# A Class-Room Introduction to Logic

## May 4, 2009

### Unit-VIII: Immediate Inference-Eduction

Filed under: Eduction: Immediate Inference,Logic — Dr. Desh Raj Sirswal @ 8:25 am

Eduction: The second form of Immediate Inference is Eduction. It has three types –Conversion, Obversion and Contraposition. These are not part of the square of opposition. They involve certain changes in their subject and predicate terms. The main concern is to converse logical equivalence.

Details are given below:

#### Conversion

An inference formed by interchanging the subject and predicate terms of a categorical proposition. Not all conversions are valid.

Conversion grounds an immediate inference for both E and I propositions That is, the converse of any E or I proposition is true if and only if the original proposition was true. Thus, in each of the pairs noted as examples either both propositions are true or both are false.

Steps for Conversion: Reversing the subject and the predicate terms in the premise.

Valid Conversions

Convertend                                       Converse

A: All S is P.                                        I: Some P is S (by limitation)

E: No S is P                                          E: No P is S

I : Some S is P                                     I : Some P is S

O: Some S is not P                              (conversion not valid)

Example:

All bags are mangoes.-A

Some mangoes are bags.-I

No men are intelligent.-E

No intelligent are men.-E

Some cows are tables.-I

Some tables are cows.-I

Some students are not cats.

(not valid)

#### Obversion

An inference formed by changing the quality of a proposition and replacing the predicate term by its complement. Obversion is valid for any standard form Categorical proposition.

Obversion is the only immediate inference that is valid for categorical propositions of every form. In each of the instances, the original proposition and its obverse must have exactly the same truth-value, whether it turns out to be true or false.

Steps for Obversion:

1. Replace the quality of the given statements. That is, if affirmative, change it into negative, and if negative, change it into affirmative.
2. Replace the predicate term by its complementary term.

Valid Obversions

Obverted                                             Obverse

A: All S is P.                                       E: No S is non-P.

E: No S is P                                        A: All S is non-P.

I : Some S is P                                    O : Some S is not non-P.

O: Some S is not P                              I: Some S is non-P.

Example:

All females are perfect beings.-A

No females are non-perfect beings.-E

No female are perfect beings.-E

All female are non-perfect beings.-A

Some female are perfect beings.-I

Some females are not non-perfect beings.-O

Some female are not perfect beings.-O

Some female are non-perfect beings.-I

#### Contraposition

An inference formed by replacing the subject term of a proposition with the complement of its predicate term, and replacing the predicate term by the complement of its subject term. Not all contrapositions are valid.

Contraposition is a reliable immediate inference for both A and O propositions; that is, the contrapositive of any A or O proposition is true if and only if the original proposition was true. Thus, in each of the pairs, both propositions have exactly the same truth-value.

Note: In contraposition the subject of the conclusion is contradictory of the predicate of the premise and predicate of the conclusion is contradictory of the subject of the premise.

Steps for Contraposition:

a. Convert the statement: reverse the subject and the predicate terms.

b. Replace both terms by their complementary terms.

Valid Contrapositions

Premises                                               Contrapositive

A: All S is P.                                      A: All non-P is non-S.

E: No S is P                                       O: Some non-P is not non-S.

(By limitation)

I : Some S is P                                    (Contraposition not valid)

O: Some S is not P                            O: Some non-P is not non-S.

Example:

All citizens are voter.-A

All non-voters are non-citizens.-A

No politicians are honest.-E

Some-non-honest are not non-politicians.-O

(by limitation)

(cannot be contraposited)

Some students are not scholarship holders.-O

Some non-scholarship holders are not non-students.-O

#### Existential Import

It is time to express more explicitly an important qualification regarding the logical relationships among categorical propositions. There must be some things a certain kind. This special assumption, that the class designated by the subject term of a universal proposition has at least one member, is called existential import . Classical logicians typically presupposed that universal propositions do have an existential import.

Exercises:

Make the conversion, obversion and contraposition of the following:

1. Some monks are not vegetarians.
2. All journalists are pessimists.
3. No reptiles are warm blooded animals.
4. Some men are happy.