Handbook of the History of Logic: - Fordham University Faculty

The Development of Supposition Theory in the Later 12 th through 14 th Centuries 241
If a term has distributive supposition in a proposition, then if you
change its quantifier sign so as to give it determinate supposition (inserting
a negation after the denoting phrase containing the term if it
changes from affirmative to negative, or vice versa) then the resulting
proposition is entailed by the original.
If a term has determinate supposition in a proposition, then if you
change its quantifier sign so as to give it merely confused supposition
(inserting a negation after the denoting phrase containing the term if it
changes from affirmative to negative, or vice versa) then the resulting
proposition is entailed by the original. 97
The ideas behind these rules are neat, but a great deal of work remains to be done.
When it was done it was within a somewhat different framework — roughly that
of the next section.
8 MODES OF SUPPOSITION: THE LATER VIEW
8.1 The Fourteenth Century Definitions of the Modes
In the 14 th century, Walter Burley, William Ockham, and John Buridan developed
a new approach to the analysis of the modes of common personal supposition. It
is not clear whether, or how, they saw their accounts as being different from those
given by earlier authors, but the accounts did differ in three important ways. (1)
The modes are defined in terms of valid inferences, not in terms of quantities such
as ‘many’ or ‘any’. (2) The modes of supposition of terms are defined globally
instead of locally, so that embedding a proposition in a larger one can alter not
just mobility but also mode of supposition. (3) In earlier accounts some good
inferences depend on whether the term in question has or lacks mobility, but rules
for these inferences are phrased in terms not of mobility but in terms of modes of
supposition. When a term has distributive but immobile supposition, rules based
on distributivity tend to fail. Conversely, a term without distributive supposition
might have the mobility needed to yield an inference that the rules deny to terms
that are not distributive. In the later theory, as a result of (1) and (2) the modes
of supposition are brought into conformity with kinds of mobility.
The new accounts define the mode of supposition of a term in a proposition 98
in terms of conditions on ascent and descent under that term in the proposition.
(A descent is similar to a quantifier instantiation step in modern logic; an ascent
97 When the only quantifier signs are ‘some’, ‘every’ and’no’, it is not possible to give an
example of this second rule. The possibility of giving such an example arises in some postmedieval
theories; see Ashworth 1974 IV.II.1 on special invented signs governing supposition.
98 Some authors held that only main terms have personal supposition in a proposition (where
a main term is one that is not part of another term). Burley DS para 5-15 argues this. But the
definitions to be given of modes of supposition apply meaningfully to any term in a proposition.
In practice, authors sometimes applied the definitions to parts of terms, even when denying that
this is possible.