Immediate Inference Three Categorical Operations

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Immediate InferenceThree Categorical Operations

• Conversion
• Contraposition
• Obversion

These operations give us rules to create
logically equivalent claims and determine in some
cases if two categorical claims are logically
equivalent.
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Immediate InferenceThree Categorical Operations

• Conversion

The converse of a claim is created by switching
positions of subject and predicate terms.

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Immediate InferenceThree Categorical Operations

• Conversion

The converse of a claim is created by switching
positions of subject and predicate terms.
E No S are P No P are S
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Immediate InferenceThree Categorical Operations

• Conversion

The converse of a claim is created by switching
positions of subject and predicate terms.
E No S are P No P are S I Some S are P Some
P are S
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Immediate InferenceThree Categorical Operations

• ConvErsIon - Valid for E I

The converse of a claim is created by switching
positions of subject and predicate terms.
E No S are P No P are S I Some S are P Some
P are S
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Immediate InferenceThree Categorical Operations

• ConvErsIon - Valid for E I

The converse of a claim is created by switching
positions of subject and predicate terms.
E No metal is house No house is metal I Some
country is pop Some pop is country
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Immediate InferenceThree Categorical Operations

• ConvErsIon - Valid for E I

Avoid the common mistake of converting an A-claim!
The fact that all H are W does not imply that all
W must be H. For example, it is true that all
employees are human, but it is not true that all
humans are employees.
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Immediate InferenceThree Categorical Operations

• ConvErsIon - Valid for E I

And avoid the similar mistake of converting an
O-claim!
If it is true that some managers are not leaders,
that does not imply that some leaders are not
managers.
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Immediate InferenceThree Categorical Operations

• Contraposition

The contrapositive of a claim is created by
(1) switching positions of subject and
predicate terms
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Immediate InferenceThree Categorical Operations

• Contraposition

The contrapositive of a claim is created by
(1) switching positions of subject and
predicate terms
(2) replacing
both terms with their complements
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Immediate InferenceThree Categorical Operations

• Contraposition

The contrapositive of a claim is created by
(1) switching positions of subject and
predicate terms
(2) replacing
both terms with their complements
A All S are P All non-P are non-S
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Immediate InferenceThree Categorical Operations

• Contraposition

The contrapositive of a claim is created by
(1) switching positions of subject and
predicate terms
(2) replacing
both terms with their complements
A All S are P All non-P are non-S O Some S
are not P Some non-P are not non-S
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Immediate InferenceThree Categorical Operations

• ContrApOsition - Valid for A O

The contrapositive of a claim is created by
(1) switching positions of subject and
predicate terms
(2) replacing
both terms with their complements
A All S are P All non-P are non-S O Some S
are not P Some non-P are not non-S
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Immediate InferenceThree Categorical Operations

• Obversion

The obverse of a claim is created by
(1) changing affirmative to negative
or vice-versa
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Immediate InferenceThree Categorical Operations

• Obversion

The obverse of a claim is created by
(1) changing affirmative to negative
or vice-versa
(2) replacing
predicate term with its complement
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Immediate InferenceThree Categorical Operations

• Obversion

The obverse of a claim is created by
(1) changing affirmative to negative
or vice-versa
(2) replacing
predicate term with its complement
A All S are P No S are non-P
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Immediate InferenceThree Categorical Operations

• Obversion

The obverse of a claim is created by
(1) changing affirmative to negative
or vice-versa
(2) replacing
predicate term with its complement
A All S are P No S are non-P E No S are P
All S are non-P
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Immediate InferenceThree Categorical Operations

• Obversion

The obverse of a claim is created by
(1) changing affirmative to negative
or vice-versa
(2) replacing
predicate term with its complement
A All S are P No S are non-P E No S are P
All S are non-P I Some S are P Some S
are not non-P
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Immediate InferenceThree Categorical Operations

• Obversion

The obverse of a claim is created by
(1) changing affirmative to negative
or vice-versa
(2) replacing
predicate term with its complement
A All S are P No S are non-P E No S are P
All S are non-P I Some S are P Some S
are not non-P O Some S are not P Some S are
non-P
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Immediate InferenceThree Categorical Operations

• Obversion - Valid for ALL

The obverse of a claim is created by
(1) changing affirmative to negative
or vice-versa
(2) replacing
predicate term with its complement
A All S are P No S are non-P E No S are P
All S are non-P I Some S are P Some S
are not non-P O Some S are not P Some S are
non-P