Handbook of the History of Logic: - Fordham University Faculty

238 Terence Parsons
7.6 Rules of Inference and Fallacies
It is clear that the modes of supposition of terms can influence what inferences
propositions containing them enter into. Attempts were made to catalogue some
principles governing these. A classic sample of these are Sherwood’s “rules” in
his chapter on kinds and modes of supposition. We have already seen his Rule
I, which gave the three principles (A-C) governing the causes of confusion and
distribution. His Rules II-V describe some consequences of relations among the
modes. I’ll first go over them to see how they are supposed to work, and then I’ll
consider some problems with them.
Rule II An argument from merely confused supposition to distributive
confused supposition does not follow.
Thus when every man sees only himself this does not follow: ‘every
man a man does not see; therefore every man does not see a man’. [IL
V.13.2 (118)]
The point here seems straightforward: the second ‘man’ in the premise is merely
confused (by the ‘every’, according to rule A) but it is distributed in the conclusion
(presumably by rule C, assuming that ‘not’ is a distributing sign here). Since it is
distributed in the conclusion, it is mobile (by rule D), and so the conclusion entails
e.g. ‘every man does not see Socrates’. But that clearly does not follow from the
premise. So the inference is clearly invalid. Sherwood sees this as an instance of a
general pattern involving a term’s changing its mode of supposition from merely
confused to distributive.
Rule III An argument from many cases of determinate supposition to
one of determinate supposition does not follow, but [only] to one of
confused supposition.
Thus when every man sees only himself this does not follow: ‘a man is
seen by Socrates, and [a man is seen] by Plato (and so on with respect
to [all] individual [men]); therefore a man is seen by every man’. But
this does follow: ‘. . . therefore by every man a man is seen’, for a
distribution has force in a succeeding phrase but not in a preceding
phrase.[Ibid]
The inference resembles what was elsewhere called “induction”: concluding that
a universal generalization is true because each of its instances are. For example, if
m1, m2,...areallthemen,thenfrom‘m1is mortal’ and ‘m2is mortal’ and ...,you
can infer ‘every man is mortal’. Abstractly put, from ‘φ(m1)’, ‘φ(m2)’, etc, infer
‘φ(every M)’. But this principle holds only when the ‘every man’ ends up with
wide scope, and this is not the case in the bad example that Sherwood discusses.
The good example, the one that does follow, differs exactly in that ‘every man’
ends up with wide scope. But this talk of “wide scope” uses modern terminology,
and the example was not discussed in these terms. Instead, what is discussed is
an effect of scope. For the shift of scope of ‘every man’ also alters the scope —