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Rules of the Syllogism

Rules of the Syllogism. First Rule of Quality (Q1). There can be only one negative premise. No B are L. negative No S are B. Negative!! No S are L. This is a violation of Q1. 2 nd Rule of Quality.

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Rules of the Syllogism

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  1. Rules of the Syllogism

  2. First Rule of Quality (Q1) There can be only one negative premise. No B are L. negative No S are B. Negative!! No S are L. This is a violation of Q1.

  3. 2nd Rule of Quality If there is a negative premise, the conclusion must be negative. If the conclusion is negative, one premise must be negative. Some M are not W. negative Some O are W. positive Some M are O. Positive This is a violation of Q2.

  4. Distribution • Remember distribution? • Distribution refers to terms. Any term that refers to every single member of a class is distributed.

  5. 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

  6. 1st Rule of Distribution • The middle term must be distributed at least once. All B are L. B is universal and distributed. No S are B.B is a negative predicate and distributed. No S are L.

  7. Are the middle terms distributed? • All A is B. • All C is B. • All A is C. • B is never distributed. A and C refer to different parts of the class B, but do not intersect. There is no common ground. AAA-2 syllogisms are invalid. • This is called the fallacy of the undistributed middle.

  8. All Communists are believers in heavy taxes.Senator Jones is a believer in heavy taxes.Senator Jones is a Communist.

  9. AAA-2 commits a D1 violation • All teenagers are bipedal. • All ostriches are bipedal. • Therefore, all teenagers are ostriches. • S=teenagers • P=ostriches • M=bipedal creatures

  10. Is this a D1 violation? • Some M is P. • All M is S. • Some S is P. • M is distributed in the minor premise. • An IAI-3 syllogism does not commit a D1 violation.

  11. IAI-3 is valid. • Some English teachers are ex-military. • All English teachers are high-school graduates. • Some high-school graduates are ex-military. • M=English teachers • P=ex-military • S=high school graduates

  12. 2nd Rule of Distribution • If a term is distributed in the conclusion, it must be distributed in the premise in which it occurs. • If the major term is distributed in the conclusion, it must be distributed in the major premise. If the minor term is distributed in the conclusion, it must be distributed in the minor premise.

  13. Fallacy of the Illicit Major • If the major term in the conclusion is distributed, the major term in the major premise has to be distributed, too. • If the major term in the conclusion is distributed and the major term in the major premise is undistributed, it commits the fallacy of the illicit major.

  14. D2 violation (major) • All robots are machines. • No humans are robots. • No humans are machines. • The major term is distributed in the conclusion, but not in the major premise. • The AEE-1 syllogism commits the fallacy of the illicit major.

  15. AEE-1 syllogisms are invalid. • All dogs are animals. • No cats are dogs. • No cats are animals. • P=animals • S=cats • M=dogs

  16. Fallacy of the Illicit Minor • If the minor term in the conclusion is distributed, the minor term in the minor premise has to be distributed, too. • If the minor term in the conclusion is distributed and the minor term in the major premise is undistributed, it commits the fallacy of the illicit minor.

  17. D2 violation (minor) • All terrorists are extremists.All extremists are radicals.Therefore, all radicals are terrorists. • Radicals is distributed in the conclusion, but not in the minor premise. • The AAA-4 syllogism is a fallacy of the illicit minor.

  18. Fallacy of the illicit minor • All whales are mammals.All mammals are animals.Therefore, all animals are whales. • S=animals • P=whales • M=mammals

  19. The easiest way to handle distribution. When you get a syllogism to analyze, figure out the distribution of each term FIRST.

  20. Some F are not W. • All F are S. • Some S are not W. In the major premise, F is undistributed and W is distributed. In the minor premise, F is distributed and S is undistributed. In the conclusion, S is undistributed and W is distributed.

  21. Some F are not W. • All F are S. • Some S are not W. • The middle term is distributed at least once, so D1 is okay. • S is undistributed in the conclusion, so we ignore it. W is distributed in the conclusion, so it must be distributed in the major premise. It is. D2 is okay.

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