A categorical syllogism is a syllogism whose premises and conclusion are in
categorical form
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Three categories are mentioned and each category is mentioned in two different
statements
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The subject term of the conclusion is called the minor term of the syllogism
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The predicate term of the conclusion is called the major term of the syllogism
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The term that does not occur in the conclusion is called the middle term of the
syllogism
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We can test whether a categorical syllogism is deductively valid by using what
are known as “the Rules of the Categorical Syllogism”
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If an argument that is a categorical syllogism meets all of these rules, the
argument is deductively valid
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If it fails to meet at least one rule, the argument is invalid
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Some of the rules concern whether a term is distributed
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A term is distributed, in a categorical statement, if that statement - all S are P -
the subject term, S, is distributed, and the predicate term, P, is not
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In an E statement - no S are P - both the subject term, S, and the predicate term,
P, are distributed

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In an I statement - some S are P - neither the subject term, S, nor the predicate
term, P, are distributed
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Finally in an O statement - some S are not P - the subject term, S, is not
distributed; however, the predicate term, P, is distributed
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The rules of the categorical syllogism are as follows
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For a syllogism to be valid, the middle term must be distributed in at least
one premise
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For a syllogism to be valid, no term can be distributed in the conclusion
unless that
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term is also distributed in at least one premise.
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For a syllogism to be valid, at least one premise must be affirmative.
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For a syllogism to be valid, if it has a negative conclusion, it must also
have a negative
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premise. And if it has one negative premise, it must also have a negative
conclusi
Summary
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Some arguments are deductively valid simply because of the way in which the
terms all, none, some, and not are used. We can test to see whether an
argument is this type of deductively valid argument using categorical logic
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In particular, the rules of the categorical syllogism are used to test whether a
categorical syllogism is deductively valid.
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Even though many everyday arguments are not explicitly written in this form,
many are implicitly syllogistic, and one can apply the rules of categorical
syllogisms once the argument has been translated into categorical form.
Module 7
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Some arguments are formally valid due to the logical relationships between
propositions
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These arguments are formally valid in what is called “propositional logic”
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This unit: how to translate an argument in English into propositional logic and test
the argument for validity using both the truth table and short truth table methods

The Basic Symbols of Propositional Logic
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Some arguments are deductively valid purely because of the formal relationships
between the propositions that they contain
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Ex: 1. My son is on the phone, or my wife is on the phone