EDUCTION.

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Presentation transcript:

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 Eduction 1. Obversion 2. Conversion 3. Contraposition 4. Inversion

Obversion Rules of Obversion Examples Retain the subject and the quantity of the obvertend Change the quality: if the obvertend is affirmative change to negative; if negative change to affirmative Contradict the predicate Examples 1. A – E Every man is trustworthy. No man is untrustworthy 2. 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 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 proposition Obverse the new proposition Obversion the process itself.

Conversion Derives the inference by interchanging the subject and the predicate. There are two types of conversion: Simple Conversion: E and I Limited Conversion: A and E O does not have a conversion Notes Convertend the given proposition Converse the new proposition Conversion the process itself

Conversion Rules of Conversion Interchange the subject and the predicate. Retain the quality of the proposition. 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 Conversion 1. 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 Conversion Truth-value of the converse A – I All men are mortal. Some mortal (beings) are men. E – O No aliens are voters. Some voters are not aliens. Truth-value of the converse Simple converses are logically equivalent to their convertends Limited converses have their truth value determined through the law of subalternation. Thus If 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: Partial Contraposition Full or complete contraposition I does not have a contraposition Notes Contraponend the given proposition Contraposit the new proposition Contraposition the process itself

Contraposition Rules of Partial Contraposition Examples The subject is the contradictory of the original predicate. Change the quality. The predicate is the original subject. Examples 1. 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 Examples The subject is the contradictory of the original predicate. The quality is the same. The predicate is contradictory of the original subject. Examples 1. 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: Partial Inversion Full or complete Inversion I and O do not have a inversion Note Invertend the given proposition Inverse the new proposition Inversion the process itself

Inversion Rules of Partial Inversion Examples The subject is the contradictory of the original predicate. Change the quality. The predicate is the original subject. Truth value follows the laws of subalternation. Note: O and I have no inversion Examples 1. 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 Examples The subject is the contradictory of the original subject. The quality is the same. The predicate is contradictory of the original predicate. Examples 1. A – I Every man is trustworthy. Some non-man are untrustworthy. 2. E – O No dogs are cats. Some nondogs are not noncats. Truth-Value Inversions follow the laws of subalternation. Thus If the invertend is true, the inverse is true. If the inverted is false, the inverse is doubtful.