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Square of opposition


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Square of opposition

  1. 1. Opposition of propositions may be illustrated in the ff. diagram for clearer comprehension: A / Every dog A E / No dog is E/ No dog is CONTRARY Everyanimal is an dog is an animal an animal S S U U B B A A L CONTRADICTORY L T T E E R R N N I / Some dogs O /Some dogs O/ Some dogs SUBCONTRARY are animals are animals are not animals are not animals
  2. 2. Eduction 1. Conversion. the formulation of a new proposition by interchanging the subject with the predicate of the original proposition without changing the quality. The original proposition is called “convertend” and the newly formulated proposition is called “converse”. Example: (observe closely the quantity and quality) Convertend: All men are not females. Converse: All females are not men. Take note that the quality is not altered in the converse. Both convertend and converse are negative.
  3. 3. Eduction There are two (2) types of conversion: the Simple and the Partial. a) Simple conversion. One whose convertend and converse have the same quantity. If the convertend is universal then the converse is also universal. If it is particular the converse is also particular. Convertible under Simple Conversion are E propositions and I propositions. E – E : No man is a dog. No dog is a man.
  4. 4. Egypt We call our dog EGYPT. He always leaves a pyramid in every room
  5. 5. Eduction There are 2 propositions that cannot be converted under simple conversion. They are the A and O. “All men are mortal cannot be converted to “All mortals are men.” An O proposition like “Some flowers are not roses.” cannot be converted simply as follows: “Some roses are not flowers.” Give examples of E–E Both combinations can be converted I–I simply
  6. 6. Partial Conversionb) Partial conversion. The quantity of the convertendis reduced from universal to particular. A is partiallyconverted to I; E is partially converted to O.Examples:A to I: All roses are flowers All trees are plants Some flowers are roses Some plants are treesE to O: No human being is a monkey Some monkeys are not human beings.
  7. 7. Rules of conversion1. Interchange the subject and predicate.2. Retain the quality.3. In simple conversion, retain the quantity.4. In partial conversion, reduce the quantity from universal to particular.5. There is no simple conversion for A proposition.
  8. 8. Eduction 2. Obversion. The process of reformulating a new proposition by maintaining the subject and quantity of the proposition but changing its quality and then replace the predicate with its contradictory. The original proposition is called “obvertend” and the new proposition “obverse”, and the process is called “obversion”. example: Every apple is a plant Every apple is not a non-plant or No apple is not a non-plant
  9. 9. Rules of Obversion The following are the rules in obverting propositions: 1. Retain the subject-term and quantity iof the obvertend. 2. Change the quality. If the obvertend is affirmative, the obverse is negative and vice-versa 3. Put the predicate in its contradictory. Under Rules 1 and 2 the ff. are obvertible: A to E E to A I to O O to I
  10. 10. Examples of Obversion A to E: All women are beautiful All women are not non-beautiful or No women are non-beautiful E to A: Every Cordilleran is not Japanese Every Cordilleran is a non-Japanese I to O: Some people are Filipinos Some people are not non-Filipinos. O to I: Some students are not brown Some students are non-brown. You will note that the obvertend and the obverse have the same meaning.
  11. 11. Same MeaningCHEATING . . . is two wrong people doing the rightthing.Can I pray while smoking? OrCan I smoke while praying?
  12. 12. Eduction 3. Contraposition. The formulation of a new proposition by undergoing the process of obversion and conversion.The original proposition is called “contraponend” and the new propositon is called “contraposit”, and the process contraposition. There are two (2) types of contraposition, the partial and the complete. For our purposes let go immediately to the complete contraposition. There are three (3) steps to follow: 1. First obvert the contraponend. 2. Then, convert the obverse. 3. Then, obvert the converse to get the contraposit. In other words the 3 steps are: obvert, convert, obvert
  13. 13. Complete contraposition/ examplesBy complete contraposition the ff. can be contraposed:A to A, E to O and O to O.Examples:A to A: Every creature is finite. (obvert) Every creature is not non-finite. (convert) Every non-finite is not a creature. (obvert) Every non-finite is a non-creature.
  14. 14. Complete contraposition/ examplesE to O: A cat is not a tree. (obvert) A cat is a non-tree. (convert) Some non-tree are cats. (obvert) Some non-trees are not non-cats.O to O: Some citizens are not voters. (obvert) Some citizens are non-voters. (convert) Some non-voters are citizens. (obvert) Some non-voters are not non-citizens.