Conditional is a Logical connective used to form expressions (formulas) of the language.
Logical implication is a relation holding between set of formulas and a formula.
Thus, they are two different concepts.
But they are strongly related: in propositional logic, for example, we have that:
the formula A → B is a tautology iff B is a logical consequence of A ...
"Will these observations lead you to question the validity of Aristotle's syllogism?"
I don't see how. And, like others commenting here, I am surprised that you are considering such a possibility -- but let me explain what I mean.
When confronted with something that defies our expectations, our understanding of the way things are, we, humans, ...