2 Basic Types of Reasoning • Deductive • Inductive
Deductive Reasoning • Attempts to provide sufficient (or conclusive) evidence for the conclusion • Deductive reasoning can be recognized by the structure of the argument and sometimes by the conclusion offered
Inductive Reasoning • Attempts to make the conclusion probable or likely—evidence is not intended to be conclusive • Typically recognized by probabilistic claims in either or both of the premises and conclusions • Includes statistical and demographic reasoning, predictions, analogies and explanations
Some Examples • Either Bob or Joe was going to win the award. Bob didn’t win, so Joe must have. • I think Wayne committed the murder. He had the motive, he had the opportunity, his bloody glove was found on the scene, and he has no alibi. • I’m sure Alice knows how to swim. After all, most people know how to swim.
More Examples • If you stop smoking, you’ll live longer. Current research shows that on average, non-smokers live 5.5 years longer than smokers. • If we elect another Republican in 2008, the debt will just get worse. The last three Republican presidents we elected all sent the debt sky-high. • Since 2 x 2=4, and 22 is the same as 2 x 2, then 22=4.
Judging Validity • A deductive argument is judged on 2 criteria: validity and soundness • An argument is valid if the truth of the premises would guarantee the truth of the conclusion • An argument is invalid if the conclusion could be false even if all the premises are true • N.B.: This judgment is purely formal—it has nothing to do with the truth of either premises or conclusions
Some Examples • Either the kitchen is on fire, or my pot roast is burning. I can see the kitchen’s not on fire, so my pot roast must be burning. • All CEOs are wealthy. Martin is wealthy, so he must be a CEO. • Only Democrats would vote for Hilary Clinton. Wade is a Democrat, so he must have voted for Hilary.
More Examples • Deceptive advertising is no different from lying. Since lying is wrong, so too is deceptive advertising. • Republicans support tax cuts for the wealthy. George is a Republican, so he must support tax cuts for the wealthy. • Republicans support tax cuts for the wealthy. John supports tax cuts for the wealthy, so he must be a Republican.
Argument Forms There are some argument form that are always valid They are: Modus Ponens, Modus Tollens, Categorical Syllogism, Disjunctive Syllogism, Hypothetical Syllogism and Constructive Dilemma
Argument Forms Continued There are two argument structures that are always invalid. They are: Affirming the Consequent and Denying the Antecedent
Soundness and Unsoundness • A deductive argument is sound is (1) it is valid, and (2) its premises are true. • A deductive argument is unsound if either (1) it is invalid, or (2) it is valid, but at least one premise is false
Some Examples • All men are mortal. Socrates is a man, therefore Socrates is mortal. • Either the moon is made or green cheese, or I’m the Pope. Unfortunately, the moon IS made of green cheese, so I’m sadly not the Pope. • If George Bush was re-elected, our economic depression was sure to continue. Our economic depression continued, so Bush was re-elected. • Only rock stars and athletes are wealthy. Since Ellen is pretty wealthy, she must be either a rock star or an athlete.