Handbook of the History of Logic: - Fordham University Faculty

256 Terence Parsons
understand ‘that man’s donkey’. The intent seems to be that the second premise
must be something like ‘Brownie is a donkey of a man whose every donkey runs’.
But this is not what is proposed. The example is frustrating because what Buridan
actually says (‘Brownie is that man’s donkey’) looks pretty straightforward, it just
happens to be a form of words for which we have no clear logical form. The second
problem is that however plausible his remarks, they do not justify the claim that
the descent condition is satisfied in a modified way. For example, the following
construal of the conjunction is clearly wrong:
Of some man this donkey is running and of some man that donkey is
running and ..., and so on for all the donkeys of that man.
For here there is clearly no possible antecedent for the anaphoric ‘that man’.
When Buridan says that ‘donkey’ is not distributed “absolutely” we must admit
that it is not distributed at all, according to the definition of distribution given
above. In fact, it has no mode of supposition at all. We can say that it has
restricted supposition, but this stands for an idea that we have not spelled out,
and that perhaps cannot be spelled out.
In general, any parasitic term will have no usual mode of supposition at all.
This will not prevent other terms from having modes of supposition; for example,
in Buridan’s sample sentence ‘man’ is indeed determinate, as Buridan says, and
‘running’ is merely confused; both of these are predicted by the rules for causes
of supposition. But parasitic terms do not have these modes according to their
definitions in terms of ascent and descent.
A special case: There is one kind of case in which an indexed term might be
said to have a mode of supposition, and this is when its free variable is bound by
a singular term. So in the sentence ‘Socrates’s every donkey is running’ wecan
say that ‘donkey’ is distributed because one can descend to:
Of Socrates this donkey is running and of Socrates that donkey is running
and ..., and so on for every donkey of Socrates
Strictly, this is an extension of our account of supposition, for we had to specify
that one is to consider all donkeys of Socrates, but it is a natural extension.
As for the rules for causes of modes of supposition, we should confine such rules
to non-parasitic terms, or at least to terms that are indexed with a variable that
is bound by a DP with a singular main term. Then, as noted at the end of the
last section, they are mostly correct.
8.7 Inferences
When the notions of modes of supposition were introduced, they brought along
with them new and useful ways to assess inferences. This already occurred with
the earlier theory, as discussed above. Many proposals made with the new terminology
were vague, and of limited usefulness. But some applications were clear