Arguments: Validity and Soundness

An argument is a set of sentences consisting of premises and a conclusion, where the premises are meant to support the conclusion.

Premise 1
Premise 2
Premise 3
…
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Conclusion
 

Terminology:

"Valid" Arguments:

An argument is valid if and only if it is impossible for the premises to be true and the conclusion false.

"Sound" Arguments:

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

So, there are two ways for an argument to be bad:

(i) One (or more) of the premises could be false
(ii) The premises could fail to support the conclusion. (There could be some gap in the reasoning).

Examples:

Example 1:
Premise 1 I wear glasses.
Premise 2 I am a philosophy instructor.
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Conclusion Therefore, at least one philosophy instructor wears glasses.

This is a good argument. It is valid and since the premises are true, it is also sound.

Example 2:
Premise 1 I am the star player on Carolina's basketball team
Premise 2 Everyone on Carolina's basketball team is over 7 feet tall.
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Conclusion Therefore, I am over 7 feet tall

This is a valid argument, but since the premises are false, it is not sound.

Example 3:
Premise 1 If my car's battery is dead, then my car won't start.
Premise 2 My car won't start.
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Conclusion Therefore, my battery is dead.

This argument is not valid (and so, even if the premises are true, it is also not sound). It's possible that both of the premises are true, but the conclusion is false. (For example, if there's a problem with the starter the car could fail to start even though the battery is not dead.)