It follows then that God is not in a genus. Thirdly, because all in
one genus agree in the quiddity or essence of the genus which is
predicated of them as an essential, but they differ in their
existence. For the existence of man and of horse is not the same; as
also of this man and that man: thus in every member of a genus,
existence and quiddity--i.e. essence--must differ. But in God they
do not differ, as shown in the preceding article. Therefore it is
plain that God is not in a genus as if He were a species. From this it
is also plain that He has no genus nor difference, nor can there be
any definition of Him; nor, save through His effects, a demonstration
of Him: for a definition is from genus and difference; and the mean of
a demonstration is a definition. That God is not in a genus, as
reducible to it as its principle, is clear from this, that a principle
reducible to any genus does not extend beyond that genus; as, a point
is the principle of continuous quantity alone; and unity, of
discontinuous quantity. But God is the principle of all being.
Therefore He is not contained in any genus as its principle.

Reply Obj. 1: The word substance signifies not only what
exists of itself--for existence cannot of itself be a genus, as shown
in the body of the article; but, it also signifies an essence that has
the property of existing in this way--namely, of existing of itself;
this existence, however, is not its essence. Thus it is clear that God
is not in the genus of substance.

Reply Obj. 2: This objection turns upon proportionate measure
which must be homogeneous with what is measured. Now, God is not a
measure proportionate to anything. Still, He is called the measure of
all things, in the sense that everything has being only according as
it resembles Him.