Obversion

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 equivalent 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 complements:

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 for us to proceed from "A" Propositions to "E" Propositions, as well as from "I" Propositions to "O" Propositions, and vice versa. However, it must be noted that 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.

Bibliography

  • Brody, 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.

Footnotes

  1. ^ 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, p.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.

See also


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Look at other dictionaries:

  • Obversion — Ob*ver sion ([o^]b*v[ e]r sh[u^]n), n. [L. obversio a turning towards.] 1. The act of turning toward or downward. [1913 Webster] 2. (Logic) The act of immediate inference, by which we deny the opposite of anything which has been affirmed; as, all …   The Collaborative International Dictionary of English

  • obversion — [ɔbvɛʀsjɔ̃] n. f. ÉTYM. V. 1900; bas lat. obversio « action de tourner vers », de obversum; → Obvers. ❖ ♦ Log. Opération par laquelle on substitue son contradictoire au prédicat d une proposition …   Encyclopédie Universelle

  • obversion — [äb vʉr′shən, əbvʉr′shən; äb vʉr′zhən, əb vʉr′zhən] n. [LL obversio < L obversus: see OBVERSE] 1. the act of obverting 2. Logic the act of inferring the obverse …   English World dictionary

  • obversion — /ob verr zheuhn, sheuhn/, n. 1. an act or instance of obverting. 2. something that is obverted. 3. Logic. a form of inference in which a negative proposition is obtained from an affirmative, or vice versa, as None of us is immortal is obtained by …   Universalium

  • obversion — ob•ver•sion [[t]ɒbˈvɜr ʒən, ʃən[/t]] n. 1) an act or instance of obverting 2) pho a form of inference in which a negative proposition is obtained from an affirmative, or vice versa, as “None of us is immortal” is obtained by obversion from “All… …   From formal English to slang

  • obversion — /ɒbˈvɜʒən/ (say ob verzhuhn) noun 1. the act or result of obverting. 2. Logic a form of inference in which a negative proposition is inferred from an affirmative or an affirmative from a negative. {Late Latin obversiōn , stem of obversiō} …  

  • obversion — äbˈvərzhən, və̄zh , vəizh also shən noun ( s) Etymology: Late Latin obversion , obversio, from obversus (past participle of obvertere) + ion , io ion logic : the operation of immediate inference that gives the obverse …   Useful english dictionary

  • Obversión lógica — Una obversión lógica es una de las operaciones que la lógica clásica tradicional admitía como operación lógica. Consiste en la modificación del juicio aristotélico de forma que cambiando la cualidad del juicio, afirmativo negativo, y negando el… …   Wikipedia Español

  • obversion — É‘b vÉœrʃn /É’b vɜːʃn n. reversal; inversion …   English contemporary dictionary

  • obversion — ob·ver·sion …   English syllables

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