Saturday, November 19, 2011

Liar and truthteller questions

Here are some fun questions:

  1. Is the answer to this question negative?
  2. Is the answer to this question positive?
  3. What is the answer to this question?
The last one is due to my six-year-old.

6 comments:

 James A. Gibson said...

How about this one: "What is this question asking?"

DL said...

1) Yes and no.
2) Maybe!
3) 42.

Dan Lower / KKairos said...

1) I can't resolve this one.
2) "Yes."
3) "The answer to this question." (Tautology but...I think it works?)

man with a computer said...

1. If it is positive, then it is negative, which means that it is positive, which means that it is negative …

2. If it is positive, then it is positive, which means that it is positive, which means that it is positive …

3. It is the answer to this question, which is the answer to this question, which is the answer to this question …

These things always mess me up.

Alexander R Pruss said...

2. If it is negative, then it is negative, which means that it is negative, which means that it is negative ...


I am not sure exactly what point my questions make, except maybe this. We are not philosophically troubled at all by questions that have no answers, like "When did you stop beating your wife?" or "Are you lying or just stupid?" But we are somehow troubled by paradoxical assertions. I wonder if one can assimilate the case of paradoxical assertions in some interesting way to the right thing to so about questions that have no answer. Maybe not--maybe the strengthened liar would kill any such move.

man with a computer said...

I think it's just the loop that is somewhat annoying. We are usually satisfied by definite answers (including "that's not possible"), not an infinitely long series of referential statements.

Someone could say that the loop itself is a satisfactory answer, much like an infinite series or the definition of an irrational number. But those things aren't troubling. Not to me at least.