Is this guy really Dracula?

February 18, 2006 6:47 AM

What's wrong with this logical deduction?

Proof that I am Dracula

(1) Everyone is afraid of Dracula.

(2) Dracula is afraid of only me.

Therefore I am Dracula.

Doesn't that argument sound like just a silly joke? Well it isn't; it is valid. Since everyone is afraid of Dracula, then Dracula is afraid of Dracula. So Dracula is afraid of Dracula, but also is afraid of no one but me. Therefore I must be Dracula!

I don't get it. I've drawn the Venn diagrams in my head, but I don't see the paradox, or why his/her reasoning is valid. Can't Dracula just be afraid of any person or set of persons without that fact having any influence on Dracula's identity according to the given premises?

posted by goodnewsfortheinsane to science & nature (16 comments total)

The "proof" assumes that fright is one-way. This is, of course, wrong, as it is possible to both strike fear in the heart of Dracula, and to be afraid of Dracula.

For example, both (1) and (2) would be true, if I were the one person in the world who could kill Dracula, yet also could be killed by Dracula (call me VanHelsing).

So, in response, this is a stupid proof that relies on a very narrow, and incorrect, interpretation of "afraid."

In short,

Therefore, I am VanHelsing

is at least as reasonable a conclusion as

Therefore I am Dracula.
posted by yesster at 6:53 AM on February 18, 2006

I read it this way.

IF human THEN fear of dracula.

Then the assumption is that most people have a lot of other fears blah blah blah.

However, if you find someone that has one fear and one fear only, they are afraid of Dracula.

Since that is the case, based on one of the premises, then you're in an A=A situation where someone with only one fear is afraid of Dracula. Since they also claim to be afraid of you, then you have to be Dracula.

Logically, that is.
posted by jessamyn at 7:06 AM on February 18, 2006

Substitute Bob for Dracula in (2). Does it make sense to you then? If Bob is only afraid of one person, and everyone is afraid of Dracula, then the one person that Bob is afraid of must be Dracula.

They are assuming when they put Dracula in (2) that Dracula is someone- you could argue that Dracula shouldn't be in the everyone in (1), and then this deduction woudn't be a proof.
posted by gus at 7:11 AM on February 18, 2006

I think it works. Everyone is afraid of Dracula. The set of "everyone," by definition, includes Dracula. Therefore, Dracula is afraid of Dracula. Next, we learn that "Dracula is afraid only of me." In other words, Dracula fears the speaker, but does not fear anyone else. When we return to the first statement, we are reminded that Dracula fears Dracula. If both statements are true, then the only way to reconcile the two statements is to conclude that the speaker is Dracula. Otherwise, Dracula would have to fear both himself and the third-party speaker (Van Helsing?), which would contradict the second statement.
posted by Faint of Butt at 7:11 AM on February 18, 2006

The trick is that the 'everybody' in premise 1 also includes Dracula. So we can derive a third statement, by substituting any name in for 'everyone':

(3) Dracula is afraid of Dracula.

(2) and (3) together -- "Dracula is afraid of Dracula" plus "Dracula is afraid of only me" -- mean that 'me' must actually be Dracula. Another implication is that the universe of discourse for this argument consists of only one thing (Dracula) -- if we were talking about two or more people, the two premises couldn't possibly both be true.

Logic professors love this sort of question. I got it in the following format last semester:

"4. Alas, love plays tricks on us all. Translate the chorus of this old jazz favorite into PLE [logical form]. Then show that it follows that the singer is his (her?) own baby.

Everybody loves my baby,
But my baby don't love nobody but me."

posted by Aaorn at 7:12 AM on February 18, 2006

Erm. I take back the part about the universe of discourse. There can be any number of people, as long as Dracula is only afraid of himself.
posted by Aaorn at 7:13 AM on February 18, 2006

I think Aaorn's example is much better - it is both more striking since you understand what it's supposed to mean right away (whereas the dracula example is a little confusing at first, to me anyway) and more convincing, because it doesn't have the issue of whether "dracula" really should be considered part of the set "everyone" (as jessamyn's translation above puts it, IF human... - and it could be argued that vampires excuse themselves from that set, what with immortality and all that).

In Aaorn's example, IF human THEN love baby, baby is included in that set, so baby must love baby too - and if baby only loves one person - etc.
posted by mdn at 7:36 AM on February 18, 2006

I don't think this is actually a paradox. It's just misleading because people don't naturally think that someone is afraid of themselves. If the third premise was "I'm afraid of myself", it would be really obvious, even moreso than "Dracula is afraid of Dracula."
posted by Big Fat Tycoon at 7:49 AM on February 18, 2006

Proof that I am Dracula

I think the title is the misleading part. The author doesn't actually accomplish this proof. He simply states:

IF everyone is afraid of Dracula
IF Dracula is afraid of only me
Then I am Dracula

The statment is internally consistent, but it rests on two obviously unsupported premises.
posted by jsonic at 8:05 AM on February 18, 2006

A. Everyone is afraid of Dracula
Therefore,
B. Dracula is afraid of Dracula
C. The only person Dracula is afraid of is me
Therefore,
D. I must be Dracula

It's really B and C that lead to the conclusion D. The confusing part is, as has already been said, that the puzzle does not grant you premise B at the outset.

The other important word in the proof is "only". If Dracula was allowed to be afraid of two things, it wouldn't be valid anymore.
posted by Hildago at 8:21 AM on February 18, 2006

As an occasional logic professor, I think Aaorm has given you the best way to understand it here. (And I think the question is better filed under religion and philosophy!) Strictly speaking, "everyone" includes Dracula here, since it picks out every single person, so premise #1 is doing most of the work. In ordinary language, "everyone" gets a different reading that rarely includes the person people are afraid of. Almost no one would think "Everyone is afraid of the Yankees" would include the Yankees outside of a logic classroom.

Nevertheless, in formal logic "every" gets the universal quantifier which doesn't exclude the object of "afraid".

When asking whether an argument is "valid" in this sense, it's best to skip the Venn diagrams and go straight for asking "Could these premises be true and the conclusion false?", since validity is harder to define graphically. And in this case "everyone" couldn't be afraid of Dracula without Dracula being afraid of Dracula.

Rest assured it's not much of a proof unless the premises are true. These premises are almost certainly false. a) no such thing as Dracula, b) not everyone has heard of Dracula, and c) why in the world would Dracula be afraid of me? So while it is most definitely valid given the universal quantifier treatment of "everyone", it is horribly unsound.
posted by ontic at 11:01 AM on February 18, 2006

The statment is internally consistent, but it rests on two obviously unsupported premises.

But according to the original link, the author is simply trying to prove that the argument is valid, not sound.

If everyone were afraid of Dracula, and Dracula fears only one thing, then the thing Dracula fears would have to be himself.
posted by Doug at 11:02 AM on February 18, 2006

Assumption (2) is nonrestrictive, thus obviating the conclusion. Drac casts no images on reflective surfaces; after centuries of being undead, his self-image will have atrophied. Thus it is unlikely that the word me refers to the Count himself, but to someone else (gus's Bob, perhaps). Not enough info to determine, however.

Logical conclusion—
Lacking mirror skills and unable to rely on others for honest feedback — since everyone fears him, per (1), Dracula truly fears only acne, a bad hair day ... and spinach teeth fangs.
posted by rob511 at 4:00 PM on February 18, 2006

I've TA'ed for a logic professor who spends one class of her logic course playing songs that can be construed to contain arguments, and she then has the class formalize them. One of the songs -- "Everybody Loves My Baby" by Doris Day -- contains a variation of this argument. Here are the relevant lyrics:

Everybody loves my baby
but my baby don't love nobody but me
nobody but me
Yes
everybody wants my baby
but my baby don't want nobody but me
that's plain to see!

The conclusion: the singer is her own baby! Oy vey! (Formalize the argument in predicate calculus for bonus points.)
posted by painquale at 5:26 PM on February 18, 2006

Ha! I hadn't noticed that Aaorn posted the same song... turns out I was his TA! (Hi, Aaron!)
posted by painquale at 5:36 PM on February 18, 2006

I'm a bit disappointed to find out that the "Everyone Loves My Baby" thing is an old chestnut. I read that in Clifford Stoll's "Cuckoo's Egg" and he gives the impression that his girlfriend came up with it on the spot.
posted by AmbroseChapel at 1:38 PM on February 20, 2006