"If everyone in front of you is bald, then you're bald." Does this logically mean that the first person is bald? Suppose we have a line of people that starts with person #1 and goes for a (finite or infinite) number of people behind him/her, and this property holds for every person in the line:  


  If everyone in front of you is bald, then you are bald.


Without further assumptions, does this mean that the first person is necessarily bald? Does it say anything about the first person at all?  

In my opinion, it means:  


  If there exist anyone in front of you and they're all bald, then you're bald.  


Generally, for a statement that consists of a subject and a predicate, if the subject doesn't exist, then does the statement have a truth value?  

I think there's a convention in math that if the subject doesn't exist, then the statement is right.

I don't have a problem with this convention (in the same way that I don't have a problem with the meaning of 'or' in math). My question is whether it's a clear logical implication of the facts, or we have to define the truth value for these subject-less statements.



Addendum:  

You can read up on this matter here (too).
You can see what's going on by reformulating the assumption in its equivalent contrapositive form:  


  If I'm not bald, then there is someone in front of me who is not bald.


Now the first person in line finds himself thinking, "There is no one in front of me.  So it's not true that there is someone in front of me who is not bald.  So it's not true that I'm not bald.  So I must be bald!"
Let's try to isolate the problematic part of the question.  Imagine you are the first person in line.  Your cell phone rings; the man on the other end says to you, "My psychic powers tell me that everyone in front of you is bald.  Am I wrong?"  How do you answer?

From the standpoint of mathematical logic, the answer is unequivocally No, he is not wrong.  This is not a "convention", but rather an inevitable consequence of how logic works:  The person on the other end of the phone would only be wrong if there were a non-bald person in front of you; since there is no non-bald person in front of you, he is not wrong.

Now here is where it gets tricky:  If he is not wrong, is he right?

If we assume a logical system in which every statement has a truth value, and there are only two possible truth values, then if he is not wrong, he must be right.  So in such a logical system it must be true that everybody in front of the first person in line is bald.

For similar reasons, the largest natural number is odd, and the final digit of the decimal expansion of $\pi$ is a 4.  These statements are true because they are not false; they are not false because there is no largest natural number and $\pi$ has no final digit.

But human language does not operate according to the principles of formal logic.  In the real world, we would not tell the person on the cell phone "You are wrong" or "You are right"; what we would say is "There is nobody in front of me."  More precisely, we would infer the tacit additional premise "There is at least one person in front of you", and reject the entire construction because that premise is false.