Deduction and Induction

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Deduction and Induction
Elementary deduction, my dear Watson
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Induction the type of argument in which the
conclusion is supposed to follow from the
premise(s) with probability.
John is a Republican, so hes probably going to
vote for Bush.
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Deduction the type of argument in which the
premises are meant to be providing such solid
support that the conclusion should be
inescapable.
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Deduction the type of argument in which the
conclusion is supposed to follow from the
premis(es) with necessity.
All men are mortal Socrates is a man So Socrates
is mortal.
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Two kinds of Goodness for Deductive arguments
Spiders are reptiles, and All reptiles are
democrats, so Spiders are democrats.
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Deduction
Valid or Invalid
Sound or Unsound
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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.
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If the premises can all be true and the
conclusion false, it is invalid.
If Ronald Reagan was assassinated, then hes
dead. So he must have been assassinated, since
hes dead.
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• SOUND An argument is sound if it
• is valid, and
• b) has all true premises

If Lincoln was assassinated, hes dead. And he
was, so he is.
What is the truth-value of the conclusion of a
sound argument?
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UNSOUND An argument is unsound if it is
invalid Or not all its premises are true or
both of the above
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Spiders are reptiles, and All reptiles are
democrats, so Spiders are democrats.
Valid, but unsound
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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.
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Induction
Strong or Weak
Cogent or Uncogent
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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.
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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 hes probably
homeless.
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• COGENT An argument is cogent if
• It is strong, and
• All its premises are true

This week is the Republican Convention, so
probably Cheney will give a speech, since the
Vice-President usually gives one.
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UNCOGENT an argument is uncogent if it is
weak Or not all its premises are true. Or both
of the above.
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Five Typical Kinds of Deductive Argument
Argument from Mathematics
Argument from Definition
Categorical Syllogism
Hypothetical Syllogism
Disjunctive Syllogism
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Argument from mathematics involves
computation   Joe must own at least ten dvds
hes been buying one a week since he got that
dvd player in June.
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Argument from definition word
meaning Charley is an ignoramus, so he doesnt
know anything
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Categorical syllogism concerns
categories Includes a quantifying word all
no some All cats are mammals, and no
mammals are fish, so no cats are fish.
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Disjunctive syllogism eitheror   Either
well get Chinese or Thai. But Bangkok Café is
closed today, so well have to get Chinese.
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Hypothetical syllogism ifthen   If
Washington was assassinated, hes dead. But he
wasnt, so hes not.
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Six Typical Kinds of Inductive Argument
Prediction
Argument from Authority
Argument by Analogy
Inductive Generalization
Causal Inference
Argument from Signs
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Prediction reasoning that something will
happen in the future   The Orioles will probably
come in last place this year because they stink.
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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 theres a history of heart
disease in her family.
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Argument from authority conclusion is based on
someones word   Senator Leahy should probably
go f himself since Vice-President Cheney said
he should.
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Argument from signs conclusion is based on a
sign   This must be his office it says 238
right there on the door.
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Argument from analogy turns on a
similarity   The world is like a huge machine
made up of smaller machines, and since machines
have intelligent creators, the world must have
one too.
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Inductive generalization moves from fewer to
more   Philosophers always write both fiction and
non-fiction. After all, Sartre and Rousseau both
did.