Monday, November 8, 2010

Evaluating Arguments

Do the premises support the conclusion?

All dogs have four legs.
A dog is a mammal.
Therefore, a human has four legs.


Absolute certainty

New premises do not affect
the validity of the argument and the
certainty of the conclusion

probability, likelihood


New premises could affect the strength of the argument and the probability of the conclusion.

An argument is VALID if the truth of all of its premises force the truth of the conclusion. If the premises are true, the conclusion must be true.

True premises & true conclusion
All animals that suckle their young are mammals.
Whales suckle their young.
Whales are mammals.

Validity doesn’t guarantee the truth of either the premises or the conclusion. There are passages with true premises and true conclusions that are not valid.

All maple trees lose their leaves in the winter.
Pine trees do not lose their leaves in the winter.
All fish live in water.

It is possible to have a valid argument with false premises:

True premises and true conclusion
True premises and false conclusion
False premises and true conclusion
False premises and false conclusion

False premises, false conclusion                      False premises, true conclusion
All insects have three eyes.                                   All fish are mammals.
A cockroach is an insect.                                       All whales are fishes.
Therefore, cockroach has three eyes.                  All whales are mammals.

Validity guarantees that if the premises are true, then the conclusion must be true. 

An argument is deductively invalid if it is possible for the conclusion to be false even though the premises are true.

True premises, false conclusion
Columbus is the capital of Ohio.
Sacramento is the capital of California.
Mike is fourteen feet tall.

An argument is sound if it is valid and its premises are true.

Greg is taller than Joe.
Joe is taller than Mike.
Therefore, Greg is taller than Mike.

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