Handbook of the History of Logic: - Fordham University Faculty

Relational Logic of Juan Caramuel 651
RA 1. Rarely anyone (almost noone) boasts of a death crime which
he or she did not commit.
PI 2. But Peter boasted of inflicting on John a serious injury in a
particular way
DI. Therefore, it would be reckless to believe that he did not accomplish
the crime
The abbreviations “RA”, “PI”, “DI” stand for syllables indicating the quantity of
the particular statement and hence, taken together, the mood of the syllogism (all
being of the first figure). Caramuel gives the following table: 23
Abbreviation Quantifier Mood The mode of the
conclusion
CA absolutely all (cuncti omnes) Camilli really certain
FA almost all (fere omnes) Fallitis morally certain
PL most/majority (plures) Placidi more probable
MA half (media pars) Magistri equally probable
PA a minority/not half (pauciores) Paridis less probable
MU many (multi) Mugavit scarcely probable
PU few (pauci ) Pudici reckless
RA almost no (rari fere nulli) Rapidi reckless
NO no (nulli) Nobilis against manifest
truth
A great amount of Moralis seu Politica Logica concerns what we would today
call the philosophy of law. However, in the second book, Caramuel analyses the
so-called moral modes and the logical properties of propositions containing them:
“it is certain that” (certum esse), “it is probable that” (probabile esse) and “it is
doubtful that” (dubium esse). 24
There does not seem to be any treatment of deontic logic operators in Caramuel’s
“Moral or Political Logic”. The closest one gets might be the operators
“must” (debeo) and “can” (possum), which Caramuel seems to be using in their
non-deontic meaning, however. He suggests, for the sake of simplicity and ease,
to reduce “it is necessary that” (N), “it is impossible that” (I) and “it is contingent
that” (C) to “must” (D) and “can” (P). Caramuel presents the following
23 Ibid., p. 44. Caramuel does not seem to distinguish corresponding positive and negative
scales. For instance, one can say very many, i.e. almost half (positive), or a minority, i.e. less
than a half (negative), in relation to the same number.
24 Ibid., Lib. II, cap. 2, sect. IX, p. 149.