4.2

• Opposition


  The relation of being against or repugnant to something that is already given
• Opposition


  • Happens if the pair of propositions given is said to be in contrast
• Four kinds of logical opposition


  • Contradictory
  • Contrary
  • Subcontrary
  • Subaltern
• Contradictory propositions


  Differ in both quantity and quality
• Contradictory propositions


  • All criminal acts are punishable by law
  • Some criminal acts are not punishable by law
• Contrary propositions


  Differ in quality not in quantity (both are universal)
• Contrary propositions


  • All winged animals are two-legged
  • No winged animals are two-legged
• Subcontrary propositions


  Differ in quality but not in quantity (both are particular)
• Subcontrary propositions


  • Some killings are just
  • Some killings are not just
• Subaltern propositions


  Differ in quantity but not in quality
• Subaltern propositions


  • All corrupt officials are dishonest
  • Some corrupt officials are dishonest
• The Four Aristotelian Propositions


  • Universal affirmative (A)
  • Universal negative (E)
  • Particular affirmative (I)
  • Particular negative (O)
• Contradictory propositions cannot be both true and both false at the same time. If one is true, the other is false and vice-versa.
• Contrary propositions cannot be both true and but they can be both false. If one is true, the other is false but not vice – versa.
• Subcontrary propositions – The propositions cannot be both false but they can be both true. That is, if one is false, the other is true but not vice-versa; if one is true, the other is unknown or doubtful.
• If the universal is true, the particular is also true but not vice-versa.
• If the particular is false, the universal is also false but not vice-versa.
• Opposition means that the proposition may be either true or false; or in some cases, the proposition is true in other cases, it is false.