Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.

4.4 Conversion Obversion And Contraposition

28,813 views

Published on

Course lecture I developed over section 4.4 of Patrick Hurley\'s "A Concise Introduction to Logic".

4.4 Conversion Obversion And Contraposition

  1. 1. 4.4 Conversion, Obversion, and Contraposition
  2. 2. Overview <ul><li>Conversion </li></ul><ul><li>Obversion </li></ul><ul><li>Contraposition </li></ul>
  3. 3. Conversion <ul><li>First type of operation we can apply to propositions. </li></ul><ul><li>Involves switching the subject term and the predicate term . </li></ul><ul><li>Conversion of both E and I type propositions will yield a statement that will necessarily have the same truth value. The original statement and its converse are said to be logically equivalent . </li></ul><ul><li>All S are P. Conversion  All P are S. </li></ul><ul><li> (A type) </li></ul>
  4. 4. Conversion, continued <ul><li>No S are P. Conversion  No P are S. </li></ul><ul><li> (E type) </li></ul><ul><li>Some S are P. (I type) Some P are S. </li></ul>
  5. 5. Conversion, continued <ul><li>Some S are not P. Conversion  Some P are not S. </li></ul><ul><li> (O type) </li></ul><ul><li>Note that the diagrams for A and O types do not match up. </li></ul><ul><ul><li>Conversion of these two types will result in a truth value that is logically undetermined. </li></ul></ul><ul><ul><li>Converting A and O types will result in a formal fallacy called an illicit conversion. </li></ul></ul><ul><ul><ul><li>Example: </li></ul></ul></ul><ul><ul><ul><ul><li>All people are happy. </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Therefore, all things happy are people. </li></ul></ul></ul></ul>
  6. 6. Obversion <ul><li>More complicated than conversion. </li></ul><ul><li>Involves two steps: </li></ul><ul><ul><li>1) Change the quality of the statement (without changing the quantity). </li></ul></ul><ul><ul><ul><li>For A and E type statements, change the quantifier (All to no, no to all) </li></ul></ul></ul><ul><ul><ul><li>For I and O statements, change the copula (are to are not, are not to are) </li></ul></ul></ul><ul><ul><li>2) Replace the predicate term with its term complement . </li></ul></ul><ul><li>Term complement </li></ul><ul><ul><li>Word or group of words that denotes the class complement. </li></ul></ul><ul><ul><li>Dog  Non-dog, person  non-person. </li></ul></ul><ul><li>Obversion works with all four types of propositions. </li></ul><ul><ul><li>A, E, I, and O types. </li></ul></ul>
  7. 7. Obversion, continued <ul><li>All S are P. No S are non-P. </li></ul><ul><li>No S are P. All S are non-P. </li></ul>
  8. 8. Obversion, continued <ul><li>Some S are P. Some S are not non-P. </li></ul><ul><li>Some S are not P. Some S are non-P. </li></ul>
  9. 9. Contraposition <ul><li>Similar to obversion, since it requires two steps as well: </li></ul><ul><ul><li>1) Switch the subject and predicate terms. </li></ul></ul><ul><ul><li>2) Find the term complement for each one. </li></ul></ul><ul><ul><li>Example: </li></ul></ul><ul><ul><ul><li>All people are happy. </li></ul></ul></ul><ul><ul><ul><li>Therefore, all non-happy things are non-people. </li></ul></ul></ul><ul><li>All S are P. All non-P are non-S. </li></ul>
  10. 10. Contraposition, continued <ul><li>No S are P. No non-P are non-S. </li></ul><ul><li>Some S are P. Some non-P are non-S. </li></ul>
  11. 11. Contraposition, continued <ul><li>Some S are not P. Some non-P are not non-S. </li></ul><ul><li>Notice that the E and I types do not appear the same when contraposition is applied. This means when they are contraposed, the new statement is logically undetermined. </li></ul><ul><li>But A and O type statements have the same diagram, so their truth values are logically equivalent (the same). </li></ul>
  12. 12. Contraposition, continued <ul><li>Illicit contraposition </li></ul><ul><ul><li>Happens when you apply contraposition to E and I type statements, and make a claim about them (even when their truth values are logically undetermined). </li></ul></ul><ul><ul><li>Example: </li></ul></ul><ul><ul><ul><li>No people are happy (No S are P). </li></ul></ul></ul><ul><ul><ul><li>Therefore, no non-happy things are non-people (No non-P are non-S). </li></ul></ul></ul><ul><ul><ul><li>Some people are happy (Some S are P). </li></ul></ul></ul><ul><ul><ul><li>Therefore, some non-happy things are non-people (Some non-P are non-S). </li></ul></ul></ul>

×