Handbook of the History of Logic: - Fordham University Faculty

The Development of Supposition Theory in the Later 12 th through 14 th Centuries 259
Not some D is E E is distributed
Every F is E E is superior to F
∴ Not some D is every F F replaces E in the first premise, adding ‘every’
8.8 Exponibles
We saw earlier that it is a general principle that an exponible proposition bears the
same logical relations to other propositions as do its exponents. This principle also
extends to modes of supposition. Buridan brings up this issue in connection with
“words that imply negations in themselves or in their exponents”. Examples are
“the verbs ‘begin’ and ‘cease’, or the words ’without’, ‘besides’, ‘only’, and several
others.” He says that such words can bring about distribution. He explains:
“...if the proposition in which such distributives occur needs to be
expounded by other propositions or by another proposition because of
its obscurity, a term can be said to have such supposition or suppositions
that it is found to have in its exponent or exponents.” [SD 4.3.7.5
(273)] 118
In some cases Ockham seems to agree with this. For example, in discussing the
proposition ‘Socrates begins to be literate’, he claims that the subject ‘Socrates’
has none of the three modes of common personal supposition; this is because it
meets none of the descent/ascent conditions. 119 He goes on to explain:
The reason why such terms have none of the aforesaid forms of supposition
is as follows: the propositions containing such terms are equivalent
to conjunctive propositions each composed of two or more propositions.
These propositions have the same subject; nevertheless, at least one of
them is affirmative and one negative so that one and the same term
has different forms of supposition in these propositions. Consequently,
these terms do not have any one of the normal forms of supposition in
the proposition whose parts are the various exponential propositions.
For example, ‘Socrates begins to be white’ is equivalent to the conjunction
‘Socrates was previously not white and now for the first time is
white’. In ‘Socrates is white’ the word ‘white’ supposits determinately;
whereas, in ‘Socrates was not white’ it has, because of the preceding
negation, confused and distributive supposition. [SL I.75 (216).]
The idea is a natural one: In the exposition of the original proposition the word in
question occurs twice, with different modes of supposition; thus there is no single
118 As an example of an exponible Buridan (SD 4.2.4) gives: “ ‘Only a man runs’ is analyzed
as ‘A man runs and nothing other than a man runs’”.
119 Actually, his argument at this point rests on his own definition of merely confused supposition,
which is slightly different from the one discussed in this chapter. This does not affect the
point made here.