Handbook of the History of Logic: - Fordham University Faculty

660 Petr Dvoˇrák
In dealing with relational syllogisms, Caramuel distinguishes the following figures
of the pure relational syllogism: 38
A is related to M Platonic figure
M is related to B
A is related to B
M is related to A Figure I
B is related to M
B is related to A
A is related to M Figure II
B is related to M
B is related to A/ A is related to B (indirect)
M is related to A Figure III
M is related to B
B is related to A/ A is related to B (indirect)
The letters A, B, M stand for terms, where M is the middle term and A, B are
the extremes. All the terms are quantified and the quantification is given by the
mood (see below). The expression “is related to” stands for a transitive verb, the
extended copula. We can see that the logical form of the syllogism
Every ant is greater than every atom
Every elephant is greater than every ant
Every elephant is greater than every atom
is that of Figure I.
Caramuel gives valid moods for each of the figures above. By way of an example,
let us present the valid moods under Figure I:
1. aa.aa.aa.
2. aa.ai.ai.
3. aa.ia.ia.
4. aa.ii.ii.
5. ai.aa.ai.
6. ai.ai.ai.
7. ai.ia.ii.
8. ai.ii.ii.
38 Caramuel deals with the pure relational syllogism in LO, Pars II, disp. IX Syllogismorum
Pure Obliquorum Formas et Figuras Expendens, pp. 432-436. Only this type of syllogism is
presented in Sousedík [1969].