the flow of logic
The goal of logic is to draw conclusions from two true arguments through their implications. However, Aristotle is generally considered a bottom-up philosopher, rejecting grandiose arguments about the Forms. This might seem paradoxical: Aristotle understands knowledge in a pattern that is bottom-up, building on arguments, but the actual logic is implicature.
Aristotle's argument about truth and contradiction
In section Γ, Aristotle argues about proper arguments either being true or false--not both. This is an argument against contradictory truths, however if Aristotle were incorrect about this argument, then the argument could potentially be both true and false. This would be a paradoxical irony, and would also undermine the whole of his philosophical corpus. The claim is more ironic because it is for all intents and purposes unverifiable. Many post-modern philosophies depend on this irony: that Aristotle's view of truth/falsity is itself not provable as true (unless you find Aristotle's argument convincing, in which case it might be considered true in a subjective sense, which adds to the irony).
Because these concepts are so integral and complex, it's easy to see why philosophy has been looked upon as a frustrating and absurd endeavor. But Aristotle is by every account one of the very best.
