CooperToons HomePage Merry History Dept. of Education CooperToons Books Previous Next

Socrates

 

"If-Then" Tables Explained
Sans Doute1

If there's one thing that causes students of philosophy to gnash there teeth and tear their hair, it's the "If-Then" Truth Table, or as the hot-shots call it, Material Implication. At first glance it looks simple:

Truth Table: If-Then Statements
A B A → B
TRUE TRUE TRUE
TRUE FALSE FALSE
FALSE TRUE TRUE
FALSE FALSE TRUE

This table has been used - whether knowingly or not - whether properly or not - for thousands of years.

After all, this table lets us analyze sentences like.

If George Washington was the First President of the United States, then he left office before Thomas Jefferson became President.

For instance, if we let:

GW was the First President of the United States A
GW left office before TJ became President B

... then we see immediately:

A ≡ TRUE
B ≡ TRUE

... and since:

A ≡ TRUE and B ≡ TRUE

... then

A → B

... has assigned values:

TRUE → TRUE

... which according to the table is TRUE.

So we can be confident that the profound pronouncement:

If George Washington was the First President of the United States, then he left office before Thomas Jefferson became President.

... is TRUE.

And consider this statement:

If George Washington was the Third President of the United States, then he left office after John Adams became President.

... which has the values of the IF and Then parts as:

FALSE → FALSE.

Now notice we are not saying George was the third president or that he left officer after John Adams. But we are saying IF George was the third president then he WOULD HAVE have left office after John was president.

We see then that the

FALSE → FALSE.

... is indeed TRUE just as the table says.

Then we can say:

If George Washington was the Third President of the United States, then he would have retired to Mount Vernon.

... which has the assignments of the IF-THEN parts as:

FALSE → TRUE.

Once more we see that the overall statement is TRUE. Again as the table stipulates.

It's only if we say something like:

If George Washington was the First President of the United States, then he would have taken office after John Adams.

... with it's

TRUE → FALSE.

... assignment that we have an overall FALSE statement. So we see the Truth Table that we have above seems to work fine.

So, what you ask querulously, is the problem?

Well, take a look at this statement.

If George Washington was the King of France, then C. S. Lewis joined the Barnum and Bailey Circus.

Here we see this is an "If-Then" statement where:

FALSE → FALSE

But look at the Truth Table! According to the table this statement is TRUE!

And you can come up with all sorts of nonsensical IF-THEN Statements which are nonetheless TRUE:

If 1 + 1 = 2, then the Pope is the Pontifex Maximus.

If Napoleon was Prime Minister of England, then Neil Armstrong was the first man to walk on the moon.

If George Custer won at the Little Big Horn, then Grover Cleveland was a singing waiter at Delmonico's.

And yet some of the greatest philosophical minds in history have used this table. And those that don't use it turn out to be weirdos, whackos, and oddballs. So we would you like to see why this Truth Table is indeed correct.

I thought you would, as Captain Mephisto said to Sydney Brand. And for a true Captain Mephistophilian explanation where you finally can say "I understand", just click here.