Some Classic Concepts
A classic syllogism has two categorical statements as premises and of course a conclusion that is itself a categorical statements. We will introduce a classification scheme for classic syllogisms. First we will identify the premises and conclusion by their form. Thus we will identify:
All liars are people to be despised.
All politicians are liars.
All politicians are people to be despised.
as an AAA since both premises and the conclusion are A statements. However this, often called the
mood does not uniquely identify a syllogism. Consider:
All liars are people to be despised.
All liars are politicians.
All politicians are people to be despised.
This too is an AAA, but it is a different argument. Notice that in each syllogism one term will occur in both premises, but not in the conclusion. This term is called the
(M)iddle term. One of the other two terms will occur in the left of the conclusion, while the other will occur on the right. The one on the left will be called the
(S)ubject term, while the on the right will be called the
(P)redicate term. In order to obtain a unique identification the concept of the
figure of the syllogism was introduced. Although the order of the premises does not, logically speaking, matter we will adopt the convention of taking the first premise to be the one that contains the predicate term, the second as the one that contains the subject term. We can now identify four figures by way of identifying the possible positions of the middle term in the premises.
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Second Figure
P - M
S - M
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Fourth Figure
P - M
M - S
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In all cases the conclusion will be S - P.
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Look back at the two AAA arguments above. The first is a first figure one. So we shall identify it as an AAA-1 argument. The second is a third figure one so we shall identify it as an AAA-3 argument.
You should now try a bit of practice with classic standard forms.
Some Practice
After that we will learn how to use Venn Diagrams to check arguments for validity.
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