An immediate inference is an

inference Inferences are steps in reasoning, moving from premises to logical consequences; etymologically, the word '' infer'' means to "carry forward". Inference is theoretically traditionally divided into deduction and induction, a distinction that in ...

which can be made from only one statement or

proposition In logic and linguistics, a proposition is the meaning of a declarative sentence. In philosophy, " meaning" is understood to be a non-linguistic entity which is shared by all sentences with the same meaning. Equivalently, a proposition is the no ...

. 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 Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...

statement form to the given statement. There are also invalid immediate inferences which are syllogistic fallacies.

Valid immediate inferences

Converse

*Given a type E statement, "No ''S'' are ''P''.", one can make the ''immediate inference'' that "No ''P'' are ''S''" which is the converse of the given statement. *Given a type I statement, "Some ''S'' are ''P''.", one can make the ''immediate inference'' that "Some ''P'' are ''S''" which is the converse of the given statement.

Obverse

*Given a type A statement, "All ''S'' are ''P''.", one can make the ''immediate inference'' that "No ''S'' are ''non-P''" which is the obverse of the given statement. *Given a type E statement, "No ''S'' are ''P''.", one can make the ''immediate inference'' that "All ''S'' are ''non-P''" which is the obverse of the given statement. *Given a type I statement, "Some ''S'' are ''P''.", one can make the ''immediate inference'' that "Some ''S'' are not ''non-P''" which is the obverse of the given statement. *Given a type O statement, "Some ''S'' are not ''P''.", one can make the ''immediate inference'' that "Some ''S'' are ''non-P''" which is the obverse of the given statement.

Contrapositive

*Given a type A statement, "All ''S'' are ''P''.", one can make the ''immediate inference'' that "All ''non-P'' are ''non-S''" which is the contrapositive of the given statement. *Given a type O statement, "Some ''S'' are not ''P''.", one can make the ''immediate inference'' that "Some ''non-P'' are not ''non-S''" which is the contrapositive of the given statement.

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

*It is false that all ''A'' are ''B'', therefore no ''A'' are ''B''. *It is false that no ''A'' are ''B'', therefore all ''A'' are ''B''.

Illicit subcontrary

*Some ''A'' are ''B'', therefore it is false that some ''A'' are not ''B''. *Some ''A'' are not ''B'', therefore some ''A'' are ''B''.

Illicit subalternation and illicit superalternation

*Some ''A'' are not ''B'', therefore no ''A'' are ''B''. *It is false that all ''A'' are ''B'', therefore it is false that some ''A'' are ''B''.

References

{{Reflist Syllogistic fallacies