How does the syllogism about Greeks, humans, and mortals demonstrate valid reasoning?

The syllogism "Every Greek is human. Every human is mortal. Therefore, every Greek is mortal" demonstrates valid reasoning by establishing a necessary logical connection between three terms through two universal affirmative premises.1

In this structure, "human" serves as the middle term, appearing in both premises but not in the conclusion. "Greek" is the minor term (the subject of the conclusion), and "mortal" is the major term (the predicate of the conclusion). Aristotle’s logic dictates that an argument is valid if its form ensures that true premises can never lead to a false conclusion. This specific pattern, known as Barbara, functions because the minor term is subsumed under the middle, which is in turn subsumed under the major term, necessitating that the minor term also falls under the major.123

Aristotle formalized this by using variables to represent the terms: "If A belongs to every B, and B belongs to every C, A belongs to every C". By abstracting the argument into this schematic form, he demonstrated that the validity of the inference depends on the logical structure rather than the specific content.13