Obversion
In
In a
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
- "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
- "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
- Aristotle
- Categorical proposition § Obversion
- Contraposition
- Conversion (logic)
- Inference
- Syllogism
- Term logic
- Transposition (logic)
Footnotes
- ^ 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
- 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.