A Rather Paradoxical Paradox

A Rather Paradoxical Paradox

    Once upon a time there was a thinker.  He liked to think about lots of things, but particularly he liked to think about people and thought itself.  One of the things that intrigued him the most was ideas about people thinking about themselves.  He loved to think about people who did not think about themselves.  In fact, he made the statement, “I think of all the people and only the people who do not think about themselves!”  For several years he lived by this statement. 
    He went about thinking thoughts in line with this statement until a logician friend of his stopped by one day and confronted him about it.  A discussion between them ensued and it went as follows:

LOGICIAN:  Hello my friend, do you have any time to chat?  Something has been on my mind lately and it is bothering me quite a lot.

THINKER:  I always have time.  What is it that bothers you?

LOGICIAN:  Don’t, take this personally, but for someone who likes thinking so much, I cannot understand how your thoughts could ever be rational.  You say that you think of all the people and only the people who do not think about themselves.  Now, I know that you are a logical man, but I am utterly unable to comprehend that you fail to realize that you stumbled into Russell’s Barber Paradox.

THINKER:  Please tell me how so.

LOGICIAN:  You see, in saying that you think of every person who does not think about himself, you are unable to account for your own thoughts.  You fall into a contradiction whether you do or do not think about yourself.  If you do think about yourself, then it is not true that you only think about people who do not think about themselves, because you are not one of them.  And since your statement makes it the case that you have to think about anyone who does not think about himself, it also would contradict your statement if you did not think about yourself at all.  It should be clear then that both roads lead to contradiction.

THINKER:  Ah, I see your problem.  You say that I must either be thinking about myself or not thinking about myself; one of those must be true, and either way my statement contradicts itself.

LOGICIAN:  You finally see!  After all these years, I can’t believe that is all it took!  Now you must change your statement, I assume.

THINKER:  Why, of course not.  Let’s consider your two options.  You see here, suppose I was thinking about myself; now if this were the case, my “self” would be undeniably the one doing the thinking.  But how could I be thinking about the self when the self is the one doing the thinking?  If you think about this for a moment you realize it is an utter impossibility.  Since it is an utter absurdity to contain myself in my thoughts, it should be clear that I can never really think about myself.  I can try to think about myself, and I can think about the act of trying to think about myself but I can never really think about myself.

LOGICIAN:  That seems like a rather odd conclusion, but I’ll grant you it anyway.  However, if you can’t do one you must do the other, and so you must be not thinking about yourself.  In which case you’re initial statement is STILL contradictory.

THINKER:  But if I never think about my “self,” if I never even consider it, then what is it?  My self must primarily exist for me before it exists in relation to anyone else.  So it must first exist in my mind before it can be said that I have a self.  But if I never have any thoughts on my “self” then it is not in my mind, and so a self cannot arise.  And so, it makes no sense to make the statement that I cannot think about myself because without thoughts on the self there is no self.
    So, if I maintain that I have a self, then I never think about it in any case.  But if I never think about it in any case, then I do not have a self.  As Shakespeare once wrote, ‘I am not what I am.’  You see, thinking about oneself is a paradox, and so my statement does not put me in a paradox because it already contains one that cancels the larger paradox out. 

LOGICIAN: I still don’t understand.  I still don’t think you have answered my question of “what about when you think about yourself?”

THINKER:  To say “what about when you think about yourself?” makes no sense as it assumes either that I can think about myself or that there even is such a thing as a self to do the thinking about itself. I do not have a self because I cannot think about it.  If I could think about it than I could have one, but fortunately for my original statement, I cannot.

LOGICIAN:  By that then logic you are falling into a paradox every time you say the word “I!”

THINKER:  Yes, I’m quite aware . . . or perhaps I’m not at all . . . depending on how you look at it.

LOGICIAN:  This is all so irritatingly confusing now, but last thing:

THINKER:  Certainly.

LOGICIAN:  If no one can think about their self, then your statement is no different than “I think of all the people and only the people who cannot draw square circles.”

THINKER:  Sure, but that does not require nearly as much thought. 

LOGICIAN:  But all your statement really means is that you think about everyone!

THINKER:  Exactly!  Why WOULD'NT I think about everyone?  People are fascinating!