# Deductive Arguments Raphael Christopher Deductive Arguments reaching an

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Deductive Arguments Raphael Christopher

Deductive Arguments • reaching an answer or a decision by thinking carefully about the known facts.

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)

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

Modus ponens (Examples)

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.

Modus tollens • The mode of taking: take Q, take P • Denying the consequent If P then Q. Not Q. Therefore, not P.

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.

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

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

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

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.

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

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

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.

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

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)

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

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

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.

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.

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.

• 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/eng lish/deductive References

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