Handbook of the History of Logic: - Fordham University Faculty

656 Petr Dvoˇrák
that of arectisadobliqua(from terms in the nominative to oblique terms), but regarded
it as a type of non-syllogistic immediate inference. 33 A step further would
be to say that the standard upright form is a special case of the oblique form;
hence, really, the oblique form is paradigmatic for any statement. We shall see
below that this is arguably the path Caramuel will eventually take.
There seem to be two possible ways of analyzing a relational statement, for
instance “every man commits some sin”:
every man is [some sin is committed by]
The first way regards the complex predicate consisting of a verb and an oblique
term to be an embedded predication; hence the oblique term is regarded to be
a (subordinate) logical subject. Hence, there are two subject-predicate structures
present within a relational statement and, consequently, two copulae. This
rather conservative view of the logical form of a relational statement accommodates
the latter statements within a quantifier-subject-copula-predicate upright
scheme, without reducing them to this form altogether. (The relational form is
clearly seen as different from the non-relational one, but not substantially, as one
can see). Caramuel takes this approach in his initial formal symbolism introduced
to grasp the logical form of the relational statement. Apart from the signs for
quantifiers “a”, “i”, “e” (all, some, no), the asterisk symbol * divides the subject
part from the predicate part. For instance, “a*i” means (every...is some..., e.g.
“every man commits some sin”). The introduction, however, of two symbols for
negation, copula negation “ñ” and quantifier negation “n”, and their possible positions
in Caramuel show that Caramuel assumes there are two copulae in relational
statements. The following are the possible places of negation:
(i) n-*-
(ii) -ñ*-
(iii) -*n-
(iv) -*ñ-
33For example: A circle is a plane figure. Therefore, whoever draws a circle draws a plane
figure.
J. Jungius (Junge), Logica Hamburgensis, hoc est, Institutiones Logicae In usum Schol. Hamburgensis
conscriptae, et sex libris comprehensae, ed. R. W. Meyer — J. J. Augustin, Hamburg
1957 (1st edition 1638), Lib. II, c. 4, § 6; Lib. III, c. 1. § 5. For the logic of relations in Jungius
cf. e.g. Ashworth [1967] and Dvo˘rák [2006].
Caramuel also suggests the reduction of oblique forms into upright ones, but more for the sake
of showing the usefulness of his new system, rather than as a necessary procedure to exhibit the
true form disguised or clouded by the oblique form, as in Jungius. Cf. Ibid., Lib. II, c. 16, § 1:
Crypsis est affectio Syllogismi oratione externa propositi, qua ejus forma ita occultatur, ut cum
sit legitimus, talis tamen non esse videatur (“Disguise is a property of a syllogism put forth in
an external linguistic formulation, in which its form is so hidden that in spite of being valid, it
does not appear so”).