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Critical Thinking: Categorical Logic: Terms, Mood, Figure; Converse, Obverse, Contraposition Let's inspect the anatomy of a categorical proposition: There are 3 quantities: Some, All, None. And there are two qualities: affirmative (e.g. All S are P) and negative (e.g., No S are P, Some S are not P). These qualities and quantities relate the subject category and the predicate category. Now lets Review the anatomy of a categorical argument. The typical categorical argument is syllogistic – this means that 3 and only 3 categories are related. If there are less than 3 categories we have an immediate inference or conversion (see below); if there are more than 3 categories then we have more than one syllogism linked together. The typical categorical syllogistic argument appears as in the diagram: Vocabulary of a Categorical Argument The major term is the predicate of the conclusion. The minor term is the subject of the conclusion. The major premise is the premise with the major term. The minor premise is the premise that does not have the major term. The middle term is the term that is in the premises but not in the conclusion. The mood of the argument is the series of sentence letter types when the major premise is listed first, the minor premise second and the conclusion third. The figure of the argument is a function of the location of the middle term. There are four figures. To determine which figure an argument is we need to inspect the location of the middle term. 1 st figure: The middle term is the subject of the major premise and the predicate of the minor http://critical-thinking.modustollens.org/ 1

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Page 1: Critical Thinking: Categorical Logic: Terms, Mood, …modustollens.org/critical_thinking/Categorical Reasoning/Critical... · Critical Thinking: Categorical Logic: Terms, Mood, Figure;

Critical Thinking: Categorical Logic: Terms, Mood, Figure; Converse, Obverse, Contraposition

Let's inspect the anatomy of a categorical proposition:

There are 3 quantities: Some, All, None. And there are two qualities: affirmative (e.g. All S are P) and negative (e.g., No S are P, Some S are not P). These qualities and quantities relate the subject category and the predicate category.

Now lets Review the anatomy of a categorical argument.The typical categorical argument is syllogistic – this means that 3 and only 3 categories are

related. If there are less than 3 categories we have an immediate inference or conversion (see below); if there are more than 3 categories then we have more than one syllogism linked together.

The typical categorical syllogistic argument appears as in the diagram:

Vocabulary of a Categorical Argument

The major term is the predicate of the conclusion.The minor term is the subject of the conclusion.The major premise is the premise with the major term.The minor premise is the premise that does not have the major term.The middle term is the term that is in the premises but not in the conclusion.The mood of the argument is the series of sentence letter types when the major premise is listed

first, the minor premise second and the conclusion third.The figure of the argument is a function of the location of the middle term. There are four

figures. To determine which figure an argument is we need to inspect the location of the middle term.1st figure: The middle term is the subject of the major premise and the predicate of the minor

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Critical Thinking: Categorical Logic: Terms, Mood, Figure; Converse, Obverse, Contraposition

premise.2nd figure: The middle term is the predicate of the major and the minor premise.3rd figure: The middle term is the subject in both the major and the minor premise.4th Figure: The middle term is the predicate in the major premise and the subject in the minor

premise. The four figures are represented in the following diagram (where M denotes the location of the

middle term):

The validity of all 256 possible categorical arguments have been evaluated as valid or invalid for many centuries. There are only 15 valid categorical argument forms; but we must be able to determine the mood and figure of any argument in order to use the table of valid forms. The 15 valid forms are:

Conclusion Figure 1 Figure 2 Figure 3 Figure 4A AAA-1E EAE-1 AEE-2

EAE-2AEE-4

I AII-1 AII-3IAI-3 IAI-4

O EIO-1 AOO-2EIO-2

EIO-3OAO-3

EIO-4

Notice that all EIO argument forms are valid.

The Six Rules.

1. Equivocation: the definition of the words or terms must remain a constant.2. Undistributed Middle: The middle term must be distributed in at least one of the premises.3. Illicit Major or Minor: Any term distributed in the conclusion must also be distributed in the premises.4. Negative Premise, Affirmative Conclusion5. Fallacy of Two Exclusive (or negative) premises6. Existential Fallacy: Two universal premises cannot yield a particular conclusion.

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Critical Thinking: Categorical Logic: Terms, Mood, Figure; Converse, Obverse, Contraposition

Distribution

A term is 'distributed' if and only if the term is applied to all the members of a category or if it says something about all the things in the category. The relations of distribution are summarized in the following table:

Subject PredicateA Yes NoE Yes YesI No No0 No Yes

Immediate Inferences and Conversions in Categorical Logic

There are three types of immediate inference or conversions in categorical logic some of which are valid and some of which are not. When we are interpreting a natural language argument using categorical statements these conversions are extremely useful for building the categorical statements.

The Converse

To form the converse we simply exchange or transpose the place of the subject and predicate without changing either the quantity or the quality.

ConverseA All S are P All P are S Invalid E No S are P No P are S ValidI Some S are P Some P are S Valid0 Some S are not P Some P are not S Invalid

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Critical Thinking: Categorical Logic: Terms, Mood, Figure; Converse, Obverse, Contraposition

The Obverse

To make the obverse of a proposition we reverse the quantity of the subject, add a 'non-' to the predicate and reverse the quality of the statement. This means that we can change the All to none or none to all and make a negative statement positive and a positive statement negative.

ObverseA All S are P No S are non-P Valid E No S are P All S are non-P ValidI Some S are P Some S are not non-P Valid0 Some S are not P Some S are non-P Valid

The Contraposition.

To form the contraposition we change the quality of the subject and the predicate and change their positions.

ContrapositionA All S are P All non-P are non-S Valid E No S are P No non-P are non-S InvalidI Some S are P Some non-P are non-S Invalid0 Some S are not P Some non-P are not non-S Valid

Summary, Converse Obverse, Contraposition

Converse Obverse ContrapositionA All S are P Invalid Valid ValidE No S are P Valid Valid InvalidI Some S are P Valid Valid InvalidO Some S are not-P Invalid Valid Valid

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