(1) We may assume the superiority ceteris paribus of the
demonstration which derives from fewer postulates or hypotheses-in
short from fewer premisses; for, given that all these are equally well
known, where they are fewer knowledge will be more speedily
acquired, and that is a desideratum. The argument implied in our
contention that demonstration from fewer assumptions is superior may
be set out in universal form as follows. Assuming that in both cases
alike the middle terms are known, and that middles which are prior are
better known than such as are posterior, we may suppose two
demonstrations of the inherence of A in E, the one proving it
through the middles B, C and D, the other through F and G. Then A-D is
known to the same degree as A-E (in the second proof), but A-D is
better known than and prior to A-E (in the first proof); since A-E
is proved through A-D, and the ground is more certain than the
conclusion.
Hence demonstration by fewer premisses is ceteris paribus
superior. Now both affirmative and negative demonstration operate
through three terms and two premisses, but whereas the former
assumes only that something is, the latter assumes both that something
is and that something else is not, and thus operating through more
kinds of premiss is inferior.
Pages:
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94