. [SorabjiPC3  :27]

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The Aristotelians, following Aristotle Top. 163b9-11, called logic an instrument (organon) and ascribed to the Stoics the view that it was a part. This relates inter alia to the debate, in which the Aristotelians complained that Stoic syllogisms failed to serve as a useful instrument (organon) for showing things. Their syllogisms were inference patterns studied for their own sake, however uninformative.

But, as Katerina Ierodiakonou has insisted, there are other arguments too deployed in the debate. The Stoics are said to argue that logic is a product (ergon) of philosophy and so either a part, or a sub-part of it. But it is not a sub-part, because its subject matter (propositions) and its purpose (here more narrowly described than the Stoics would have liked, as showing how things may be deduced) [32] is different from that of other parts. The Aristotelians reply that logic is analogous to hammer and anvil, which, though products of the smith’s art, are not parts, but instruments, of that art. Logic is also an instrument of other disciplines, to which it could not be so subordinated if it were an actual part of philosophy. Olympiodorus   adds on the Aristotelian side the argument that logic is not part of philosophy, because its subject matter (utterances) and its purpose (generating demonstrations) is different from that of philosophy taken as a whole.

Ammonius as a Platonist takes a third view to be more appropriate. Logic can be merely an instrument and in Aristotle’s hands it is, when he offers his rules of syllogism in terms of As, Bs and Cs. But Plato had often used arguments involving concrete examples, and so in his hands logic is often a part of philosophy.

Plotinus   1.3 [20] 4-5 (not translated) took a different view again and contrasted Aristotelian logic as an instrument with Platonic dialectic as a part, and the best part, of Philosophy. [SorabjiPC3:32-33]

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LÉXICO: lógica e afins