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.
------------------
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.

The formalism fetish

The legal world is easily impressed by formalism.

For example, suppose a judge is called upon to decide what constitutes negligence, and says:

"To determine whether an act is negligent, we must balance the costs to the defendant of ensuring that no harm comes about against the probability of harm occurring and the magnitude of the possible harm."

I would say that's a sensible judge. So would the legal community.

But if the judge used symbols to represent the concepts in that statement, and specified that we take the product of the probability of the harm occurring and the magnitude of the possible harm, the reaction would be totally different.

I would still say that's a sensible judge. The legal world, however, would say: "OH MY GOD! WE CAN USE SYMBOLS TO REPRESENT A COMMON SENSE CONCEPT! THIS GUY IS THE MOST BRILLIANT JURISPRUDE IN THE WORLD! LET'S NAME A BODY PART AFTER HIM! LET'S FOUND AN INFLUENTIAL SUBFIELD OF LAW ON THE BASIS OF THIS FORMULA, WHICH WILL USE A CLOAK OF FORMALITY TO DISGUISE THE FACT THAT IT BEARS ONLY A PARTIAL AND TENUOUS RELATIONSHIP TO REALITY!"


















The body part I'm referring is, of course, the hand; the formula is B < PL; and the pseudodiscipline is Law and Economix. The lesson: If you want to really impress legal professionals, dress up an ordinary insight in formal clothing.

EDIT (April 5): ANNOUNCING the Law Formalization Project; wherein from time to time I suggest ways to formalize legal ideas.