Probability question -

[The_Other_Waldo_Pepper]

@Little_Nemo

I was able to solve the situation you described pretty easily (and I explained how I did it).

But it was in the other casket.

[k9bfriender]

Simplest case. I have a casket that says, “The portrait is in this casket.”

You open it up, and it’s not there. Is that a paradox?

No, it’s just that the person who wrote on the casket was lying.

Logic puzzles only result in paradox if the laws of the universe are beholden to them.

[Chronos]

Thanks, @DPRK . I was thinking of that one, too, but couldn’t remember exactly how it went.

[Little_Nemo]

@Oly

In this revised version, what is the objectively correct answer and why?

A.

Because A says you have a 25% chance of choosing the correct answer at random. And 25% is the probability that you will choose a correct answer randomly if you have four possibilities to choose from.

[DPRK]

@Little_Nemo

I was able to solve the situation you described pretty easily (and I explained how I did it). I have a hard time accepting that Martin Gardner got the wrong answer.

Quoth Gardner:

The error he makes is in assuming that the statement on the silver casket is ei­ther true or false. This problem involves us in the modern concept of metalan­guages. It is only permissible to discuss the truth values of a particular language in a larger language, or metalanguage, that contains the first language as a sub­set of its terms. When a language refers to its own truth values, the result is often a logical contradiction. Without meta-statements about the truth or falsity of the casket inscriptions or information about how their truth values are related the inscriptions can be meaningless.

Indeed, in the stated problem Portia never said none of the inscriptions was self-contradictory.

[DPRK]

You can find it all in this book:

What Is The Name Of This Book? : Raymond M. Smullyan : Free Download, Borrow,...

But not the question in the OP— not sure where that comes from