In traditional logic, obversion is a "type of immediate inference in which from a given proposition another proposition is inferred whose subject is the same as the original subject, whose predicate is the contradictory of the original predicate, and whose quality is affirmative if the original proposition's quality was negative and vice versa".[1] The quality of the inferred categorical proposition is changed but the truth value is the same to the original proposition. The immediately inferred proposition is termed the "obverse" of the original proposition, and is a valid form of inference for all types (A, E, I, O) of categorical propositions.
The universal affirmative ("A" proposition) is obverted to a universal negative ("E" proposition).
"All S are P" and "No S are non-P"
"All cats are animals" and "No cats are non-animals"
The universal negative ("E" proposition) is obverted to a universal affirmative ("A" proposition).
"No S are P" and "All S are non-P"
"No cats are friendly" and "All cats are non-friendly"
In the particular affirmative the quantity of the subject term remains unchanged, but the predicate term of the inferred proposition negates the complement of the predicate term of the original proposition. The particular affirmative ("I" proposition) is obverted to a particular negative ("O" proposition).
"Some S are P" and "Some S are not non-P"
"Some animals are friendly creatures" and "Some animals are not unfriendly creatures."
In the obversion of a particular negative to a particular affirmative the quantity of the subject also remains unchanged, and the predicate term is changed from simple negation to a term of the complementary class. The particular negative ("O") proposition is obverted to a particular affirmative ("I" proposition).
"Some S are not P" and "Some S are non-P"
"Some animals are not friendly creatures" and "Some animals are unfriendly creatures."
Note that the truth-value of an original statement is preserved in its resulting obverse form. Because of this, obversion can be used to determine the immediate inferences of all categorical propositions, regardless of quality or quantity.
In addition, obversion allows us to navigate through the traditional square of logical opposition by providing a means to proceed from "A" Propositions to "E" Propositions, as well as from "I" Propositions to "O" Propositions, and vice versa. However, although the resulting propositions from obversion are logically equivalent to the original statements in terms of truth-value, they are not semantically equivalent to their original statements in their standard form.
^Quoted definition is from: Brody, Bobuch A. "Glossary of Logical Terms". Encyclopedia of Philosophy. Vol. 5–6, p. 70. Macmillan, 1973. Also, Stebbing, L. Susan. A Modern Introduction to Logic. Seventh edition, pp. 65–66. Harper, 1961, and Irving Copi's Introduction to Logic, p. 141, Macmillan, 1953. All sources give virtually identical explanations. Copi (1953) and Stebbing (1931) both limit the application to categorical propositions, and in Symbolic Logic, 1979, Copi limits the use of the process, remarking on its "absorption" into the Rules of Replacement in quantification and the axioms of class algebra.
Bibliographyedit
Brody, Bobuch A. "Glossary of Logical Terms". Encyclopedia of Philosophy. Vol. 5–6. Macmillan, 1973.
Copi, Irving. Introduction to Logic. MacMillan, 1953.
Stebbing, Susan. A Modern Introduction to Logic. Cromwell Company, 1931.
January 01, 1970
obversion, also, categorical, proposition, traditional, logic, obversion, type, immediate, inference, which, from, given, proposition, another, proposition, inferred, whose, subject, same, original, subject, whose, predicate, contradictory, original, predicate. See also Categorical proposition Obversion In traditional logic obversion is a type of immediate inference in which from a given proposition another proposition is inferred whose subject is the same as the original subject whose predicate is the contradictory of the original predicate and whose quality is affirmative if the original proposition s quality was negative and vice versa 1 The quality of the inferred categorical proposition is changed but the truth value is the same to the original proposition The immediately inferred proposition is termed the obverse of the original proposition and is a valid form of inference for all types A E I O of categorical propositions In a universal affirmative and a universal negative proposition the subject term and the predicate term are both replaced by their negated counterparts The universal affirmative A proposition is obverted to a universal negative E proposition All S are P and No S are non P All cats are animals and No cats are non animals The universal negative E proposition is obverted to a universal affirmative A proposition No S are P and All S are non P No cats are friendly and All cats are non friendly In the particular affirmative the quantity of the subject term remains unchanged but the predicate term of the inferred proposition negates the complement of the predicate term of the original proposition The particular affirmative I proposition is obverted to a particular negative O proposition Some S are P and Some S are not non P Some animals are friendly creatures and Some animals are not unfriendly creatures In the obversion of a particular negative to a particular affirmative the quantity of the subject also remains unchanged and the predicate term is changed from simple negation to a term of the complementary class The particular negative O proposition is obverted to a particular affirmative I proposition Some S are not P and Some S are non P Some animals are not friendly creatures and Some animals are unfriendly creatures Note that the truth value of an original statement is preserved in its resulting obverse form Because of this obversion can be used to determine the immediate inferences of all categorical propositions regardless of quality or quantity In addition obversion allows us to navigate through the traditional square of logical opposition by providing a means to proceed from A Propositions to E Propositions as well as from I Propositions to O Propositions and vice versa However although the resulting propositions from obversion are logically equivalent to the original statements in terms of truth value they are not semantically equivalent to their original statements in their standard form See also editAristotle Categorical proposition Obversion Contraposition Conversion logic Inference Syllogism Term logic Transposition logic Footnotes edit Quoted definition is from Brody Bobuch A Glossary of Logical Terms Encyclopedia of Philosophy Vol 5 6 p 70 Macmillan 1973 Also Stebbing L Susan A Modern Introduction to Logic Seventh edition pp 65 66 Harper 1961 and Irving Copi s Introduction to Logic p 141 Macmillan 1953 All sources give virtually identical explanations Copi 1953 and Stebbing 1931 both limit the application to categorical propositions and in Symbolic Logic 1979 Copi limits the use of the process remarking on its absorption into the Rules of Replacement in quantification and the axioms of class algebra Bibliography editBrody Bobuch A Glossary of Logical Terms Encyclopedia of Philosophy Vol 5 6 Macmillan 1973 Copi Irving Introduction to Logic MacMillan 1953 Copi Irving Symbolic Logic MacMillan 1979 fifth edition Stebbing Susan A Modern Introduction to Logic Cromwell Company 1931 Retrieved from https en wikipedia org w index php title Obversion amp oldid 1176464771, wikipedia, wiki, book, books, library,
