How to tell invalid from valid arguments

An example of an invalid argument:

All men are moral.
Socrates is moral.
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Socrates is a man.

An example of a valid argument:

All men are moral.
Socrates is moral.
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Socrates is a man.

Q.E.D.

The easiest way to tell a valid argument is to check if it ends in Q.E.D.. Formally speaking, Q.E.D. is a function from arguments to valid arguments. Therefore if an argument ends in Q.E.D., it is valid.

This does not mean that if an argument does not end in Q.E.D., it is not valid. Many arguments - perhaps as many as an infinite number of them - do not end in Q.E.D., yet are valid. Aristotle gave several examples of valid arguments, and he lived before the properties of Q.E.D. were even discovered.

If an argument doesn't end in Q.E.D., determining whether it is valid is a complicated, multi-factored affair involving strokes, arrows and tonks. You pretty much have to be an expert to figure it out. Therefore, if matters of substantial consequence depend on the validity of the argument, hire a professional logician. Most professional logicians charge reasonable rates and can figure out validity in an hour or less. There's a directory here.

A note of warning: here are some logicians who are specialists, possessing expertise in things you've probably never heard of, like "many-valued logic" and "second order logic". They charge more per hour than ordinary logicians, but their specialized skills are not necessary for most kinds of argument. Better to be safe and call a regular logician first. They can always refer you to a specialist if they don't have the expertise for the task.