Handbook of the History of Logic: - Fordham University Faculty

Developments in the Fifteenth and Sixteenth Centuries 639
semantic link between particular non-logical terms. I dub these ‘non-formal’. Such
arguments were discussed under the heading of ‘materially valid consequences’, by
those logicians who continued to include sections on consequences in their texts,
and who used the substitution criterion of formality. 144 In the case of arguments
that are not deductively valid but are nonetheless acceptable, we might be talking
about incomplete arguments, notably enthymemes, that need to be re-expressed as
formal deductive arguments, or we might be talking about those arguments whose
premisses merely support the conclusion, or in some way make it reasonable to
accept the conclusion. Only the latter are properly dubbed ‘informal’.
At this point, we face another problem. As discussed in Part One, Agricola
and Ramus had excluded maxims and rules from the parts of dialectic devoted to
invention. This reduced or even eliminated the room for informal argumentation
connected with the Topics. Moreover, Agricola had accepted the four standard
types of argumentation as the subject of dialectical judgement, while Ramus insisted
that the syllogism, whether Aristotelian as in the Scholae, or reformed, as
in his Dialectica, was the general object of discussion under judgement. We also
have to take into account the rejection of specifically medieval material by many
sixteenth-century logicians. This meant that in a simplified logic manual there
was no discussion of types of conditional statement or of types of consequence,
any more than there was serious discussion of the standard types of argumentation.
Accordingly, it is only in those texts that are more heavily scholastic and
Aristotelian in their approach that we find anything more than a hand-waving hint
that there are indeed informal argumentative devices. I will consider just a few
examples.
I will start with conditionals and consequences. In his commentary on Peter
of Spain, Eck divides consequences into those that are merely inferential (illativa
tantum), those that are both inferential and convincing (illativa et probativa),
and those that are merely convincing (probativa tantum). Merely convincing consequences
are those in which the antecedent does not entail the conclusion, but
support it with reference to the Topics. They are persuasive, and are used in ethics
and rhetoric. 145 That is, they do not really belong to logic.
Petrus Fonseca is less dismissive. Contrary to the view held by Peter of Spain
that all conditionals are either necessary or impossible, Fonseca, like Nifo before
him, 146 allows for conditional statements that are contingent; 147 and he also argues
that that while all formal consequences are necessary, material consequences can
144 For the issues here, see the previous chapter on medieval theories of consequence. For those
who used the containment criterion of formality, the labels attached to what I call non-formal
consequences will differ.
145 Johannes Eckius, In summulas Petri Hispani (Augsburg, 1516), f. c vb. “Probativa tantum
est in qua antecedens non de necessitate infert consequens, tamen probat probabiliter et topice.”
He subsequently adds “consequentiam probativam non esse simpliciter bonam consequentiam
sed esse persuasivam, et in moralibus ac rhetoricis multum frequentatam, ut Hupertus fuit solus
cum Catherina in loco suspecto, ergo stupravit eam”.
146 Niphus, Dialectica ludicra, f.78vb,f.79rb.
147 Fonseca, Instituições Dialécticas, p. 198.