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.