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Demonstrating the validity of an argument using syllogisms

Understand the validity of syllogisms - basic patterns of reasoning - with examples like Modus Ponens, Disjunctive Syllogism, and Modus Tollens. Explore how to analyze arguments step by step in the context of premises. Learn the art of justifying each logical step to reach conclusions effectively.

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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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