Valid+and+Invalid+Arguments

Valid Arguments

__An argument is **valid**__ __if:__

The premises **necessarily lead to the conclusion** Or When all the premises are true, the conclusion **must be true** Or It is impossible to come to a false conclusion when all the premises are true

__Examples__ Either P or Q. Not P, therefore Q. Either Jim or Bob will win the arm wrestle. Jim lost. Therefore Bob won.

If P then Q. P, therefore Q. If Matthew pays the fine, he will get his car back. Matthew pays the fine, therefore he gets his car back.

If P then Q. If Q then R. Therefore, If P then R. If Larry gets the job, he will buy himself a new car. If Larry buys himself a new car, he will need car insurance. Therefore, if Larry gets the job, he will need car insurance.

Incidentally – an argument can be untrue and still be valid, if all the premises logically lead to the conclusion, so:

All cats are reptiles. Bugs Bunny is a cat. Therefore Bugs Bunny is a reptile.

…is absolutely valid, but it isn’t **sound** (a sound argument is both true and valid)

Invalid Arguments

__An argument is invalid if__

It is **possible for the conclusion to not be true**, even when all the premises are true or If the conclusion may be true, but this is only **weakly related** to the premises.

__Examples__

Jade Goody was a racist. Jade Goody got cancer. Therefore, being a racist is bad. (the conclusion is true, but has got nothing to do with the premises)

I have always had Nokias and they have never broken on me. Therefore, I will always buy a Nokia. (it may be a good reason to buy a Nokia, but it doesn’t **necessarily** follow that all Nokias will have be of a similar quality to the phones you’ve had before)