DIAGRAM 1
R. Ishmael’s Rule No. 1, concerning a-fortiori argument, can be represented by a triangular star, at the center of which is the middle item (R) through which the three other items, P, Q, and S are related to each other.
Diagram 1a
The a-fortiori argument may also be represented, with reference to the comparative propositions that underlie it, as ordering items P, Q, and S, according to their position in a common continuum R:
Diagram 1b
This diagram is based on the following syllogisms:
Figure 1 | Figure 2 | Figure 3 | Figure 4 |
Rp > Rq | Rp > Rq | Rp > Rq | Rp > Rq |
Rq > Rs | Rp < Rs | Rs > Rp | Rs < Rq |
So, Rp > Rs | So, Rq < Rs | So, Rs > Rq | So, Rs < Rp |
Note that the four figures of a-fortiori should not be confused with the four of syllogism they imply, which are, in the order shown: the fourth, third, first and second figures.