Talk:Horse paradox

For a May 2005 deletion debate over this page see Wikipedia:Votes for deletion/Horse paradox

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I moved this:

A similar paradox is a proof (by Raymond Smullyan) that all horses have thirteen legs. First take all your horses and paint them red. Now look at the horses. If all the horses have thirteen legs, then we can stop. But what if one or more of the horses don't have thirteen legs? Well, that would be a horse of a different colour! However, we've painted all the horses red, so it would actually be a horse of the same colour. Hence, we have a contradiction, so by reductio ad absurdum, all horses have thirteen legs.

I don't see why a horse that doesn't have 13 legs would have a different color. It would still be red, like all the horses. AxelBoldt 20:02 22 Jun 2003 (UTC)

It's a phrase: "horse of a different colour". Martin 21:34 22 Jun 2003 (UTC)

What does that phrase mean? AxelBoldt 20:55 24 Jun 2003 (UTC)

I would like to know too. In any case it is a word play, not a logical paradox, and doesn't belong here. -- Arvindn 06:58 25 Jun 2003 (UTC)

To answer Axel, "horse of a different colour" is a (chiefly American? British?) slang phrase that means roughly "one that does not fit the expected pattern". So this example is cute but has nothing to do with math or logic. Incidentally, I have usually heard this logical paradox referred to as "the billiard ball paradox", not the "horse paradox", proving that all billiard balls are the same colour. -- Revolver

Smullyan's argument has everything to do with logic: the ontological argument is a logical argument for the existence of God that many believe is flawed due to semantic issues, just as Smullyan's "proof" is flawed. To be sure, it has nothing to do with formal logic, or with math. Martin 20:46 26 Jun 2003 (UTC)

Agreed, Smullyan's argument is an example of a proof that is flawed based on semantics, so yes it is related to logic. My formal bias shines through. I wouldn't say that it is "similar" to the original horse paradox, though, because the horse paradox fallacy is based on a technical (i.e. purely mathematical) mistake in applying induction, namely the assumption that two sets have nonempty intersection, when in fact they do not. This is not a semantic mistake. It's a very interesting example to consider if you're discussing paradoxes in general. I'm just not sure if it's useful here, because it's a different type of logical paradox (a paradox of a different colour...sorry :-/), and because the root of the paradox lies is a fairly culture-specific slang expression that may not be familiar to a lot of readers outside North America or England. With regard to the name, I didn't mean to suggest it should be changed or anything, but I have heard "billiard ball paradox" so often, that there should probably be an entry for this pointing to the horse paradox entry. (I haven't tried to make any of these pointers yet.) Revolver

Maybe if there was a wordplay paradox article, or something? I see your point, though. I wouldn't really mind if it was moved elsewhere - as long as there's a link from here to there :) Martin 16:22 28 Jun 2003 (UTC)

Good grief, I looked up "billiard ball paradox" on google, and apparently this name is shared with a paradox in theoretical physics about time travel. Too many paradoxes, not enough names! Revolver

OK, I guess I'm highly biased towards formal logic too. In my mind "logical paradox" is implicitly "formal logical paradox". BTW, the paradox page implies that too:

The identification of a paradox based on seemingly simple and reasonable concepts has often led to significant advances in science, philosophy and mathematics.

Look at this one which is a more obvious word-play: "A penny is better than nothing. Nothing is better than eternal bliss. Therefore a penny is better than eternal bliss." Would you consider that a logical paradox? (Just to see how far apart our viewpoints are :-) -- Arvindn 04:05 27 Jun 2003 (UTC)

Yeah, I think I would (the version I heard related to peanut butter sandwiches). Quite an important one, imo, because it shows why you probably shouldn't reify concepts like "nothing" and "existence". But hey, I'm an amateur. Martin 16:22 28 Jun 2003 (UTC)

I'm happy with leaving Smullyan's story in since it is amusing, but I also wouldn't call it a paradox, and I don't think it has anything to do with logic or semantics. If it did, it could be formulated in any language, but it only works in English. AxelBoldt 02:41 28 Jun 2003 (UTC)

I'd like to point out that Smullyan's story, apart from the language-dependent "flaw" mentioned above, also has a logical fallacy. Just if one or more horses don't have 13 legs, we can't say they don't belong to the group. In fact (in our world) they form the whole group (since all horses have 4 legs). We can only deduce that a horse that doesn't have 13 legs is of a different color (doesn't belong to the group) if we also know there is also a horse with 13 legs. -- Paddu 18:50 29 Jun 2003 (UTC)

I think that should be added. AxelBoldt 23:02 29 Jun 2003 (UTC)

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I always thought that "the horse paradox" referred to the story I added. It was what I thought of when I first saw the article title.

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I know another "paradox" which is actually a word play and is somewhat related to horses. Don't know, maybe it sounds quite silly in English, but in Russian it's a bit confusing and funny.

Let's prove that unicorns exist. We mean true unicorns here, not rhinoceroses or something else, we mean a mythical creature that resembles a horse with a single straight horn on its forehead.

To prove that set something exists, we can for instance, prove that some specific subclass of it is non-empty. To prove that rectangles exist, it suffices to prove that squares exist.

So, let's prove that there is a subclass of unicorns that is non-empty, i.e. that exists. For determinancy, let's prove that existing unicorns exist. First, consider that existing unicorns don't exist. But that's a contradiction---how can something that exists (existing something) not exist? Therefore, we've come to conclusion that existing unicorns exist.

Now, if some (existing) unicorns exist, this means that unicorns in general exist. Statement proven.

Don't take this seriously ;)

Paul Pogonyshev 23:01, 16 Jul 2004 (UTC)

11 horse paradox

The puzzle needs either a wriggle wording (I have inserted the words "in his stable") or expanding in some way, to explain how the Lawyers horse "counts". E.G. the lawyer (or in some verions a folk-tale hero type) says "I will solve your problem. I'll lend you my horse....")

Is this an entry for bad jokes or serious conundrums?

Removal of other paradoxes

In the VfD discussion Wikipedia:Votes for deletion/Horse paradox, I count 4 votes for keeping only the first section, 2 votes for keeping the whole article, 6 keep/cleanup votes that do not specify what to do, and 5 delete/merge votes. Therefore, I deleted the other "paradoxes". -- Jitse Niesen 01:19, 8 Jun 2005 (UTC)