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Venn Diagrams Distribution of Terms

Venn Diagrams Distribution of Terms. Venn diagrams explain the relationships between classes. n on-members. members. a nything not dogs. dogs. Triple H. t he planet Mars. cats. Making assertions. Find a key word in your premise, and abbreviate: For example, “Mr. Sell is awesome.”

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Venn Diagrams Distribution of Terms

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  1. Venn DiagramsDistribution of Terms

  2. Venn diagrams explain the relationships between classes. non-members members

  3. anything not dogs dogs Triple H the planet Mars cats

  4. Making assertions • Find a key word in your premise, and abbreviate: • For example, “Mr. Sell is awesome.” • We’ll use S for Sell. • We’ll name the class represented by the circle ‘awesomeness,’ and put it in italics above the circle.

  5. awesomeness S

  6. Let’s add something outside the class of awesomeness. • Vegetables, for instance, are not awesome. • What should we abbreviate ‘Vegetables are not awesome’ to?

  7. awesomeness S V

  8. Interpret the following Venn diagram. • S = Mr. Sell; V = vegetables; H = Mr. Hawthorne awesomeness S V H

  9. When we have two circles that overlap, we can compare two classes to each other. S P

  10. For instance: awesomeness teachers S H V

  11. We can even diagram the 4 forms of logical sentence. • A • All S are P • E • No S are P • I • Some S are P • O • Some S are not P

  12. A: All pro wrestlers are great athletes. pro wrestlers athletes

  13. Form E:No psychos are pleasant houseguests. pleasant houseguests psychos

  14. Form I:Some students are hard workers. students hard workers X

  15. Form O:Some clergy are not immoral. clergy immoral X

  16. Draw a Venn diagram for this sentence:Some pardoners are dishonest people. pardoners dishonest people X

  17. All mammals breathe air. mammals air-breathers

  18. Some teachers are not musicians. teachers musicians X

  19. Part 2:Distribution of Terms • What is distribution of terms? • A term in a statement is ‘distributed’ when a statement tells us something about all the members of its class.

  20. E: No S is P.(No psychos are pleasant houseguest.) • S refers to all the members of S. S is distributed. • P refers to all the members of P. P is distributed. pleasant houseguests psychos

  21. I: Some S is P.(Some students are hard workers.) • Only some of S is referred to. It is undistributed. • Only some of P is referred to. It is undistributed. students hard workers X

  22. A: All S are P.All pro wrestlers are great athletes. • All of S is referred to. S is distributed. • We can’t say something that refers to all P, though. P is undistributed. • Try reversing the statement. It doesn’t hold. pro wrestlers athletes

  23. O: Some S is not P.Some clergy are not immoral. • S is easy. It is undistributed. • P, however, is different. It can be said that all immoral people are different from at least one clergyman. It is therefore distributed. clergy immoral people X

  24. How do we remember which terms are distributed? NEGATIVE S U B J E C T NIVERSAL P R D I C A T E

  25. If the subject is universal, the subject is distributed.If the predicate is negative, it is distributed.All other terms is undistributed. NEGATIVE S U B J E C T NIVERSAL P R D I C A T E

  26. Which are distributed and undistributed? • All S is P. • Subject is distributed. Predicate is undistributed. • No S is P. • Subject and predicate are distributed. (Remember: No S is P = All S is not P.) • Some S is P. • Subject and predicate are undistributed. • Some S is not P. • Subject is undistributed. Predicate is distributed.

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