LESSON 6 – EQUIVALENT PROPOSITIONS(For Classroom purposes only)

EQUIVALENT PROPOSITIONS

-It means saying the same thing in 2 or more different ways; it is also known as EDUCTION

TWO TYPES OF EDUCTION

1. FORMAL - validity of the statement is based on the quality of the proposition2. MATERIAL – validity of the statement is base on the meaning of terms or the thought-content of

the sentence.

PURPOSE OF EDUCTION: Is to transform sentences used in an argument that is not in a strict syllogistic form into a valid syllogism. FORMS OF EDUCTION:

CONVERSION

1. SIMPLE CONVERSION – proceeds by simply interchanging the subject term and predicate term while retaining the quality and quantity of the proposition.

Note: only E and I are subject to simple conversion (E is converted to E; I is converted to I) except in singular propositions whose predicates are singular.

Ex. E – men are not angels I – some students are leaders E – angels are not men I – some leaders are students

Exception ex. My Brother is my only friend ----to----- My only friend is my brother.

2. CONVERSION BY LIMITATION – proceeds by interchanging the subject and predicate terms and changing the quantity of the proposition from universal to particular.

Note: only A and E can be partially converted (A is converted to I; E is converted to O)

Ex. A – Every dog is a mammal E –Filipinos are not stupid I – some mammals are dogs O – Some stupid people are not Filipinos

OBVERSION – the subject term and the quantity of the original proposition is retained. ONLY THE QUALITY IS CHANGED.Note: 1. Only (A and E ) ; (I and O) can be interchanged 2. Requires an understanding of the class complement of termsSuch as:

CONTRADICTORY CONTRARY1. Good and bad 1. Coward and hero2. Black and White 2. winner and loser3. Introvert and extrovert 3. high and low

4. Human and non-human 4. hot and cold

Illustration of obversion:

OBVERTEND OBVERSEA All A are B to A No A are non-BE No A are B to E All A are non-BI Some A are B to I Some A are not non BO Some A are notB to O Some A are non B

CONTRAPOSITION – proceeds by replacing the subject term by the compliment of the predicate term and replacing the predicate term by the compliment of its subject term.

STEPS:STEP 1. OBVERT - All men are rational beingsSTEP 2. CONVERT - No non-rational beings are menSTEP 3. OBVERT - All non-rational beings are non-menNote: Contraposition is valid on A and O only, otherwise its educted form would be committing the fallacy of illicit contraposition.

INVERSION – formulation of a new proposition whose subject is the contradictory of the original subject.

TYPES:PARTIAL –quality is changed, but the predicate is the same as in the original proposition.Note: only A and E are subject to partial inversion (A to O; E to I)

COMPLETE – quality is unchanged but the predicate is the contradictory of the original predicate.Note: only A and E are subject to complete inversion (A to I; E to O)

PROCEDURE TO FOLLOW: Complete (OCOC); partial (OCOCO)

O 1. E No S is non PC 2. E No non P is SO 3. A All non P is non SC 4. I Some non S is non PO 5. O Some non S is not P

Important note: there is no official rule as to when a particular eduction should be used but as a help to students, the following tips could be observe.

1. If there are 2 complementary class diff, use contraposition2. If there is only 1 complementary class difference, use obversion3. If classes are simply reverse, use conversion4. If classes matched, use table of opposition