Deduction and Induction Elementary deduction, my dear Watson…
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Transcript of Deduction and Induction Elementary deduction, my dear Watson…
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 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 ofInductive 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 bothfiction and non-fiction. After all, Sartreand Rousseau both did.
Deduction
Valid/ invalidSound/ unsound
Argument from mathematics
Argument from definition
Categorical Syllogism
Hypothetical Syllogism
Disjunctive Syllogism
Induction
Strong/ badStrong/ weak Cogent/ uncogent
PredictionCausal inferenceArgument by Analogy
Inductive Generalization
Appeal to AuthorityArgument from Signs