A logically correct deductive argument is said to be valid.

A valid argument is one in which the conclusion must be true — can’t be false — if the premises are true. (Note that the premises don’t have to be actually true for an argument to be valid.)

Some argument forms — ways of constructing arguments — guarantee validity. Arguments that are put together correctly have valid argument forms, and are guaranteed to be valid. Modus Ponens, Modus Tollens, Hypothetical Syllogism, Disjunctive Syllogism, are examples of valid forms. If an argument has a valid form, it is valid (logically correct). You can prove that an argument is valid simply by showing that it has a valid form.

On the other hand, some argument forms guarantee invalidity. Arguments that have invalid forms are guaranteed to be invalid. If the form is invalid, the conclusion does not follow from the premises, even if the premises and conclusion are all true. Affirming the Consequent and Denying the Antecedent are examples of invalid forms. If an argument has an invalid form, it’s invalid. You can prove that an argument is invalid simply by showing it has an invalid form.

Suppose, however, that you’re an ordinary person on the street. You  haven’t studied valid and invalid forms, or techniques of symbolic logic (like truth tables or truth trees). Is there any intuitive way you as a non-specialist can determine if an argument is invalid (not logically correct)?

The answer is YES. You can show an argument is invalid by showing that its form is invalid. You can show its form is invalid by showing that the form can lead to an obviously false conclusion when the premises are obviously true.

To show invalidity, just do the following:

1.      Determine the form of the argument whose validity is in question.

2.      Attempt to construct another argument of the same form with obviously true premises and an obviously false conclusion.

3.      If you succeed, you have shown the original argument invalid.

This method works because a valid argument form guarantees validity, and validity means it’s impossible for the conclusion to the false if the premises are true. If the premises had been true, and the form valid, the conclusion could not have been false. (The argument would have been sound: valid, with all true premises.) So the very fact that the form allows true premises and a false conclusion shows it can’t be a valid form. And if the form of an argument is invalid, the argument is invalid.

Example:

You are confronted with the following argument:

“If I were the President, I’d be famous. So I’m not famous, since I’m not the President.”

The conclusion indicator “so” tells you the conclusion is “I’m not famous”.

So the argument is:

Premise:        If I were President, I’d be famous.

Premise:        I’m not President.

Conclusion:    I’m not famous.

The argument obviously is an instance of the invalid form Denying the Antecedent, but we’re supposing you don’t know that.

Step 1: Determine the form of the argument whose validity is in question.

Premise:        If A, then B.

Premise:        Not A (or “A is not the case”).

Conclusion:    Not B (or “B is not the case”).

Step 2: Now that you’ve extracted the form, try to construct an argument of the very same form with all true premises and a false conclusion. For example:

Premise:        If Robert Redford were  President, he’d be famous. (true)

Premise:        Robert Redford is not President. (true)

Conclusion:    Robert Redford is not famous. (false)

Note that the premises are true, but the conclusion is false (Robert Redford is famous).

The following argument would work too:

Premise:        If I am decapitated, I’ll die. (true)

Premise:        I won’t be decapitated. (very probably true)

Conclusion:    I won’t die. (alas, false)

This method of showing invalidity is called the Refutation by Logical Analogy, and people use it all the time (“That’s just like arguing …”). The neat thing is, it really does show invalidity!

Try it yourself.

Use the method of Refutation by Logical Analogy to show the invalidity of the following arguments:

1.      All Presidents live in the White House. Bill Clinton lives in the White house, so Bill Clinton is the President.

2.      If there’s a government conspiracy to cover up the existence of extraterrestrial visitors, then the government would deny any knowledge of UFOs. The government does deny any knowledge of UFOs. This proves there is a conspiracy to cover up the existence of extraterrestrial visitors.

3.      All persons have skin. Howdy Doody isn’t a person, though, so Howdy Doody doesn’t have skin.