v] .
PROP. [II] Two substances whose attributes are different have
nothing in common.
Proof.- (2:1) Also evident from [D.iii] . For each must exist in itself, and
be conceived through itself; in other words, the conception of one does not
imply the conception of the other.
PROP. [III] Things which have nothing in common cannot be
one the cause of the other.
Proof.- (3:1) If they have nothing in common, it follows that one cannot
be apprehended by means of the other ([A.v] ), and, therefore, one cannot be
the cause of the other ([A.iv] ). Q.E.D.
PROP. [IV] Two or more distinct things are distinguished one
from the other either by the difference of the
attributes of the substances, or by the difference
of their modifications.
Proof.- (4:1) Everything which exists, exists either in itself or in
something else ([A.i] ), that is (by [D.iii] and [D.v] ), nothing is granted
in addition to the understanding, except substance and its modifications.
(2) Nothing is, therefore, given besides the understanding, by which several
things may be distinguished one from the other, except the substances, or,
in other words (see [A.iv] ), their attributes and modifications. Q.E.D.
PROP. [V] There cannot exist in the universe two or more
substances having the same nature or attribute.
Pages:
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25