Handbook of the History of Logic: - Fordham University Faculty

692 Russell Wahl
This is no surprise, given that the disjunction is taken as exclusive. What they
call the “copulative syllogism” actually is a parallel to the disjunctive syllogism,
since it involves a negated conjunction. Here only the one form of argument is
allowed,
∼ (P · Q)
P
∴∼ Q
The other form,
∼ (P · Q)
∼ P
∴ Q is explicitly excluded. Unfortunately there is no further development of
these syllogisms nor attempts to see the connection between disjunction and conjunction.
That insight would have to wait.
Arnauld and Nicole see these syllogisms as syllogisms which contain the entire
conclusion in one premiss, and thus see their general method as covering these
kinds of syllogisms as well.
9 DILEMMAS AND FALLACIES
The remainder of the third part of the Logic focuses on mistakes in reasoning.
This concern is consistent with their account of logic as a tool for distinguishing
truth from falsehood. The authors see not just accounts of correct reasoning but
also various considerations which might lead someone to draw a false conclusion
as part of the subject of logic. Many of these considerations have to do with
factors quite separate from what would now be considered logical considerations.
In fact, a treatment of informal fallacies fits nicely with the overall view of logic
as propounded by Arnauld and Nicole, and does not fit well with a more formal
account of logic. The brief chapter on dilemmas (Part III, 16) nicely characterizes
dilemma arguments as ones where a whole topic or field is divided up, and then
negative or positive conclusions are drawn from each part. The concern is not
with the formal properties of such arguments but with the dangers of dilemma
arguments and the easy fallacies which may occur in these arguments. The first
fallacy is what we would call a “false dilemma,” where the alternatives do not
exhaust the field. The second is simply when one of the arguments from one
of the parts does not hold. While they do not use these terms, a response to a
dilemma citing the first charge would be “going between the horns” and a response
to one citing the second charge would be “grasping a horn”. The authors mention
a third caution with respect to dilemma arguments, namely that dilemmas which
draw contrasting extremes from the different parts can often be turned around
into counter dilemmas.
The account of dilemmas does not involve the form of the argument, but rather
the truth of the premisses, or the difficulty with a subordinate argument which