Difference is possible in two ways
“Two or more distinct things are distinguished from one another either by the
difference of the attributes of the substances or by the difference of the
affections of substance” (1P4). That is, there are two types of difference:
formal and modal difference. I’m
just going to address formal difference.
Substances with different attributes are distinct formally, because they possess separate, independent essences. An
attribute is what “the intellect perceives of substance as constituting its
essence”(1D4). But really, we are saying substance insofar as it is expressed
by this attribute. One might wonder why Spinoza distinguishes between substance
and attribute at all, since it will turn out that each attribute must be able
to be conceived by itself, which is part of the definition of substance.
The answer is that if he cannot
distinguish substance from attributes, then there are an infinite number of
attributes, possibly, but we have no explanation for that nor for the
possibility of God’s existence. In addition to a concept of difference, Spinoza
needs one that explains unity.
Otherwise, there will be no reason to believe that there is any relation
between different attributes, and, eventually, the world would be separated
into an infinite number of possible worlds, each of which possessing an
absolutely unique essence. In other words, in order for Spinoza to think unity
in “Nature” whatsoever, he has to posit a distinction between substance and attributes,
by which attributes are distinct, but this does not mean that substances are
different.
In some ways, Spinoza’s proof for
the existence of God amounts to an argument that there is no reason to
distinguish substances from one another, since they are distinct only in
attribute, they could be the same
single substance. 1P5, P6 and P10 speak of the irreducibility of the attributes
(or substance conceived by the different attributes). P7, P8 and P9 are all
premises towards P11, establishing the necessary existence, infinity and
“reality or being”. P9 is
especially important, because only on these grounds are we lead to conceive a
reason for a substance containing more than one attribute. But the proofs of
P11 seem to depend primarily on the necessary existence of God. The first is simply the ontological
proof, that existence necessarily belongs to, or “is involved in”, his essence.
The second claims that the absolutely infinite being is not a contradictory
notion, or there is no reason contrary to such a being. The third proof is a posteriori, following the supposition
that if anything exists, an omnipotent being exists. But P11 is then supplemented
by P12, P13 and P14, which go towards establishing not merely that a single
substance is a non-contradictory idea, but also that God must be an eminently
simple being.
