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Demonstrating the validity of an argument using syllogisms

Demonstrating the validity of an argument using syllogisms. A SYLLOGISM is a valid argument – usually a basic pattern of reasoning that is frequently used. The following are examples of syllogisms. MODUS PONENS P Q P  Q. DISJUNCTIVE SYLLOGISM P Q ~ P  Q.

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Demonstrating the validity of an argument using syllogisms

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  1. Demonstrating the validity of an argument using syllogisms

  2. A SYLLOGISM is a valid argument – usually a basic pattern of reasoning that is frequently used. The following are examples of syllogisms. MODUS PONENS P Q P  Q DISJUNCTIVE SYLLOGISM P Q ~ P  Q MODUS TOLLENS P Q ~ Q  ~ P   < An argument can be analyzed two premises at a time.

  3. p r ~ r p s < s  q q

  4. ~ p Modus Tollens p r P Q ~ r ~ Q p s <  ~ P s  q Each premise is a piece of information. The first two premises yield a new piece of information, ~p. This can now be used with the third premise. q

  5. p r ~ p ~ r p s < s  q q

  6. s p r Disjunctive Syllogism ~ p P Q < ~ r ~ P p s < Q s  q q

  7. p r ~ p ~ r s p s < s  q q

  8. q Modus Ponens p r P Q ~ p ~ r s P p s <  Q s  q q

  9. p r ~ r p s < The premises will not necessarily be arranged in order, with premises that fit together placed together. s  q q

  10. p s < p r s  q ~ r ~ r p s < s  q p r q

  11. p s p s < < s  q s  q ~ r ~ r p r p r q

  12. p s < s  q ~ r Number the premises for reference. p r q

  13. 1. s  q 2. ~ r 3. p s < 4. p r q

  14. 1. s  q 2. ~ r Move the conclusion 3. p s < 4. p r q q

  15. 1. s  q 2. ~ r 3. p s < 4. p r q q

  16. 1. s  q Modus Tollens P Q 2. ~ r ~ Q 3. p s <  ~ P 4. p r Every step of the process must be justified. The reason for writing statement 5 is clear when you combine statements 2 and 4 using the syllogism Modus Tollens. 5. ~ p 2 , 4 , MT q

  17. 1. s  q 2. ~ r 3. p s < 4. p r 5. ~ p 2 , 4 , MT q

  18. 1. s  q Disjunctive Syllogism P Q < 2. ~ r ~ P 3. p s < Q 4. p r 5. ~ p 2 , 4 , MT 6. s 3 , 5 , DS q

  19. 1. s  q 2. ~ r 3. p s < 4. p r 5. ~ p 2 , 4 , MT 6. s 3 , 5 , DS q

  20. 1. s  q Modus Ponens P Q 2. ~ r P 3. p s <  Q 4. p r 5. ~ p 2 , 4 , MT 6. s 3 , 5 , DS 7. q 1 , 6 , MP q

  21. 1. s  q 2. ~ r You are finished when you reach the given conclusion ( in this case “q” ). There is a reason given for each statement that is deduced from the given premises. 3. p s < 4. p r 5. ~ p 2 , 4 , MT 6. s 3 , 5 , DS 7. q 1 , 6 , MP q

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