Q&A: The Liar Paradox?
The Liar Paradox?
Question
What do you think of this application of the liar paradox:
A murderer comes up to someone, pulls out a gun, and says to him: I am going to kill you; you have no way to save yourself. However, if you give up on your life and know that you have absolutely no hope, then I will let you go. We are talking about a case where he really can know whether his victim gives up or not by some means or other, and likewise we are assuming that in fact he really has no chance of escaping by natural means.
Seemingly, the loop is as follows: if he does not give up, then he needs to give up; and if he does give up, then again he should not give up. And it is exactly like the liar paradox—I understood that the liar paradox is defined this way: whenever something involves a contradiction with itself, such that if it exists / is true, it can no longer exist / be true.
My question is whether there is some added element here, or whether it is simply the paradox in another form?
Answer
This has nothing to do with the liar paradox. It is a different paradox with the same logical structure. You can read about the liar paradox on Wikipedia.
Discussion on Answer
That is exactly what I wrote. It is not the liar paradox, but it has the same logical structure (it belongs to the same type: self-reference). I think that if you search here you will find columns about this.
Thank you. I did in fact read Wikipedia. (In the English Wikipedia there is a list of paradoxes; one category of logical paradoxes is SELF-REFERENCE paradoxes, and the logical structure you mentioned is described as follows: “These paradoxes have in common a contradiction arising from either self-reference or circular reference, in which several statements refer to each other in a way that following some of the references leads back to the starting point.” So the liar paradox is “self-reference,” and the paradox I suggested is “circular reference.”)