# Deduction and Induction Elementary deduction, my dear Watson…

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Deduction and Induction Elementary deduction, my dear Watson…

Induction: the type of argument in which the conclusion is supposed to follow from the premise(s) with probability. John is a Republican, so he probably voted for Bush.

Deduction: the type of argument in which the premises are meant to be providing such solid support that the conclusion should be inescapable.

Deduction: the type of argument in which the conclusion is supposed to follow from the premise(s) with necessity. All men are mortal Socrates is a man So Socrates is mortal.

Two kinds of Goodness for Deductive arguments Spiders are reptiles, and All reptiles are democrats, so Spiders are democrats.

Deduction Valid or Invalid Sound or Unsound

Valid: An argument is valid when it is impossible for the premises to all be true and the conclusion be false. Jones is a citizen because she can vote, and only citizens can vote.

If the premises can all be true and the conclusion false, it is invalid. If Ronald Reagan was assassinated, then he’s dead. So he must have been assassinated, since he’s dead.

SOUND: An argument is sound if it a)is valid, and b) has all true premises What is the truth-value of the conclusion of a sound argument? If Lincoln was assassinated, he’s dead. And he was, so he is.

UNSOUND: An argument is unsound if it is invalid Or not all its premises are true or both of the above

Spiders are reptiles, and All reptiles are democrats, so Spiders are democrats. Valid, but unsound

Two kinds of Goodness for Inductive arguments Every Secretary of Defense so far has been a woman, so the next one will probably be a woman too.

Induction Strong or Weak Cogent or Uncogent

Strong: An argument is strong if it is more likely that the conclusion would be true, given the premises, than that it would not be. The next President is probably going to be man, since all Presidents so far have been.

Weak: an argument is weak if it is not strong, I.e., if it is not more likely that the conclusion would be true given the premises, than that it would not be. Turner is an orthodontist, so he’s probably homeless.

COGENT: An argument is cogent if a)It is strong, and b)All its premises are true Today is Labor Day, so probably all kids will head back to school tomorrow, since Labor Day is usually the end of summer break.

UNCOGENT: an argument is uncogent if it is weak Or not all its premises are true. Or both of the above.

Five Typical Kinds of Deductive Argument Argument from Mathematics Argument from Definition Categorical Syllogism Hypothetical Syllogism Disjunctive Syllogism

Argument from mathematics: involves computation Joe must own at least ten dvd’s; he’s been buying one a week since he got that dvd player in June.

Argument from definition: word meaning Charley is an ignoramus, so he doesn’t know anything

Categorical syllogism: two premises plus conclusion concerns categories (names of classes) includes quantifying words “all” “no” “some” All cats are mammals, and no mammals are fish, so no cats are fish.

Disjunctive syllogism: “either…or” Either we’ll get Chinese or Thai. But Bangkok Café is closed today, so we’ll have to get Chinese.

Hypothetical syllogism: “if…then” If Washington was assassinated, he’s dead. But he wasn’t, so he’s not.

Six Typical Kinds of Inductive Argument Prediction Argument from Authority Argument by Analogy Inductive Generalization Causal Inference Argument from Signs

Prediction: reasoning that something will happen in the future The Orioles will probably come in last place this year because they stink.

Causal inference: from effect to cause or from cause to effect (turns on knowledge of cause and effect) Smith should stop smoking cigarettes, especially since there’s a history of heart disease in her family.

Argument from authority: conclusion is based on someone’s word Senator Leahy should probably go f… himself since Vice-President Cheney said he should.

Argument from signs: conclusion is based on a sign This must be his office; it says 238 right there on the door.

Argument from analogy: turns on a similarity between things The world is like a huge machine made up of smaller machines, and since machines have intelligent creators, the world must have one too.

Inductive generalization: moves from fewer to more Philosophers always write both fiction and non-fiction. After all, Sartre and Rousseau both did.

Deduction Valid/ invalid Sound/ unsound Argument from mathematics Argument from definition Categorical Syllogism Hypothetical Syllogism Disjunctive Syllogism

Induction Strong/ bad Strong/ weak Cogent/ uncogent Prediction Causal inference Argument by Analogy Inductive Generalization Appeal to Authority Argument from Signs