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Immediate Inference Three Categorical Operations

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Presentation on theme: "Immediate Inference Three Categorical Operations"— Presentation transcript:

1 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.

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

3 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

4 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

5 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

6 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

7 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.

8 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.

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

10 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

11 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

12 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

13 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

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

15 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

16 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

17 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

18 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

19 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

20 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


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