Ensign Steve

"If the moon is made of green cheese, then I'm the king of France."

I remember hearing this claim in logic class, but I can't remember the point of it. It's an if/then statement, but the if part will always be untrue, so the then part is irrelevant. Does this claim have truth-value? If so, what is it? If I remember correctly, logicians are in disagreement about the answers to those last two questions, but the debate is entirely academic.

Is there a point to this type of claim? Other than causing mischief: "If you can drink that whole case of beer without getting sick, then I'll give you $100." Or making outrageous claims without having to back them up: "If god exists, then you'll have all the evidence you need when you die and go to hell."

I have been mulling over it since I read these two comments by Scorpion in this thread:

Note: I'm not picking on Scorpion. He himself acknowledges that his claim was an "easy way out."

Keith Russell

I think the point of such statements is to show the outrageousness of the first statement, by claiming that if it is true, then other, equally outrageous statements could also be true.

From Indiana Jones and the Last Crusade (available for the first time on DVD in November!):

"But if you're a Scottish lord, I'm Mickey Mouse!"

K

ex-xian

It's an example of one of the ways that a material implication can be a true statement. Logically, an if-then statement doesn't necessarily imply causality.

To say "If S, then P" <=> ~(S & ~P). Or, it is not the case that S is true and P is not. On a truth table, a material implication works like this:

S P S => P
-----------------
T T T
F T T
F F T
T F F

As you can see, the only case that an implication is false, is if the antecedent is true and the consequence if false.

If I say "If the moon is made of green cheese, then I'm the king of France," both parts are false, therefore the whole statement is true.

With regard to Scorpion's statement, what happens to the left side of the statement isn't what is important in isolation. It is possible for the left side to be true or false and the statement to be true based on the truth value of the right side.

edit to add:
For some reason, the truth table looks different after the post is made. There should be 3 columns, with one column of T's and F's corresponding to the S, the P, and the S=>P.

John Page

The claim is false. What the moon is made of does not affect the succession to France's throne. Even if the protagonist is the KofF, the causal relationship proposed does not exist.

Cheers, john

ex-xian

Not so. A material implication doesn't imply causality.

"If the moon is made of green cheese, then I am the king of france."

If the statement is false, then the moon is made of green cheese, and I am not the king of france. Obviously, the moon is not made of green cheese, therefore, I am not the king of france.

Scorpion

Hi,

Here's an excellent page explaining the implication paradoxes.

The gist of it is summed up like this:

-S-

John Page

But isn't "if" treated as "if and only if"? I can pretty much guarantee that changing the material that the moon is made of does not affect who is the King of France.

With all due respect, I think your truth table has analyzed the truth functionality of the statement "The moon is made of green cheese and I am the King of France".

Irrespective of truth table analysis the claim is false when tested against reality - the reason being you will discover contradictory results such that "For some moons not made of green cheese I am the King of France and for some moons not made of green cheese I am not the King of France". This is like taking observations to produce the middle two lines of your analysis as contradictory results. Then again, who said logic was reasonable?

Cheers, John

Dr. Retard

No, it's not "if and only if". It's "if". They're quite different. One's a conditional, one's a biconditional. Imagine if Queen had released "Cycle Race"!

And even "if and only if" statements have jack to do with causality. "'2+2=4' if and only if 'if p, then not-not-p'" is a true biconditional. But the antecedent and consequent don't bear any causal relation to each other.

Causality, whatever it is, isn't borne by some logical operator.

John Page

How about Proposition X "If this proposition is false another completely unconnected proposition will be true". According to your analysis, Proposition X can be true!

The KofF proposition claims "I am the King of France", not "I could be the King of France".

Try this in a court of law - if the evidence is not causally connected to to the claim it is immaterial - as in "If the moon is made of green cheese, ex-xian is a murderer". You should be aquitted, yes?

BTW, I think Keith hit the nail on the head on the "point" of proposing such a claim.

Cheers, John

ex-xian

An "if, then" is a material implication or a conditional, the truth table works as I illustrated above. An "if and only if" statement is known as a material equivalence or a biconditional. A biconditional works both ways, the truth table for it is:
S--P--S<=>P
T--T----T
T--F----F
F--T----F
F--F----T

Your examples are perfectly illustrate the paradoxes in implication. It implies things that seem intuitively untrue.

The website that Scorpion referenced explains the conditional better than I did before. I suggest you read it to get a better understanding of how the conditional works.

edit to format truth table