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 mortalSocrates is a manSo Socrates is mortal.

Two kinds of Goodness for Deductive arguments

Spiders are reptiles, andAll reptiles are democrats, soSpiders are democrats.

Deduction

Valid or Invalid

Sound or Unsound

Valid: An argument is valid when it isimpossible for the premises to all betrue 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, andb) has all true premises

What is the truth-value of the conclusionof 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, andAll reptiles are democrats, soSpiders are democrats.

Valid, but unsound

Two kinds of Goodness forInductive 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 beman, 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’sprobably 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 MathematicsArgument from Definition

Categorical SyllogismHypothetical 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 ofInductive Argument

Prediction

Argument from Authority

Argument by Analogy

Inductive GeneralizationCausal 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 bothfiction and non-fiction. After all, Sartreand Rousseau both did.

Deduction

Valid/ invalidSound/ unsound

Argument from mathematicsArgument from definitionCategorical Syllogism

Hypothetical SyllogismDisjunctive Syllogism

Induction Strong/ bad

Strong/ weak Cogent/ uncogent

PredictionCausal inferenceArgument by AnalogyInductive GeneralizationAppeal to AuthorityArgument from Signs