BadgerJelly » September 8th, 2017, 1:55 am wrote:Mitch said -The truthteller's answers all have the truth-value T, so if left is correct, he would answer (in reply to the question "Is left correct?"): "Yes, left is correct". So, for the truthteller, the truthful answer to Q is Yes; and he truthfully answers it "Yes".

The liar's answers all have the truth-value F, so if left is correct, he would answer (in reply to the question "Is left correct?"): "No, left is not correct". So, for the liar, the truthful answer to Q is No; but (being a liar) he falsely answers it "Yes".

If right is correct, then for the truthteller the truthful answer to Q is No; and he truthfully answers it "No".

If right is correct, then for the liar the truthful answer to Q is Yes (he would say left is correct in order to lie consistently); but he falsely answers Q "No".

I completely agree. This is what I meant by a "double-negative" in the answer. The correct, and truthful, answer is squeezed out of the liar.

Someguy -

Do you really see a problem with the above? I think the main confusion arises due to mixing up "truth value" with "truth".

I agree with what you quoted. But that's only the warmup to the question. The statement S is false because it's not a biconditional. But I've said that quite a number of times (without anyone logically refuting me) and my saying it more isn't going to help.

But ok, one last time for the night.

Two statements: P = "The correct door is on the left"; and Q = "The speaker is a truthteller."

We wish to evaluate the truth value of P <=> Q or P iff Q (these mean the same thing).

To do this, we have to show that P => Q and Q => P. You can't do that and Mitch can't either, because neither implication is true.

So the biconditional P <=> Q is false. Therefore the truthteller will ALWAYS say it's false and the liar will ALWAYS say it's true, in either case giving no information about the door.

And like I say, if I'm wrong, somebody show me I'm wrong. I'm open to the possiblity. To show me I'm wrong you have to show that P <=> Q is true. How can you do that? I claim you can't. Proof: What if the good door is on the left and the speaker is a liar? Then P and Q have opposite truth values. QED. I'm going to bed.