Raijin came up with an interesting one.
[20-33-04] RaijinSpark: You're not unique. Everyone else is. Therefore you are not?
The first obvious sign is that the truth of the conclusion is in the first premise: this is
petitio principii, or "begging the question".
Is the truth expressed in the reasoning possible? Maybe. Let's replace «unique» for «yellow».
• • • • • You are not yellow, everyone else is, you are not. Looks okay, this must be possible.
However, if you can't help the feeling something's wrong, then you're right to feel that way.
The problem is the meaning and implications of the word «unique» in itself. In most contexts, we say a being A is unique to express that the collection and sum of characteristics in being A exist only in A. Which means there
doesn't exist a being B whose sum of characteristics is a replica of A, A==B is impossible.
Confused? Let's think more simply. If something is unique, then it can't be equal to anything else. If something is not unique, then there must be something equal to it.
You==Unique => Nothing's equal to you
You!=Unique => Something's equal to you
You are not unique, everyone else is. You = Red face
Case 1: ☺ ☻ ♥ ♦ ♣
Case 1: Since «everyone else is unique», there's no one in "everyone" that can be equal to "you". «You are not unique» is false.
Case 2: ☺ ☺ ☻ ♥ ♦
Case 2: «You are not unique», true, because there's someone equal to you. However, if that is so, then there's someone in «everyone» that is equal to you. Therefore, that someone is not unique, because «you» are equal to it.
Phew, that took some time and I'm not sure if I was thorough. Maybe my reasoning is wrong. Find me a counterexample xP