Handbook of the History of Logic: - Fordham University Faculty

654 Petr Dvoˇrák
the two provided that it possesses at least a minimal degree of probability.
Finally, a mixture of epistemic and theological modes is dealt with: self-evident
proposition, demonstrative, evident, morally certain, de fide. The middle part
of this particular Herculean task ends with the discussion of theological modes
having to do with censure: different degrees and types of erroneous doctrinal
propositions. 29
3 RELATIONAL LOGIC
By far the most interesting contribution of Caramuel to formal logic is his oblique
logic. A key part of this is what we would call relational logic dealing with the
formal structure of relational statements and their properties (Pars I of Logica
Obliqua, pp. 407-429) and the theory of argument consisting of such propositions
(Pars II, pp. 429-503). 30
Propositio obliqua seu discreta or relational statement is a statement including a
complex predicate which could be further analyzed and whose analysis is important
from the point of view of securing and determining validity within an argument.
Apartfromaverb, 31 this complex predicate consists of the so-called terminus
obliquus, oblique term, grammatically a noun in a case other than the nominative
(casus obliquus). For instance, in the statement “every man commits some sin” the
term “sin” is oblique, for the Latin equivalent peccatum would be in the accusative
form. In contrast, the subject term “man” is in the nominative (terminus rectus).
Thus oblique logic contrasts with “upright” logic dealing with statements in which
both terms, the so-called extremes, are recti or upright. 32 The oblique predicate
term or extreme, called connotatus by Caramuel, is what we would call the second
member of a binary relation, while the upright subject term or extreme, called
connotans by Caramuel, would be the first member.
As for the form of oblique statements or propositions, Caramuel recognizes three
types or genera: The first type, called preposition by Caramuel, places the oblique
29 Ibid., art. IV and V, p. 61-67.
30 Properly speaking, logica obliqua covers more than relational logic, for Caramuel treats also
propositional logic under the same heading (the so-called “hypothetical” propositions). The
meaning of the term “discrete” will become clear below.
Caramuel’s relational logic was presented for the first time in the studies of S. Sousedík (and
K. Berka) in the 1960s and early 70s, cf. Sousedík [1969] and Berka–Sousedík [1972]. Since then
only very few studies have appeared, for instance, Hernández [1992]. So far the most extensive
treatment can be found in Dvoˇrák, [2006]. Besides relational logic, the latter monograph also
explains the problem of non omnis in Labor II of the Herculean Labors and selected issues from
Metalogica, e.g. logical paradoxes (insolubilia), change of propositional truth value, future contingents,
etc. It also covers an interesting polemic of Leibniz against Caramuel on antistrephus.
For the truth-value of propositions about future contingents in particular cf. Dvoˇrák [2002].
31 The verb is called “adjective” in contrast with the copula “to be” which is traditionally
called “substantive”, for it was viewed as a substance of which the predicate is an accident.
Hence Caramuel calls statements of this type “adjective”.
32 It is quite interesting to note that in Caramuel’s work an analogical contrast exists within
his theory of architecture, i.e. that between architectura recta and obliqua. Cf. J. Caramuel,
Architectura civil recta y oblicua, Vigevano 1678.