Handbook of the History of Logic: - Fordham University Faculty

Relational Logic of Juan Caramuel 649
The talk of compossible combinations of expressions reminds one of possible
worlds discourse. Indeed, Caramuel speaks of possible worlds (mundos possibiles)
in Metalogica in relation to divine knowledge. 17 As has been stated, book X of
“Metalogic” applies logic to various philosophical and theological problems. His
aim is to clarify the various logical stages in God’s knowledge and thus draw a
parallel between human knowledge related to decision-making and that of God. As
one knows (i) possible characters, say a, e, i, o, and u, (ii) the production of this or
that character conditional on the knowledge of movements of the pen and (iii) the
actual character to be written based on the decision which character to write, so
God knows (i)’ possible worlds a, e, i, o, u, (iii)’ that e is or will be realized while
a, i, o, u will not, based on the previous decree of his will. Strangely enough, the
theological parallel of (ii), i.e. (ii)’, God’s conditional (or middle) knowledge, is not
mentioned (probably because Caramuel regards it explanatorily superfluous, as is
clear from his adherence to the Thomist theory of physical pre-determination).
We see Caramuel use possible worlds in theological models and theories. 18 Possible
worlds also serve in philosophical explanations, e.g. in explaining the ontological
status and foundation of possibilia. And once again, a parallel between
grammar and metaphysics is used. Characters now represent neither possible
worlds, nor possibilia, but perfections: as characters combine into words, so do
perfections into possible creatures. As words combine into statements and those
into books, so creatures combine into possible worlds (from today’s perspective we
could regard statements as corresponding to states of affairs). The books actually
written represent the actual world (hunc mundum), and those capable of being
written all possible worlds (omnes possibiles). 19 For Caramuel, the rules governing
the combinations of perfections and creatures (determining what is possible) are
probably ultimately grounded in the divine essence, as his example shows, for he
sees God as identical with all possible (simple) perfections, thinking all possible
strings of perfections (possibilia and possible worlds), while creating some of them
17 Metalogica,, Lib. X, Theological Theses (on God’s omniscience and omnipotence), Thesis I,
p. 190ff. For Caramuel on possible worlds cf. Dvoˇrák [2000].
18 Earlier on in Metalogica (Lib. X, Pars II, Positiones Metaphysicae, Thesis VIII, p. 74) one
can find a neat theological speculation employing possibilia; this time to clarify and understand
matters of dogmatic nature. Consider the following application: when God wanted to create
Adam, A, he first came to know, by the first type of knowledge – the knowledge of simple
apprehension — a great number of people- whom he could have created had he so wished: B, C,
D. . . etc. (note that here individual characters stand for possibilia, i.e. individual occupants of
possible worlds). By the same act of knowing by which God knows A, he also knows the whole
of his posterity. Since effects become individual through their causes, no descendant of Adam
could have been created by any descendant of B and vice versa. By choosing A God relegated
B, C, D. . . etc. to the ranks of the purely possible. Yet Adam sinned, and the Original Sin
afflicts all of his descendants, future ones as well as merely possible ones. This does not afflict
the descendants of B, so God chose the Virgin Mary, the mother of God, who was exempt from
the Original Sin, from among B’s posterity, implanting her miraculously among the descendants
of Adam. By doing so he suspended the validity of the principle of the essentiality of origin
(effects being individuated by their causes), to put it in Kripkean terms. Thus in Caramuel, the
principle is only physically necessary, not logically necessary.
19 Grammatica Audax, Pars III, med. IV, art. VI, p. 119.