Deductive Arguments

1. Deductive Arguments Raphael Christopher

2. Deductive Arguments • reaching an answer or a decision by thinkingcarefully about the known facts.

3. Deductive Arguments • The premise is true so the arguments must be true too • Properly formed deductive arguments  valid arguments • Effective way to organize arguments (even premises are uncertain)

4. Modus ponens • The mode of putting: put P, get Q • Explain and defend both of its premises If P then Q.  P. Therefore, Q.

5. Modus ponens (Examples)

6. Modus ponens (Examples) • “If she looks too close, then she will see less/little”  she looks too close, therefore she looks a little/less. • “If Driver on cellphones do have more accidents, then driver should be prohibited from using them”  Drivers on cellphones do have more accidents, therefore driver should be prohibited from using cellphones.

7. Modus tollens • The mode of taking: take Q, take P • Denying the consequent If P then Q.  NotQ. Therefore, notP.

8. Modus tollens (Examples) “the disappearance of a famous racehorse the night before a race and the murder of the horse’s trainer.” • “If the visitor were stranger, then the dog would have barked.”  The dog did not barked. Therefore the visitor was not stranger.

9. Hypothetical Syllogism • Valid as long premises form “if P then Q” • Q is the consequent If P then Q. If Q then R.  Therefore, if P then R

10. Hypothetical Syllogism (Examples) • “if you study hard, then you will pass this course”. • “If you pass this course, then you will be successful”.  therefore, if you study hard, then you will be successful

11. Disjunctive Syllogism • We only can choose P or Q (not both) • If we choose the one premises, assume others wrong P or Q.  NotP. Therefore, Q.

12. Disjunctive Syllogism (Examples) • Either we hope for progress by improving morals or we hope for progress by improving intelligence. • We can’t hope progress by improving morals  Therefore, we must hope for progress by improving intelligence.

13. Dilemma • Hedgehog’s dilemma • The option have unpleasant consequences P or Q. If P then R If Q then S  Therefore, R or S.

14. Dillema (Examples) • Either we become close to each others or we stand apart. • If we become close to each others, we suffer conflict and pain. • If we stand apart, we’ll be lonely.  Therefore, either we suffer conflict and pain or we’ll be lonely

15. Reductio ad absurdum • Reduction to Absurdity • From the assumption we’d have to conclude Q  show the Q is false. • Final Conclusion P must be true To prove P. Assume the opposite: not P.

16. Reductio ad absurdum (Examples) • Prove: The world does not have a Creator in the way a house does • Assume: The world does have a Creator in the way a house does. The Creator is imperfect  but: God cannot be imperfect  The world does not have a creator in the way a house does

17. Deductive Arguments in several steps • Combination from the basic forms • Last inferences: we can eliminate all other factors, and choose the right one (extended disjunctive syllogism)

18. Example • Holmes remarked that Watson visited certain post office that morning, and furthermore he sent off a telegram.

19. Obesrvation • Watson has a little reddish mold on his boots. • Watson wrote no letter this morning • Watson already has a drawer full of stamps and cards

20. Modus Ponen • If Watson has a little reddish mold on his boots, then he has been to the wigmore street office this morning.  Watson has a little reddish mold on his boots, therefore he has been to the wigmore street office this morning. • If Watson has been to the wigmore Street Post Office this morning, then he either mailed a letter, brought stamps or cards, or sent a wire  Watson has been to the wigmore Street Post Office this morning, therefore he either mailed a letter, brought stamps or cards, or sent a wire.

21. Modus Tollens • If Watson had gone to the post office to mail a letter, he would have written the letter this morning, the he would written the letter this morning.  Watson didn’t wrote the letter this morning, therefore Watson didn’t go to the post office to mail a letter. • If Watson had gone to the post office to buy stamps and cards, he would not already have a drawer full of stamps and cards.  Watson have a drawer full of stamps and cards, therefore he didn’t go to post office to buy stamps and cards.

22. extended disjunctive syllogism • Watson has been to the wigmore Street Post Office this morning, therefore he either mailed a letter, brought stamps or cards, or sent a wire. • Watson did not mail a letter. • Watson did not buy a stamp or cards. • Therefore, Watson sent a wire at the wigmore street post office this morning.

23. References Weston, A. (2009). A rulebook for arguments. Indianapolis, Ind: Hackett Pub. Co. http://changingminds.org/disciplines/argument/syllogisms/modus_tollens.html https://dictionary.cambridge.org/dictionary/english/deductive

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