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Immediate Inference Three Categorical Operations

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.

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Immediate Inference Three Categorical Operations

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  1. 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.

  2. Immediate InferenceThree Categorical Operations • Conversion The converse of a claim is created by switching positions of subject and predicate terms.

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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.

  8. 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.

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

  10. 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

  11. 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

  12. 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

  13. 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

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

  15. 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

  16. 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

  17. 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

  18. 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

  19. 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

  20. 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

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