Immediate Inference Three Categorical Operations

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Presentation transcript:

Immediate Inference Three 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.

Immediate Inference Three Categorical Operations Conversion The converse of a claim is created by switching positions of subject and predicate terms.

Immediate Inference Three 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

Immediate Inference Three 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

Immediate Inference Three 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

Immediate Inference Three 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

Immediate Inference Three 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 writers are human, but it is not true that all humans are writers.

Immediate Inference Three Categorical Operations ConvErsIon - Valid for E & I And avoid the similar mistake of converting an O-claim! If it is true that some revolutionaries were not patriots, that does not imply that some patriots were not revolutionaries.

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

Immediate Inference Three 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

Immediate Inference Three 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

Immediate Inference Three 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

Immediate Inference Three 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

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

Immediate Inference Three 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

Immediate Inference Three 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

Immediate Inference Three 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

Immediate Inference Three 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

Immediate Inference Three 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

Immediate Inference Three 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