Handbook of the History of Logic: - Fordham University Faculty

The Nominalist Semantics of Ockham and Buridan 399
the time provided by the tense of the verb and the context (of the utterance or,
for example, the actual interpretation of a written predication). This last remark,
however, introduces two other essential elements into the picture, namely, the verb
needed for the predication, i.e., the copula, along with the time it co-signifies, and
the supposition (reference) of the subject.
Supposition
As we have seen, the via antiqua analysis of signification provides a number of different
semantic values for any common term: their immediate significata (whether
those should be identified as the formal concept, objective concept, or the common
nature represented by these concepts, or all these in a sequence), their ultimate
significata (the individualized natures, forms or “property instances” of individuals),
and the merely indirectly signified individuals themselves. Ordinarily, we use
concrete common terms to talk about these last-mentioned items. When we in fact
use a term in a proposition to talk about these, namely, about the individuals in
which the ultimate significata of the term are actual, then the term is said to be in
personal supposition, standing (or to use the common neologism, suppositing) for
its personal supposita. When it stands for its (various) immediate significata (or
even perhaps its ultimate significata or its significata in relation to its supposita,
etc.), 20 then it stands in simple supposition. And when it is used to stand for
itself (or similar tokens of the same type), then it is said to be in material supposition.
For example, ‘man’ in ‘Man is a species’ stands for the objective concept
of humans, i.e., it has simple supposition, but in ‘A man is a rational animal’
it has personal supposition, and in ‘Man is a noun in English’, it has material
supposition.
Attributing supposition, i.e., a context-dependent referring function to common
terms stands in stark contrast with the Fregean conception, on the basis of which
Peter Geach has repeatedly criticized the medieval idea of common personal supposition.
21 However, one can clearly reconstruct this semantic function of common
terms by using restricted variables, i.e., variables that are exactly like the variables
of standard quantification theory, except they range not over the entire universe
of discourse but only over the extension of their matrix. For instance, the sentence
‘A man is a rational animal’ in this reconstruction would not have to be formalized
by using an unrestricted variable bound by an existential quantifier, forcing us to
introduce a conjunction to provide the correct truth conditions of the original. In-
20 Walter Burley, for example, presents an elaborate system of distinctions for various sorts of
simple supposition in his Tractatus de suppositionibus, in S.F. Brown, “Walter Burleigh’s Treatise
De suppositionibus and its Influence on William of Ockham”, Franciscan Studies, 32 (1972), pp.
15-64. he also changed his mind about parts of his doctrine in his On the Purity of the Art
of Logic. For details, see Spade, P.V., “Walter Burley on the Kinds of Simple Supposition”,
Vivarium, 37(1999), pp. 41-59. But we find similar distinctions in other “older” authors as well.
21 See Geach, P. T., Reference and Generality, Cornell University Press: Ithaca, NY, 1962, c.
2, sect. 28, pp, 34-36; Peter Geach, “Nominalism,” Sophia 3(1964), pp. 3-14, reprinted in his
Logic Matters, Berkeley and Los Angeles: University of California Press, 1980, pp. 298-301.