Handbook of the History of Logic: - Fordham University Faculty

658 Petr Dvoˇrák
view of relational form as paradigmatic which guides A. de Morgan in his Formal
Logic, 1847 and later works in developing his relational logic, far more powerful
than Caramuel’s, because more general.
As A. de Morgan does, Caramuel recognizes eight basic logical forms of relational
statements. These are gained from possible logical forms of relational
statements based on equivalences. One can find two equivalence rules used in
Caramuel’s writing: 36
1. nx ↔ y where x and y stand for contradictories (e.g. e and i)
2. xn ↔ y where x is any statement (e.g. e) and y is its contrary or subcontrary
(e.g. a)
What we get are two equivalent eight-member sets of forms: 37
ai ee
aa ein
ii ine
ia inin
ea ain
ei ae
ina iin
ini ie
Based on their logical relationships of oppositions, the forms in both of these
sets could be arranged into two squares of oppositions (with the traditional relationships):
the second way is more akin to the strategy of making the predicate more precise by analyzing
its embedded predicational structure, as in Fred Sommers (The Logic of Natural Language,
Clarendon, Oxford 1982). In a marginal note Caramuel recognizes relational syllogism to have
four terms; cf. LO, Pars II, disp. IX, p. 432.
36 LO, Pars I, disp. I, De Aequipollentia Propositionum, pp. 411-412.
37 LO, Pars I, disp. I, De oppositione obliquarum, pp. 412-413.