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Eduction (Logic Slide 6)

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  • 1. EDUCTION Eduction The formulation of a new proposition by the interchange of the subject and the predicate of an original proposition and/or by the use or removal of negatives. Kinds of Formal Eduction 1. Conversion 2. Obversion 3. Contraposition 4. Inversion
  • 2. Conversion is the formulation of a new proposition by interchanging the subject and predicate of an original proposition but leaving its quality unchanged. Kinds of Conversion a. Simple Conversion b. Partial Conversion Note: Convertend - the original proposition Converse - the new proposition Conversion - the process itself
  • 3. Simple Conversion the conversion is simple if the quantity of the converse is the same as the quantity of the convertend. - E to E - I to I Partial Conversion the conversion is partial if the quantity of the proposition is reduced from universal to particular. - A to I - E to O
  • 4. Rules for Conversion 1. Interchange the subject and the predicate; 2. Retain the quality; 3. Do not extend any term. Example of Simple Conversion: - E to E No cat is a dog. No dog is a cat. - I to I Some houses are white. Some white (things) are houses. Note: - Often it is advisable to reduce proposition to logical form. - Beware of converting A propositions by simple conversion. - O propositions cannot be converted. - The actual existence of a subject may not be asserted in the converse if it has not been asserted in the convertend.
  • 5. Exercise: Give the converse of the following (if they have) Example of Partial Conversion: - A to I All men are mortal. Some mortal (beings) are men. - E to O No aliens are voters. Some voters are not aliens. 1. Every A is a B. Some B is an A. 2. No A is a B. No B is an A. 3. Some A is a B. Some B is an A. 4. Some A is not a B. No converse 5. Some dogs are very fierce animals. Some very fierce animals are dogs. 6. Giraffes are animals with long necks. Some animals with long necks are giraffes
  • 6. 7. Some men are not very good orators No converse 8. Some of the most cheerful people I know are continually sick. Some continually sick (person) are the most cheerful people I know. 9. Good example is the most effective way of influencing another to good. Some of the most effective way of influencing another to good is through good example. 10. What is sauce for the goose is sauce gander. No converse. Criticize the following examples. First, note whether the propositions are A, E, I, or O. Then, applying the rules for conversion, state whether the inference is valid or invalid. 1. All men have free will; therefore all having free will are men. 2. All truly democratic governments respect human rights; therefore all government that respect human rights are truly democratic.
  • 7. 3. If all whales are mammals, there can be no doubt that some mammals are whales. 4. If it is true that democracies are free countries, all free countries must be true democracies. 5. Some football players are good students; therefore some good students are football players . 6. Some football players are not good students, therefore some good students are not football players. 7. Some animals are not dogs, therefore some dogs are not animals. 8. No mere man is entirely without sin; therefore none who is entirely without sin is a mere man.
  • 8. Obversion the formulation of a new proposition by retaining the subject and quantity of an original proposition, changing its quality, and using as predicate the contradictory of the original predicate. It also involves either the use or removal of two negatives: the use or omission of one negative changes the quality, the use or omission of the other negative changes the predicate to its contradictory. Note: Obvertend - the original proposition Obverse - the new proposition Obversion - the process itself
  • 9. Rules for Obversion 1. Retain the subject and the quantity of the obvertend; 2. Change the quality. If the obvertend is affirmative, the obverse must be negative; and if the obvertend is negative to obverse must be affirmative; 3. As predicate, use the contradictory predicate of the original proposition. - A to E “Every cat is an animal” to “ No cat is a non-animal” - E to A “No cat is a dog” to “ Every cat is a non-dog” - I to O “Some house is white” to “ Some house is not non-white” - O to I “Some house is not white” to “ Some house is non-white”
  • 10. Exercise: Give the converse of the following (if they have) 1. Every A is a B. No A is a non-B. 2. No A is a B. Every A is a non-B. 3. Some A is a B. Some A is not a non-B. 4. Some A is not a B. Some A is a non-B 5. Wood is inflammable. Wood is not non-inflammable. 9. Parts of Asia are not habitable. Parts of Asia are non-habitable. 6. Wood is not magnetic. Wood is non-magnetic. 7. All men are mortal. All men are not immortal. 8. He is ineligible. He is not eligible. 10. Asbestos is noninflammable. Asbestos is not inflammable.
  • 11. Criticize the following examples. State whether the inference is valid or invalid. 1. All men are mortal; therefore no men are immortal. 2. No stone is immortal; therefore every stone is mortal. 3. No murderer will enter the kingdom of heaven; therefore all murderers are ones who will not enter the kingdom of heaven. 4. His lecture was not without humor; hence, it must have had some humor. 5. His rendition was not particularly inspiring; hence, it must have been somewhat uninspiring. 6. If the officer was not tactful, he must have been tactless. 7. No mere man is entirely free from sin; therefore every mere man is somewhat blemished with sin. 8. If all soldier are combatants, no soldiers are noncombatants. 9. What is not visible is invisible. 10. Some judges are unjust; therefore some judges are not just.
  • 12. Contraposition is the formulation of a new proposition whose subject is the contradictory of the original predicate. Kinds of Contraposition a. Partial Contraposition b. Complete Contraposition Note: Contraponend - the original proposition Contraposit - the new proposition Contraposition - the process itself
  • 13. Rules for Partial Contraposition 1. The subject is contradictory of the original predicate. 2. The quality is changed. 3. The predicate is the original subject. To get Partial Contraposition 1. Obvert 2. Converse the obverse Symbols and their Partial Contraposition - A to E - E to I - O to I - I no partial contraposit
  • 14. Rules for Complete Contraposition 1. The subject is contradictory of the original predicate. 2. The quality is not changed. 3. The predicate is the contradictory of the original subject. To get Complete Contraposition 1. Obvert 2. Converse the obverse Symbols and their Complete Contraposition - A to A - E to O - O to O - I no complete contraposit 3. Obvert the converse of the obverse
  • 15. Example Partial Contraposition: (Contraponend) Every dog is an animal, Obvert: No dog is a non-animal Convert: No non-animal is a dog (Contraposit) Complete Contraposition: (Contraponend) Every man is mortal, Obvert: No man is non-mortal, Convert: No non-mortal is man, Obvert: Every non-mortal is a non-man (Contraposit)
  • 16. Exercise: Give the contraposit of the following (if they have) 1. Every A is a B. 2. No A is a B. 3. Some A is a B. 4. Some A is not a B. 5. All voters are citizens. 9. All belonging to the class will go to the museum. 6. No aliens are voters. 7. Some blackboards are green. 8. No atheist are Christian. 10. Some Asiatics are not favorably disposed towards Americans.
  • 17. Criticize the following examples. State whether the inference is valid or invalid. 1. If dogs are animals, no non-animals are dogs and all non-animals are non-dogs. 2. Some animals are dogs; therefore some dogs are not animals; hence, too, some non-dogs are non-animals. 3. Whatever is fungus is a plant; hence whatever is not a plant is not a fungus. In other words, non-plants are non-fungi; that is nothing but plants are fungi. 4. Whatever is inseparable from a thing is found wherever the thing is found; hence, what is not found wherever a thing is found is not inseparable from the thing. 5. Since all ruminants are cloven-hoofed, as soon as we see that an animal is not cloven-hoofed, we see that it is not a ruminant. 6. A good definition is convertible with the term defined; hence, what is not convertible with the term defined cannot be a good definition.
  • 18. 7. No animals that do not suckle their young are mammals; therefore some non-mammals are animals that do not suckle their young. 8. Since all reptiles are vertebrates, we can be sure that all non-vertebrates are not reptiles. 9. If no non-vertebrates are reptiles, it follows that all non-reptiles are non-vertebrates. 10. Since no atheist are Christians, only non-Christians are atheist.
  • 19. Inversion is the formulation of a new proposition whose subject is the contradictory of the original subject. Kinds of Inversion a. Partial Inversion b. Complete Inversion Note: Invertend - the original proposition Inverse - the new proposition Inversion - the process itself
  • 20. Rules for Partial Inversion 1. The quality is changed. 3. The predicate is the same as the original proposition. To get Partial Inversion 1. Obvert 2. Convert Symbols and their Partial Inversion (Only A & E can be Inverted) - A to O - E to I 3. Obvert 4. Convert 5. Obvert
  • 21. Rules for Complete Inversion 1. The quality is not changed. 2. The predicate is the contradictory of the original predicate. To get Complete Inversion 1. Convert 2. Obvert Symbols and their Complete Inversion (Only A & E can be Inverted) - A to I - E to O 3. Convert 4. Obvert
  • 22. Example Partial Inversion: (Invertend) Every cat is an animal, Obvert: No cat is a non-animal, Convert: No non-animal is a cat, Complete Inversion: (Invertend) No cat is a dog, Convert: No dog is a cat, Obvert: Every dog is a non-cat, Convert: Some non- cat is a dog, Obvert: Every non-animal is a non-cat, Convert: Some non-cat is a non-animal, Obvert: Some non-cat is not an animal. (Inverse) Obvert: Some non-cat is not a non-dog. (Inverse)