Handbook of the History of Logic: - Fordham University Faculty

240 Terence Parsons
The premise is tautological, but the conclusion would usually be considered to
be false. However, the conclusion results from the premise only by changing a
determinate ‘man’ to a merely confused one. Rule IV says that the inference
should be good, but it isn’t. The problem arises because putting a term in the
antecedent of a conditional can affect its mobility, and thus the inferences that
can be drawn using it. If there is no effect on its mode of supposition, then it is
not trustworthy to state principles of inference in terms of modes of supposition
as in Rule IV.
A parallel example can be constructed for Rule V.
(The 14 th century view discussed in the next section holds that the modes of
supposition are affected by context in the way that mobility is affected in this
theory.)
Problem 2: What stays the same?
Here is an easy counterexample to Rule V, which says that an inference from
distributive supposition to determinate is valid:
Every donkey is an animal.
Some donkey is every animal.
The reason for the fallacy is blatant: we did not just change the subject from
distributive to determinate, we also changed the predicate from merely confused
to distributive. Apparently, the rule should specify that nothing else can change
in the proposition when the rule is applied. But something else often changes; for
example, some word switches position with another, and this may affect both of
their modes. Perhaps what is meant then is that except for the quantifying sign
of the term under discussion, the same words must be used in the premise and
conclusion, and their grammatical relations must not change, and the modes of
supposition of the other terms must remain the same. William’s examples of good
inferences obey these constraints. But there are comparable simple cases which
are not addressed. Consider the inference:
so
Every girl gives every present to some boy
Every girl gives some boy every present
The constraints are obeyed by that inference (since nothing changes mode of supposition),
but it is invalid, indicating that one cannot infer a distributed subject
from a distributed subject. In other words, this is an invalid inference in which no
term changes mode of supposition.
The following restricted rules seem to be valid: 96
96 Karger [1984, pp. 100–102] states some more general circumstances in which versions of rules
II, IV and V all hold. She also adds a rule stating circumstances under which two propositions
are equivalent when their corresponding terms have the same modes of supposition.