##
Enthymemes

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as a substitute for attending lectures.

An enthymeme is a categorical syllogism with
one premise left unstated. We can use what we know about categorical syllogisms
to reconstruct the missing premise.
####
Position and Terms

First, from the conclusion we will be able to identify the premise we have
been given as either the major or the minor premise.
If the subject term of the
conclusion occurs in the premise, it is the minor premise, while if the
the predicate term of the
conclusion occurs in the premise it is the major premise. The other term
given in the premise must be the middle term. Whichever premise we have
been given the missing premise must be the other. Thus if we have been
given the minor premise then the missing one must be the major premise
and should be placed first and should have the major term as well as the
middle term in it. On the other hand, if we have been given the major premise
then the missing one must be the minor premise and should be placed second
and should have the minor term as well as the middle term in it. In this
way we can quickly identify the position of the premise in the argument
and the terms which belong to the missing premise.
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Type of Proposition and Order of Terms

Determining the type of proposition
and the order for the terms is somewhat more difficult. At this point one
should be guided by the principle of charity. In many cases one could easily
construct an invalid argument, but this may not be the premise the originator
had in mind. One ought instead to try to build a valid
syllogism. Then if the enthymeme turns out to be invalid after your
best efforts, the reason will be because it is unavoidably invalid rather
than because you deliberately made it so. In other words, the fault will
lie with the argument rather than with you. On the other hand, if the argument
turns out to be valid, but you disagree with the conclusion, you will likely
be able to attack one of the premises as untrue. Indeed, people will sometimes
leave out an unreasonable premise in the hope that the audience will not
bother to reconstruct the premise and so will not notice how unreasonable
it is. Of course, there is a slight possibility that the given premise
is the unreasonable one. Finally, do not overlook the possibility that
you are wrong and the argument sound. (A **sound argument** is a valid
argument with all true premises.)

In attempting to make the argument valid, one makes use of the rules
from the rule method. One can quickly
determine whether the premise must be affirmative or negative. If the conclusion
is affirmative, the missing premise must also be so. If the conclusion
is negative, the missing premise must be negative, unless the other premise
is negative, in which case the missing premise must be affirmative. In
this way one eliminates two proposition types. Whether the missing premise
is particular or universal may sometimes be determined by the requirements
of distribution. If the middle
term is undistributed in the given premise, it will need to be distributed
in the missing premise; so if one already knows that the missing premise
is affirmative, this will show that it must be an A-form
and the middle term must be in the subject position. On the other hand,
if the missing premise must be negative, the distribution of the middle
term alone will not determine the type. In such a case one would look at
the term in the conclusion which is also in the missing premise. If the
term is distributed in the conclusion it must also be so in its premise.
Thus if both the middle term and the term form the conclusion required
distributing, one would need an E-form
proposition.

**Note:** Meeting the requirements of all the rules may be impossible
(for example, one cannot distribute both terms and have an affirmative
premise). Such an argument is simply invalid. One would choose to distribute
as many of the terms as possible but which term you distribute is arbitrary
(your choice).

**Note:** The order of the terms is already being determined as
we apply the rules about distribution. The order of terms will not matter
in the cases of E and
I propositions
(your choice).

**Note:** If the rules concerning distribution do not require a
universal proposition rather than a particular, the principle of charity
would favour a particular proposition over a universal. We have no reason
to assume that the originator of the argument would have claimed more than
he or she needed to claim.

**Note:** If the argument is about things which do not exist or
you have been instructed to evaluate the argument using the Venn
Diagram method, you will wish to also use a fifth rule in this reconstruction
process, namely: If the conclusion is particular, one premise must also
be particular. **Do not use this rule unless you are reconstructing an
enthymeme about things which do not exist or one to which you have been
instructed to apply the Venn Diagram method.**