4.3

• Logical Equivalence or Eduction

  An inference in which the meaning of the original proposition is made clear in the second by the use and removal of negatives, and by interchanging the position of the subject and predicate of the original proposition
• Four kinds of logical equivalence

  • Conversion
  • Obversion
  • Contraposition
  • Inversion
• Conversion


  • A form of eduction that involves interchanging the position of the subject and predicate terms
  • Rules: Interchange subject and predicate, retain the quality of the proposition, do not overextend a term
  • Types: Simple conversion, Partial conversion
• Conversion

  • No saints are sinners - E to E
  • Some students are artists - I to I
  • All actors are artists - A to I
• Obversion


  • A process of eduction that involves changing affirmative propositions into negative propositions
  • Rules: Retain the subject and its quantity, change the quality, put the contradictory or contrary of the original predicate
• Obversion

  • All farmers are men of patience - A to E
  • Few men are gifted - I to O
  • Some leaders are not honest - O to I
• Contraposition


  • A combination of Obversion and Conversion, has an interchange of subject and predicate
  • Types: Simple contraposition, Complete contraposition
  • Rules: Obvert the given, convert the obverse, obvert the converse
• Contraposition

  • All doctors are trained to cure - A to No non-trained to cure are doctors
  • No dead is capable of tales - E to Some non-capable of tales are dead
  • All law implementers are law-abiding - A to All non-law abiding are non-law implementers
• Inversion

  • Formulating a new proposition called Inverse from a given proposition called Invertend
  • Types: Simple Inversion, Complete Inversion
  • Rules: Contradict the subject, change the quantity, change the quality of the copula, retain/change the predicate
• Inversion

  • All writers are readers of novels - A to Some non-readers of novels are not writers
  • No liars tell the truth - E to Some non-liars are tellers of truth
  • All cars are green - A to Some non-green are non-cars