An immediate inference is an

inference Inferences are steps in logical 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 distinct ...

which can be made from only one statement or

proposition A proposition is a statement that can be either true or false. It is a central concept in the philosophy of language, semantics, logic, and related fields. Propositions are the object s denoted by declarative sentences; for example, "The sky ...

. 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. 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 In term logic (a branch of philosophical logic), the square of opposition is a diagram representing the relations between the four basic categorical propositions. The origin of the square can be traced back to Aristotle's tractate '' On Int ...

, 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