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*Immediate inference*

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Immediate inference

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**immediate inference**is an inference which can be made from only one (:wikt:statement|statement) or proposition.BOOK, Churchill, Robert Paul, Logic: An Introduction, 1990, St. Martin's Press, New York, 0-312-02353-7, 21216829, 2nd, 162, Immediate inference is the assumption, without interveningâ€”or 'mediating'â€”premises, that because one categorical statement is true (or false), a logically equivalent categorical statement must also be true (or false)., For instance, from the statement "All toads are green." we can make the immediate inference that "No toads are not green." 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

- Given a type
**E**statement, from the traditional square of opposition, "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 are syllogistic fallacies called**illicit contrary**,

**illicit subcontrary**, and

**illicit subalternation**. Cases of incorrect application of the contradictory relation are so infrequent, that an "illicit contradictory" fallacy is usually not recognized.

### 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 (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*.

## See also

## References

{{Reflist}}**- content above as imported from Wikipedia**

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