Handbook of the History of Logic: - Fordham University Faculty

Logic in the 14 th Century after Ockham 475
from anything), and that has led many commentators to believe that these are the
only kinds of material consequences that Ockham recognizes. This matter cannot
be settled at this point, but some have also raised the hypothesis that Ockham’s
notion of material consequence would go beyond such specific cases (see [Schupp,
1993; Kaufmann, 1993]).
Buridan, by contrast, is crystal clear concerning his distinction between formal
and material consequence. His very terms are: ‘Formal consequence means that
[the consequence] holds for all terms, retaining the form common to all. Or [...]
a formal consequence is that which, for every proposition similar in form which
might be formed, it would be a good consequence.’ [Buridan, 1976, 22-23]. A
material consequence is one that does not satisfy this criterion but only the modal
criterion.
While it is not immediately obvious why Ockham chose this nomenclature for
his distinction 46 , in the case of Buridan the terminology espouses perfectly the
traditional Aristotelian notions of form and matter: the matter of a proposition is
defined by its categorematic terms, while its form is defined by its syncategorematic
terms. Thus, a formal consequence is one that holds in virtue of its form (the
meaning of its syncategorematic terms); a material consequence is one that does
not hold in virtue of its form alone but also in virtue of its matter (the meaning of
its categorematic terms). Another way of describing Buridan’s criterion is with the
notion of substitutivity: a formal consequence is one that holds in all substitutional
instances of its categorematic terms.
Buridan’s use of the substitutional criterion is remarkable in that it is immune to
much of the recent criticism against this criterion, most notably in [Etchemendy,
1990]. This is so because the substitutional criterion is applied only to consequences
which already satisfy the modal criterion of incompatibility between the
truth of the premise and the falsity of the conclusion. Under purely substitutional
accounts of (logical) consequence, a clearly invalid logical consequence such as ‘Bill
Clinton was a president of the USA, thus Bill Clinton was male’ comes out as valid
if ‘Bill Clinton’ is seen as the only non-logical term of the consequence (as it happens
to be so that, thus far, all presidents of the USA have been male, and thus all
substitutional instances for ‘Bill Clinton’ will also validate the consequent). But
in Buridan’s account, this putative consequence would not be considered as a valid
consequence in the first place, since it is not incompatible for somebody to be the
president of the USA and not be a male (in fact this may happen even in the
foreseeable future); therefore, it cannot be a formal consequence because it is not
a consequence to start with. Buridan’s account is best seen as what Shapiro [1998]
has coined the ‘hybrid’ notion of formal (logical) consequence (which he presents
as the most accurate conceptual characterization of logical consequence), that is,
46 Ockham’s choice of the term ‘formal consequence’ seems to be related to John Duns Scotus’
notion of ‘formal distinction’. Moreover, references to consequentia formalis can be found in
Scotus’ writings, for example in his Quaestiones super libros Elenchorum (p. 77oftheVivès
edition of Opera Omnia). On the relation between Scotus and Ockham on this matter, see
[Martin, 2004].