Handbook of the History of Logic: - Fordham University Faculty

Peter Abelard and His Contemporaries 85
propositions leading to hypothetical syllogisms. This way of organizing material is
overtly embraced by Abelard in the Dialectica, in his attempt to depart from the
commentary format. So it can be taken as representing his most basic intuitions
on how the subject matter of logic should be organized.
I will structure my discussion below accordingly. Part 1 deals with words,
categorical propositions and categorical syllogisms. Part 2 deals with topics, hypothetical
propositions and hypothetical syllogisms. These two parts complete the
treatment of Abelard, and Part 3 turns to his contemporaries and their schools.
PART 1: ABELARD ON WORDS, CATEGORICAL PROPOSITIONS AND
CATEGORICAL SYLLOGISMS
The foundation-laying program for categorical syllogisms undertaken by Aristotle
in De interpretatione amounts to this: describe the propositional basis for
those syllogisms, but first describe the lexical basis for those propositions. More
than anything else that lexical basis is provided by subject and predicate terms,
which typically are general names. This is indeed the most foundational issue in
Abelardian logic: the semantics of general names, which, in Abelard’s hands, is
inseparable from the metaphysical problem of universals.
It would have been impossible for any logician of this time to do logic without
directly encountering this metaphysical problem. The very language in which
categorical syllogisms are formulated makes it unavoidable. While it is comfortable
and intuitive to an English speaker to pluralize both subject and predicate terms
in a proposition like “All men are animals,” the practice initiated by Aristotle and
transmitted by Boethius is to formulate the proposition with both terms in the
singular: “All man is animal” (Omnis homo est animal). This way of speaking can
be taken quite literally as representing the content of the proposition. Here, for
instance, is Boethius’ explanation of the example: “Therefore we define to be in
the whole, or not to be in the whole, thus: to be in the whole, or to be predicated
of all, is said when nothing of the subject is able to be discovered of which what is
predicated is not able to be said. For nothing of man is discovered of which animal
is not able to be said” [Boethius, 1891, 809D–810B]. This description suggests that
a universal proposition expresses a relation between two single and distinct items,
in this case man and animal, one of which (in this case man) is in the whole of the
other (animal). The proposition is then simply telling us how these items relate.
This language is of course used for the other entries in the Aristotelian square
of opposition:
A: All man is animal E: No man is animal
I: Some man is animal O: Some man is not animal.
The content of the I-form can then be rendered as “Animal is in part of man,” the
content of the E-form as “Animal is in none of man,” and the content of the O-form
as “Animal is not in the whole of man.” These formulations are understandable
but also questionable. Indeed, the question is unavoidable: what sort of things