Section 7:
The Syllogism
, Barker, pp. 4450.
***Read the section, then the following additional comments.
For the next little while the focus of our attention will be on the
syllogism
.
To qualify as an
authentic syllogism, an argument must follow some very strict rules; in order to be a valid
syllogism it must observe even more rules.
First the basic ones:
1.
A syllogism consists of three categorical sentences:
two premises and a conclusion.
2.
The three categorical sentences share exactly three category terms among themselves.
That
means that each term appears twice.
E.g.
All wheels are round objects.
All tires are wheels.
Therefore, all tires are round objects.
Note that there are three terms, “wheels,” “round,” and “tires.”
Each term shows up in two
different sentences.
3.
The term, “wheels,” appears in the two premises, but not the conclusion.
There will always
be one such term in a syllogism.
We call the term that is in both premises, but not the
conclusion, the
middle
term.
4.
The other two terms, “round” and “tires,” both show up in the conclusion.
“Tires” is the
subject of the conclusion, “round” is the predicate.
5.
The term that is the
predicate
of the conclusion is called the
major
term.
We write the
premise that contains the major term first, and we refer to it as the
major premise
.
6.
The term that is the
subject
of the conclusion is called the
minor
term.
We write the
premise that contains the minor term second, and we refer to it as the
minor premise
.
Thus
in our example, “round” is the major term, “tires” is the minor term.
If we were to invert major and minor premises, the logical validity of the syllogism would
not be changed, but we would not be able to apply our standard evaluation techniques to it.
7.
Based on the categorical sentences used in a syllogism, we have the
mood
of the syllogism.
In the example, there are three A sentences used; consequently the mood of the syllogism is
AAA.
Theoretically, there can be EAE, III, OAI, or any other possible combinations of
categorical sentences to be the moods of syllogisms.
You will shortly realize that many
moods are so patently invalid that there is little need to worry about them.
1
LESSON 4
Categorical Logic, Part 3
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8.
Where in a syllogism the middle term appears reveals to us the
figure
of a syllogism.
There
are four possible combinations, so syllogisms come in four figures.
The convention of how
to determine the figure of a syllogism is well portrayed by Barker’s “shirt collar” diagram on
page 45.
Here is another summary:
first
second
third
fourth
major premise:
mid
maj
maj
mid
mid
maj
maj
mid
\


/
minor premise:
min
mid
min
mid
mid
min
mid
min
9.
If you apply the categories of mood and figure to our example, you see that its mood is
AAA; it is in the first figure.
We shall abbreviate this classification as “AAA1.”
Let us look at what happens if we take the same example and put it into different figures:
AAA1:
All wheels are round objects.
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 Spring '11
 BrentKelly
 Logic, Syllogism, Barker, Traditional logic, Syllogistic fallacy

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