Handbook of the History of Logic: - Fordham University Faculty

Relational Logic of Juan Caramuel 661
We see that our specimen of a pure relational syllogism is of mood 1 (called
Parat astra famam by Caramuel).
Our second specimen syllogism
Every man commits some sin
Every sin is a moral fault
Therefore, every man commits some moral fault
is of the mixed type, as already known. The four figures could be distinguished
also for the mixed relational syllogism. 39 Our example is of the most common
Platonic figure:
A is related to M
MisB
A is related to B
As we can see, the mood is ai.a.ai, and it is one of the valid moods Caramuel states
for this figure. (Caramuel gives names to the moods; the one at issue is dubbed
Altis ab astris):
aa.a.ai. ein.a.ai.
aa.a.ii. 25. ein.a.ein.
ae.a.ain. ein.a.ii.
ae.a.ea. ia.a.ii.
5. ae.a.iin. ian.a.iin.
ae.a.ina. ian.a.ina.
ai.a.ai. 30. ina.a.iin.
ai.a.ein. ie.a.iin.
ai.a.ii. ie.a.ina.
10. ai.a.iin. ine.a.ine.
ain.a.ain. ine.a.ii.
ain.a.ea. 35. ien.a.ii.
ain.a.ina. ii.a.ii.
ea.a.ain. iin.a.iin.
15. ea.a.ea. ina.a.iin.
ea.a.iin. ina.a.ina.
ea.a.ini. 40. ine.a.ii.
ee.a.ai. ine.a.ine.
ee.a.ee. ini.a.iin.
20. ee.a.ein. ini.a.ina.
ei.a.ain.
ei.a.ea.
ei.a.iin.
39Caramuel treats the mixed relational syllogism in LO, Pars II, disp. XI De Syllogismo
Obliquo Mixto, pp. 442-457.