Logic Question - If true, then false?

Hi Guys,

I am trying to come up with an example where: "If a statement is true, then it is false" - without it being paradoxical, but I can't think of any (Sunday morning here!)... however I know you can have statements like that.

Can anyone think of a simple (or not) example?

Thanks,

Prime

 

Log in or Sign up to hide all adverts.

It's not possible by the way you describe it. There is a law that was developed by Aristotle, or Plato (my knowlege of philosophers is failing me) that states simply, this:

~(P ^ ~P)

This means that there cannot be a coexistence of a single proposition being both true and false. If something is true, then it is not false by definition. Likewise, if something is false, then it can't true.

Now, on the other hand, a conditional statement doesn't have to be true. So the proposition "If P is true, then P is false" is always a false proposition. However, the actual conditional is still going to be a paradox, even if the proposition as a whole has an actual true/false value.

 

Log in or Sign up to hide all adverts.

Well, it sounds like you're after Epiminides' Liar Paradox (IIRC).

It's usually given in the form: "This statement is false."

 

Log in or Sign up to hide all adverts.

Guys, thanks for the answers. I am not after the liar's paradox, I am trying to find an example of "if something is true, then it is false"; but of course not both at the same time.

I came up with this so far:

Consider the statement, "All things are subjective". If all things were subjective, then nothing would be absolutely true except for that statement, but if that statement is true then it would be false because it is an absolute statement and hence not subjective.

Or perhaps this example: "Nothing is true". If it's true that nothing is true, then it is false because then that very statement would be true. So, if it is true then it must be false. I don't think this is a liar's paradox because it is not self-referential, i.e. its falsity doesn't mean everything is false.

Does that make sense or am I just making my head spin for nothing?

Prime

 

I once tested TRUE=FALSE on a computer algebra system. It's response was "UNKNOWN".

 

If all things except that statement were true, then that would necessarily make that statement false.

Pretty much the same scenario as above.

That's my vote.

Prestilinguidation is not philosophy, and it is certainly not science.
It's nonesense.
It is sometimes interesting nonsense, but nonsense, none the less.

 

How about "I thought I made a mistake but I was mistaken"

Please Register or Log in to view the hidden image!

 

Prine: Here is an example of what I think you are trying to get at:

There is a well-known phrase/law that states "every rule has an exception." However, for this statement to be true, it would also mean that it also had an exception itself (i.e there exists at least one rule without an exception). Of course, if this last statement is true, then it makes the original statement false, and vice versa. If the statement is true, then it must be false.

 

Or how about: "I am always right. But one time I thought I was wrong - it turns out I was mistaken"

 

"All statements are true."

If true, then the statement "this setence is a question" is true. However, we know it is false. So the original statement is false. Contradiction.

If false, then at least one statement is false.

I sense something deeper with this, so I am going to look into it.

 

I like that, I'll take some time to think about it and I'll come back to you tomorrow.