Handbook of the History of Logic: - Fordham University Faculty

The Assimilation of Aristotelian and Arabic Logic up to the Later Thirteenth Century 299
impossible should follow, as Aristotle says in the Prior Analytics (32a18-20). If
one were to assume that every animal is rational then something impossible would
follow, since horse and ass would be rational. A consequence of this is hence that
an essential differentia is never present in the genus, but it is instead what is added
to the genus from outside. How this is supposed to be understood becomes clearer
in Averroes’ discussion of the next definition proposed by Porphyry. Let me quote
this passage in whole before I expand on it. He writes:
[Substantial] differentia has also been defined as that which is predicated
of a number of things differing in respect to species, by way of
stating which thing it is, not what it is. For when asked what man
is, we first reply by giving his genus, saying that he is animal, and
then when asked which animal he is, we reply that he is rational. The
definition of man is completed only through the whole of this. The
reason is that everything is composed either of matter and form, or
things analogous to matter and form. Genus is analogous to matter,
and differentia is analogous to form, and consequently the unity formed
by genus and differentia is the substance of the thing insofar as it is
in the mind, just as its matter and form are its substance insofar as it
exists outside the mind. 48
Differentiae are predicated of a number of things by way of stating which thing
it is and not what it is. So, the differentia does not tell us what the thing it is
predicated of is; it instead gives us the answer to the question: ‘What’s it like?’,
and the answer is: ‘It is rational!’ It thus gives you the essence of the thing. The
question: ‘What is it?’ refers back to the genus, and the answer to that question
is: ‘It is an animal!’ It is only when we combine the answers to these two question
that we get the definition of the thing, that is, rational animal. The reason this
is the case, he explains, is because everything is composed of matter and form.
In the definition of a species both matter and form are needed. The genus brings
the matter and the differentia brings the form and together you get the species.
This is the Aristotelian arithmetic of natural things, that is, ‘Genus + Differentia
= Species’ or Matter + Form = Substance’.
As can be noted at the end of the quote above, Averroes implies a distinction
between the concepts in the mind and the things in the world they signify. In the
mind, we form the definition ‘Human Being is a Rational Animal’ and in the extra
mental world we have particular humans, which are composites of matter and
form. The complex term ‘rational animal’ signifies together the composite, but
separately each part of the composite. The differentia hence signifies the rational
soul, which is the substantial form of the human being. The essence of a human
is, of course, its rational soul.
Averroes does not say much about differentia in his commentary on Aristotle’s
Categories, which, of course, is because Aristotle himself does not say a whole lot
48 Averroes, Middle Commentary on Porphyry’s Isagoge, 15-6.