The Subject of Logic: “Syllogisms”
All Aristotle’s logic revolves around one notion: the deduction (sullogismos).
A thorough explanation of what a deduction is, and what they are composed of, will necessarily lead us through the whole of his theory.
What, then, is a deduction? Aristotle says:
A deduction is speech (logos) in which, certain things having been supposed, something different from those supposed results of necessity because of their being so. (Prior Analytics I.2, 24b18-20)
Each of the “things supposed” is a premise (protasis) of the argument, and what “results of necessity” is the conclusion (sumperasma).
The core of this definition is the notion of “resulting of necessity” (ex anankês sumbainein).
This corresponds to a modern notion of logical consequence:
X results of necessity from Y and Z if it would be impossible for X to be false when Y and Z are true.
We could therefore take this to be a general definition of “valid argument”.