EDUCTION

Eduction

• An immediate inference that involves the reformulation of a given proposition by the interchange of the subject and the predicate of a given proposition or the use or removal of the negatives.

• Kinds of Formal Eduction1. Obversion2. Conversion3. Contraposition4. Inversion

Obversion• Rules of Obversion

1. Retain the subject and the quantity of the obvertend2. Change the quality: if the obvertend is affirmative change to

negative; if negative change to affirmative3. Contradict the predicate

• Examples1. A – E Every man is trustworthy. No man is

untrustworthy2. E – A No man is indispensable. Every man is dispensable.3. I – O Some creatures are lucky. Some creatures are not

unlucky.4. O – I Not all commodities are expensive. Some commodities are

inexpensive.

1. His lecture is not without humor. So, it must have humor.2. All soldiers are combatants. Hence, no soldiers are noncombatants.

Obversion• Truth-value of the obverse

1. To determine the truth-value of the obverse, always remember that the obvertend and the obverse are logically equivalent, that is, they have the same truth value.

Note:Obvertend the given propositionObverse the new propositionObversion the process itself.

Conversion• Derives the inference by interchanging the

subject and the predicate.• There are two types of conversion:

1. Simple Conversion: E and I2. Limited Conversion: A and E3. O does not have a conversion

• NotesConvertend the given propositionConverse the new propositionConversion the process itself

Conversion• Rules of Conversion

1. Interchange the subject and the predicate.2. Retain the quality of the proposition.3. Do not extend the term, that is, a particular term

cannot be universal term

• 2 Kinds of Conversion: Simple Conversion and Limited Conversion

• Examples of Simple Conversion1. E – E No flowers are fruits. No fruits are

flowers.2. I – I Some animals are mammals. Some mammals are

animals.

Conversion• Examples of Limited Conversion1. A – I All men are mortal. Some mortal (beings) are

men.2. E – O No aliens are voters. Some voters are not

aliens.

• Truth-value of the converseSimple converses are logically equivalent to their

convertendsLimited converses have their truth value determined

through the law of subalternation. ThusIf the convertend is true, the converse is true.If the converse is false, the converse is

doubtful.

Contraposition• The formulation of a new proposition whose

subject is the contradictory of the original predicate

• There are two types of contraposition:1. Partial Contraposition2. Full or complete contraposition3. I does not have a contraposition

• NotesContraponend the given

propositionContraposit the new propositionContraposition the process itself

Contraposition• Rules of Partial Contraposition

1. The subject is the contradictory of the original predicate.

2. Change the quality.3. The predicate is the original subject.

• Examples1. A – E Every man is trustworthy. No

untrustworthy (person) is a man.2. E –I No dogs are cats. Some non-cats are

dogs.3. O – I Not all citizens are voters. Some non-voters

are citizens.

Contraposition• Rules of Full Contraposition

1. The subject is the contradictory of the original predicate.

2. The quality is the same.3. The predicate is contradictory of the original

subject.

• Examples1. A – A Every man is trustworthy. Every

untrustworthy (person) is a non-man.2. E – O No dogs are cats. Some non-cats are not

non-dogs.3. O – Not all citizens are voters. Some non-voters

are not non-citizens.

Inversion• The formulation of a new proposition whose

subject is the contradictory of the original subject

• There are two types of Inversion:1. Partial Inversion2. Full or complete Inversion3. I and O do not have a inversion

• NoteInvertend the given propositionInverse the new

propositionInversion the process itself

Inversion• Rules of Partial Inversion

1. The subject is the contradictory of the original predicate.

2. Change the quality.3. The predicate is the original subject.Truth value follows the laws of subalternation.Note: O and I have no inversion

• Examples1. A – O Every man is trustworthy. Not every

non-man is trustworthy.2. E – I No dogs are cats. Some non-dogs are cats

Inversion• Rules of Full Contraposition

1. The subject is the contradictory of the original subject.2. The quality is the same.3. The predicate is contradictory of the original predicate.

• Examples1. A – I Every man is trustworthy. Some non-man are

untrustworthy.2. E – O No dogs are cats. Some nondogs are not noncats.

Truth-ValueInversions follow the laws of subalternation. Thus

If the invertend is true, the inverse is true.If the inverted is false, the inverse is doubtful.