Handbook of the History of Logic: - Fordham University Faculty

The Nominalist Semantics of Ockham and Buridan 429
abstract common terms, with the function of suppositing for the significata of the
predicates representing our concrete common terms. Furthermore, at this point it
will be also inevitable to introduce a copula with the function of asserting the existence
of these significata. However, since these significata cannot be regarded as
entities in the same sense in all cases, we would have to distinguish several senses
of existence, and introduce further sub-domains into our domain of interpretation
accordingly. Finally, we should also represent the function of the copula asserting
the significata of entire propositions, which could then serve to provide a simple
Aristotelian formula for the definition of truth-in-a-model, grounding a definition
of validity. These adjustments, however, already involve major departures from
the standard construction of quantification theory.
As we have seen, the via moderna analysis is actually much closer, at least
in the first approach, to standard quantification theory. Indeed, the function
attributed to predicate letters (that of denoting subsets of the domain or of its
Cartesian products with itself) is not a far cry from the nominalist conception of
the signification of common terms, according to which these terms signify certain
individuals of the domain, or their ordered collections in the case of connotative
terms. And the identity sign is clearly a good representation of the function of the
copula in accordance with the via moderna conception.
However, again, if we need to represent the finer details of the via moderna
conception, we need to depart considerably from the standard construction of the
semantics of quantification theory. In the first place, although using restricted
variables to represent common terms in personal supposition yields “the right results”
concerning the square of opposition and syllogistic, nevertheless, it does so
at the expense of representing simple common terms (say, F ) as complex variables
with an intrinsic propositional structure embedded in their matrix (‘x.F x’,
amounting to something expressible as ‘thing that is an F ’). But according to
our via moderna authors it is the simple term ‘man’, for example, that has this
referring function, and not a complex term like ‘thing that is a man’. In fact Buridan
would pointedly distinguish the two in various contexts. So, to represent this
feature of via moderna semantics, we would need to devise “term-logics” along the
lines proposed by Lesniewski, Lejewski, Henry, Sommers and Englebretsen.
However, even if all the finer details of via moderna semantics were neatly represented
in a semantic theory that describes the semantic features of an object
language in a distinct meta-language, the entire construction of the semantic theory,
as we have seen, would be radically unfaithful to Buridan’s conception. In the
first place, the global split between object-language and meta-language would not
do justice to his sophisticated conception of ontological commitment, offering a
genuine third alternative “between” Quine’s and Meinong’s. In the second place,
it would preclude his intriguing treatment of Liar-type paradoxes with all their
implications concerning the theory of truth. Finally, it would also be incapable
of representing Buridan’s “relentlessly” nominalist account of logical validity in a
semantically closed, token based system.
To approach these issues, therefore, one might provide a semantic construction