I've been reading an old logic text (Deductive Logic. George Stock. 1888) and he describes something very like Aristotle's notion of a definition, but in his description, it is clearly a matter of intensions, of concepts alone. His notion of a definition is entirely analytical; you analyze the content of a concept, and come up with no new knowledge of the thing being defined, only a clearer understanding of your own judgment. This contrasts with my understanding of Aristotle's notion of definitions in which the point of a definition is to understand the form of a thing in order to reveal, new, non-analytical knowledge of the thing.
So I have two questions.
Is my understanding of Aristotle wrong, or is this account of definition different from Aristotle's?
I associate Aristotle's definitions with essentialism, which I understand as being an ontological position about things. Is my understanding of essentialism wrong? Is it really just a case (as the book I'm reading seems to imply) that an essential property is simply one that is analyzed from the concept of the thing? Is it purely a matter of intensions and not extensions?