The Diagonal Lemma Fails in Aristotelian Logic

Gödel's theorem does not need an introduction. But it is generally not acknowledged that all instances of Gödel's sentence are vacuous (see below). On the contrary Aristotelian logic permits only sentences that are not vacuous. The consequences of these observations are surprising. What does the article title mean? First of all by " Aristotelian logic " we will understand the logic of the traditional syllogism. By " classical logic " we will mean modern symbolic logic. It is well known that the laws of Aristotelian logic are valid only if all the terms refer to non-empty sets.