Friday, January 6, 2012

Friday Paradox:

I'll occasionally post a paradox or puzzling case on a Friday. Today's is an old one--4th century B.C. It's from Eubulides.

The Horn Paradox:
(1) You don't have horns.
(2) If you have not lost something, you still have it.
(3) You have not lost any horns.
(4) Therefore, you (still) have horns. (This follows from (2) and (3))
(5) But (4) contradicts (1) and so we're saddled with a paradox.

If you think you've got a solution to the paradox, please share it with the rest of us by making a comment to this post.


Jesse Steinberg said...

A paradox is a set of statements that, on their own, each seem true. But, taken together, the statements result in a contradiction or a puzzle is formed. The trick for solving a paradox is thus to find the "weak link" in the set.

Hannah Anderson said...

The horn paradox, which I think basically goes: If we assume that you have whatever you haven't lost, then from the observation that you've never lost horns, you therefore must have horns, but of course you don't have horns. This is also an only apparent paradox. It is just the result of a bad initial premise. No, I can't say that you have whatever you haven't lost. We can say, you have whatever you previously had and haven't lost."

Jesse Steinberg said...

Well done. I think that's the right reply, Hannah. The problem is indeed the second premise. We should revise it to read something like this:

2* If you haven't lost something, then either you still have it or you never had it in the first place.

But then when we look at the new argument with the more plausible premise, we see that the paradox has evaporated.

As Hannah says, since I never had any horns, the fact that I never lost any horns does not entail that I still have them.

Anonymous said...

Well thanks Hannah, just answer the question and give no one a chance geez. Sorry Jesse, I would have said the answer but Ms. Anderson said it faster :).

Jesse Steinberg said...

Haha... You've got the Barber Paradox and the others that are to come.

There will be a new one on Friday at about 10 am.

Kevin Morgan said...

For whatever reason, I'm terrible at these. But I'm going to take a wild guess and say that you never had horns. But point 4 states that you still have horns. So that's where I get stumped.

Anonymous said...

This is an interesting discussion.

I agree that the premise: "If you haven't lost something, then you still have it" is quetionable. I would go further and say that there is no way that you can lose something if you never had it. I can't lose a watch that I never had. So, the premise is not only false, but makes no sense.

Anonymous said...

Maybe that which is lost is the opportunity to acquire horns. Therefore you don't have horns based on this loss. Given that If you haven't lost something, then you still have it is absolute. It doesn't say If you have not lost horns, you still have horns: That is addressed in (3).


KelseyMilliron said...

I still feel like the problem comes with (2) This is where there is error in this paradox. Just because you have not lost something does not mean you still have it. You would have to have it in the first place to lose it and if you don't have it you neither have lost it or ever obtained it so therefore even if you have not lost it you do not necessarily have it. For example, 1) I do not have 1million dollars 2/3) I have never lost 1million dollars, but I still do not have 1million dollars 4/5) I do not have 1million dollars even though I have never lost it I do not have 1million dollars.