An immediate inference is an inference which can be made from only one statement or proposition.[1] For instance, from the statement "All toads are green", the immediate inference can be made that "no toads are not green" or "no toads are non-green" (Obverse). There are a number of immediate inferences which can validly be made using logical operations, the result of which is a logically equivalent statement form to the given statement. There are also invalid immediate inferences which are syllogistic fallacies.

Valid immediate inferences

See also: Categorical proposition § Operations on categorical statements

Converse

Main article: Converse (logic)

Obverse

Main article: Obversion

Contrapositive

Main article: Contraposition (traditional logic)

Invalid immediate inferences

Cases of the incorrect application of the contrary, subcontrary and subalternation relations (these hold in the traditional square of opposition, not the modern square of opposition.) are syllogistic fallacies called illicit contrary, illicit subcontrary, and illicit subalternation, respectively. Cases of incorrect application of the contradictory relation (this relation holds in both the traditional and modern squares of opposition.) are so infrequent, that an "illicit contradictory" fallacy is usually not recognized. The below shows examples of these cases.

Illicit contrary

Illicit subcontrary

Illicit subalternation and illicit superalternation

See also

References

  1. ^ Churchill, Robert Paul (1990). Logic: An Introduction (2nd ed.). New York: St. Martin's Press. p. 162. ISBN 0-312-02353-7. OCLC 21216829. Immediate inference is the assumption, without intervening—or 'mediating'—premises, that because one categorical statement is true (or false), a logically equivalent categorical statement must also be true (or false).
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