Handbook of the History of Logic: - Fordham University Faculty

148 Ian Wilks
This indeed is the approach of the Melidunenses, Montani, and Parvipontani
alike, although they differ in how this approach is carried through. The
Melidunenses adapt Abelard’s view more directly, taking the argument to consist
of the enuntiabilia corresponding to the premises used in establishing the conclusion;
the arbitrariness of the sounds or letter shapes constituting the spoken or
written expressions of those enuntiabilia therefore in no sense imparts arbitrariness
to the argument as a whole. The Montani and Parvipontani have a more
complex account. They view the relation of premises to conclusion as implicational
rather than inferential, so that “A therefore B” is construed as being at
heart the conditional “If A then B.” For both of these groups the argument is
the enuntiabile expressed by such a conditional. Given an inference like “Socrates
is a man; therefore Socrates is an animal,” the Parvipontani take the argument
as being the enuntiabile corresponding to this conditional: “If Socrates is a man
he is an animal.” The Montani adopt much the same approach, except that the
conditional takes a more general form: “If something is a man it is an animal.”
The enuntiabile corresponding to this conditional form is thus identified as the argument
of “Socrates is a man; therefore Socrates is a mortal,” of “Plato is a man;
therefore Plato is a mortal,” and of all other possible substitution instances of this
form. Finally, the response of the Porretani lies a little apart from these others in
appealing not to an enuntiabile at all but to a relation of terms, in particular the
relation of the middle term to the others. The argument is simply this relation.
Since the relation is assuredly an objective one, it thus avoids what appears to be
the problem with holding that an argument is nothing but the meaningful words
of which it is composed [Iwakuma, 2004, pp. 318–320].
There is controversy not only about the nature of an argument but about the
very relationship between syllogisms and topical inferences. Recall that Abelard
distinguishes between complete and incomplete entailment, ascribing to syllogisms
the status of being complete by virtue of their syntactic form. The strength of
topical inferences is understood, as we have seen, in a very different way [Stump,
1989, pp. 96–97]. This is a unique view at the time Abelard initially propounds
it [Green-Pederson, 1987, p. 198]. His predecessors typically view syllogisms as
deriving their strength in the same way all topical inferences do, and topics are
assigned to them, just as to other inferences. The topics for syllogisms simply tend
to be descriptions of the relevant syllogistic mood, descriptions set in the form of
topical rules. Abelard’s insistence that there is something fundamentally distinct
about the syllogism that sets it apart from other inferences is therefore a novel
view, and is regarded in his own time as a characteristic view, both of himself and
of the Nominales. The view that syllogisms are at heart inferences, best expressed
as conditionals with the conclusion as consequent, naturally encourages the notion
that they, like other conditionals, require topical warrant; but the implicative (as
opposed to inferential) approach to the syllogism taken by other schools therefore
encourages some level of dissent from Abelard’s view. The Montani and Porretani
both maintain that the inferential linkage at work in syllogisms is ultimately a
matter of the topical relations that exist between their terms; logical form then