5.1 Notes
In general, a
syllogism
is simply a deductive argument consisting of two premises and a
conclusion:
If you don’t know what a syllogism is, then you shouldn’t be able to graduate.
You don’t know what a syllogism is.
Therefore, you shouldn’t be allowed to graduate!
So, in a broad sense, a
categorical syllogism
is a deductive argument with two premises
and a conclusion where each (of the propositions) is a categorical proposition.
There
must also be a total of three terms, each of which appear only twice in distinct
propositions of the syllogism. Like the following:
All soldiers are patriots.
No traitors are patriots.
Therefore, no traitors are soldiers.
The three terms in the syllogism are given names depending on their location within the
argument.
First, there’s the
major term
: it is the predicate of the conclusion.
In the
above case, the major term is ‘soldiers’.
Second, there’s the
minor term
: it’s the subject
of the conclusion.
In the above case, the minor term is ‘traitors’.
Finally, there’s the
middle term
: it’s the term that doesn’t occur in the conclusion, but which appears in
either premise.
Here, that term is represented by ‘patriots’.
The premises of the syllogism are also given names.
The
major premise
is the one that
contains the major term.
The
minor premise
is the one that contains the minor term.
In
the above case (as will be the case for any categorical syllogism in standard form), the
first premise is the major premise, and the second premise is the minor premise.
As was the case for categorical propositions proper, there is a
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 Spring '08
 Barrett
 Logic, 1 m, 3 m, Syllogism, Traditional logic, P M M S

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