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Socrates

 

"If-Then" Tables Explained
Sans Doute

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.

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!

But hold on! Some of the greatest 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.