5
We must not fail to observe that we often fall into error because
our conclusion is not in fact primary and commensurately universal
in the sense in which we think we prove it so. We make this mistake
(1) when the subject is an individual or individuals above which there
is no universal to be found: (2) when the subjects belong to different
species and there is a higher universal, but it has no name: (3)
when the subject which the demonstrator takes as a whole is really
only a part of a larger whole; for then the demonstration will be true
of the individual instances within the part and will hold in every
instance of it, yet the demonstration will not be true of this subject
primarily and commensurately and universally. When a demonstration
is true of a subject primarily and commensurately and universally,
that is to be taken to mean that it is true of a given subject
primarily and as such. Case (3) may be thus exemplified. If a proof
were given that perpendiculars to the same line are parallel, it might
be supposed that lines thus perpendicular were the proper subject of
the demonstration because being parallel is true of every instance
of them.
Pages:
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30