Handbook of the History of Logic: - Fordham University Faculty

478 Catarina Dutilh Novaes
pared to the very different formulations of the distinction formal vs. material
consequence. An important difference, however, is that, while for some authors
(Pseudo-Scotus, Buridan) the absolute vs. as-of-now distinction is posterior to the
formal vs. material distinction and applies only to material consequences, there
are also authors (e.g. Peter of Mantua — cf. [Pozzi, 1978, 61]) who present the
absolute vs. as-of-now distinction as primary, and who see the formal vs. material
distinction as applying only to absolute consequences (as-of-now consequences are
always material consequences). In the latter case, clearly the distinction can no
longer be cast in terms of the modal value of the missing premise, since at least in
some cases of absolute formal consequences (e.g. valid syllogisms) there is in fact
no missing premise. Alternatively, for Peter of Mantua, an as-of-now consequence
is a consequence in which the contradictory of the consequent can indeed be true
at the same time as the antecedent, but not at the time indicated by the copula or
verb in question (the present if the verb is present-tense, the past if it is past-tense
etc.).
For a while, modern commentators have been particularly interested in as-ofnow
consequences (in particular with respect to Ockham — cf. [Mullik 1971]), as
some of them (cf. [Bohener, 1951]) saw these consequences as possible forerunners
of modern material implication. The first problem with this association, as already
argued, is that it seems unfitting to view medieval consequences as conditional
sentences/implications (material or otherwise). Moreover, as-of-now consequences
are contingent only insofar as the truth of the ‘missing premise’ is contingent. For
the rest, the logical relation of necessity between the propositions involved is just
as tight as with other consequences, provided that the missing premise is true —
if the missing premise is true, then the truth of the antecedent is incompatible
with the falsity of the consequent. In other words, as-of-now consequences display
a stronger logical relation than mere truth-functional material implication.
The modern reader may be wondering: what is the point in distinguishing these
different kinds of consequences? Is it yet one of those futile exercises that logicians
of all times tend to be fond of, but with no practical application? Not so; the reason
for such distinctions is in fact very practical: the different rules of consequences
(to be presented in the next section) apply to specific kinds of consequences. That
is, some rules apply only to formal or absolute consequences; others apply to
material or as-of-now consequences. And such rules are extremely useful for the
purposes of construing an argumentation; in fact, it seems that construing valid
arguments is really the ultimate purpose of theories of consequences. But for a
sound application of such rules, it is essential to identify the kind of a consequence
in question, whence the importance of these criteria being as clearly formulated
and effective as possible.