Categorical Syllogisms

Standard Form Categorical Syllogisms
In order to understand standard form categorical syllogisms it will be helpful to define several words and phrases:

•Syllogism – a deductive argument in which the conclusion is drawn from two premises.

•Categorical syllogism – a deductive argument consisting of three categorical
propositions with exactly three shared terms, two terms per proposition.

•Standard form categorical syllogism – a categorical syllogism consisting of
standard form categorical propositions arranged in a specific order, with the major
premise stated first, then the minor premise, and then the conclusion.

•Major term – the term occurring in the predicate of the conclusion in a standard
form categorical syllogism.

•Minor term – the term occurring in the subject of the conclusion in a standard
form categorical syllogism.

•Middle term – the term occurring in both the major and minor premises of a
standard form categorical syllogism, but not in the conclusion.

•Major premise – the premise of a categorical syllogism that contains an instance
of the major term.

•Minor term – the premise of a categorical syllogism that contains an instance of
the minor term.

Note: the major and minor premises are not determined by their placement in a
categorical syllogism, but by terms that are contained within them.

Both premises of a syllogism contain the middle term, but only the major premise and the conclusion contain the major term, and only the minor premise and the conclusion contain the minor term.

In the following argument the minor premise is stated first, then the major premise, and then the conclusion:

All disciples are Saints.
Some disciples are preachers.
Therefore some saints are preachers.

The major term in this argument is “preachers,” because it is the term in the predicate of the conclusion.

The minor term is “saint,” because it is the term in the subject of the conclusion. The first premise contains the minor term, so it is the minor premise. The second premise contains the major term, so it is the major premise.

This is a valid categorical syllogism, but it is not a standard form syllogism, because the premises are not stated in the standard order with the major premise being stated first. It should be noted that “standard form” is simply a matter of convention or definition.

There is nothing that makes a standard form syllogism “better” than a non-standard form syllogism, and in fact arguments that are not in standard form are sometimes seen to be more persuasive, because they can be written or spoken in a more natural format.

Consider the standard form syllogism below,

Some disciples are preachers.
All disciples are Saints.
Therefore some saints are preachers.

With this more natural statement of the same argument:

It must be true that some saints are preachers, since all disciples are saints, and
some disciples are preachers.

Even in this form the argument is a bit stilted, since it still conforms to the rigors of standard form categorical propositions, but most would prefer the latter to the former in everyday language.

However, it is easier to work with standard form categorical syllogisms, so for this
purpose it is to be preferred over the less rigorous arguments.


Mood and Figure

All standard form categorical syllogisms can be described in terms of their mood and
figure. The mood of a syllogism is represented by the three letters that represent the type of each proposition in the syllogism. So a standard form syllogism with three universal affirmative propositions has a mood of AAA. However, the mood of a syllogism does not fully characterize its form. For example consider these two arguments each of which has a mood of AAA.

Major premise: All men are mortal.
Minor premise: All preachers are men.
Conclusion: All preachers are mortal.

Major premise: All Christians are men.
Minor premise: All preachers are men.
Conclusion: All preachers are Christians.

Both of these arguments have a mood of AAA, but they differ in how the middle term is
placed. The first argument places the middle term in the subject of the major premise, and the predicate of the minor premise, but the second argument places the middle term in the predicate of both major and minor premises. So, although both have the same mood, they differ in form.

Next time we will see the 4 Figures and how they work! keeping checking!