Immediate inferences help us work in the simplest possible arrangements of categories. Valid immediate inferences result in claims that mean the same thing as the originals from which they are derived.

The three immediate inferences described below are first shown in the Formal Language section operating on claims that are already in standard form. Only occasionally will actual situations make things so convenient for us, however. The Natural Language section that follows the formal description provides a few representative examples of immediate inferences that one might encounter in everyday situations.

Formal Language

convErsIon (valid for E- and I-claims)

How it's done:

Switch positions of subject and predicate.

No X are Y --> No Y are X (valid)
All V are C --> All C are V (invalid)

contrApOsition (valid for A- and O-claims)

How it's done:

Switch positions of subject and predicate.
Replace both terms with their complements.

Some D are not S --> Some non-S are not non-D (valid)
Some F are B --> Some non-B are non-F (invalid)

obversion (valid for all four claim types)

How it's done:

Change positive to negative or negative to positive.
Replace the predicate term with its complement.

All Z are Q --> No Z are non-Q (valid)
Some G are P --> Some G are not non-P (valid)

Natural Language

Conversion

Conversion is only valid for E- and I-claims. It's not an especially interesting operation when it's done right. Conversion is sometimes misapplied to universal affirmative (A-) claims. Here are a few of the possibilities of valid conversions that mean the same thing as their originals:

Original: No works of Russian literature are carried by this store.
Converse: None of the works carried by this store is Russian literature.

Original: There are bass in this lake.
Converse: Some of the fish in this lake are bass.

Contraposition

Contraposition is valid only for A- and O-claims. The applications of contraposition are significantly more complex in practice than those of conversion. Here are a few contrapositions:

Original: All current customers will receive a loyalty discount.
Contrapositive: People who don't receive a loyalty discount are not current customers.

Original: If you go on the Germy Stringer Show, you'll immediately get involved in an ugly situation.
Contrapositive: If you haven't been involved an ugly situation, you haven't been on the Germy Stringer Show.

Original: There are some non-permanent workers here who aren't unreliable.
Contrapositive: Some reliable people aren't permanent workers here.

Obversion

Obversion always works if it's done right. The results obtained by the operation of obversion are the least intuitive of the three types of immediate inference.

Original: Only CDs with good videos sell really well.
Obverse: None of the CDs that sell really well don't have good videos.

Original: No one has entered the Forbidden Temple and returned.
Obverse: Everyone who has returned has not entered the Forbidden Temple.