Traditional Logic I: Chapter 9 - Obversion, Conversion, and Contraposition

Partial Conversion of the A Statement

A statements can be partially converted. If an A statement is true, it can be converted into a true I statement, but it must be done in a slightly different way.

Change Quality: No S is P ----->

All S is P

Obvert: No S is P ----->

All S is not P

Contrapose: All S is P ----->

All non-P is non-S

Contrapose: All men are mortal ----->

All non-mortals are non-men

Double Negation of I Statements Rule 4)

Apply the rule of double negation.

Conversion

Interchange the subject and predicate.

Double Negation of I Statements Rule 2)

Make the second 'not' a 'non' and attach it to the predicate word with a dash.

Convert: No S is P ----->

No P is S

Change Quality: All S is P ----->

No S is P

Obvert: All S is P ----->

No S is not P

Double Negation of I Statements Rule 3)

Place an 'im,' 'un,' 'in,' or an 'ir' at the beginning of the predicate-term.

Double Negation of I Statements Rule 1)

Simply place two 'not's at the beginning of the predicate term.

Convert: Some S is P ----->

Some P is S

Change Quality: Some S is not P ----->

Some S is P

Change Quality: Some S is P ----->

Some S is not P

Obvert: Some S is not P ----->

Some S is not P

Obvert: Some S is P ----->

Some S is not non-P

Partially Convert: All dogs are animals ----->

Some animals are dogs

Contrapose: Some S is not P ----->

Some non-P is S

The Rule of Double Negation

The rule of double negation says that a term which is not negated is equivalent to a term that is negated twice (and vice versa).

In logic, the way we say two statements are logically the same (even though they may use slightly different words) is by calling them __________ __________.

logically equivalent

To obvert a sentence, you must do two things:

1. Change the quality of the sentence. 2. Negate the predicate.

Contraposition

1. Obvert the statement. 2. Convert the statement. 3. Obvert the statement again.