A Fallacious Aphorism: My enemy's enemy is my friend
Robleh Wais 5/26/18
The above statement you've no doubt heard in your lifetime. Did you know it's an example of flawed reasoning? It might appear to be on solid
ground at first glance.
I believe it is modeled on an arbitrary principle in algebraic math that states the operation of multiplication on any two negative real numbers
produces a positive real number. That is the non-technical description. We learn it in pre-algebra and never question it. We should challenge it. It's
just a convention and not strictly speaking right. In fact, a Dutch mathematician did, Luitzen Brouwer, but this essay is not about that subject, so
we won't digress to it. The allusion to this principle comes when we think of an enemy as a negative; then it would seemingly follow that the enemy
of an enemy is a friend, roughly speaking. Is this true? Stop to think that you can have many friends as well as enemies. Just because you and
another person share enemies does not imply that you and the other person should be friends. It is in the realm of possibility that all three of you are enemies, for varying reasons.
We'll look at this idea in depth.
First, we look at the positive interpretation of this idea. Suppose three of you are friends for different reasons. So, your various friendships are not
necessarily connected. You can be friends with one person because that person, perhaps uh, that person saved your life once. Then
you could be friends with another because you are her lover, and friendship is necessarily a subset of a love relationship. Can you think of anybody
who is in love, who is not simultaneously a friend of their lover? Add to that, you have a friend you met at a conference and found you share the
same views and philosophical outlook, and you consider him a like-minded colleague. You meet regularly to go to events and have intellectual
discussions, play games together, etc. So, we have three friends of yours, presented and described. Add to this configuration that none of these three
friends of yours know each other. Ask yourself, should any of these friends consider themselves friends because they are friends of yours? If we
apply the algebra of two positive make a positive, then any one of your friends should be mutual friends, right? Let's go further and suppose that
two of these mutual friends of yours meet, that is, your girlfriend and your life-saving friend. The life-saving friend sees your glamorous paramour
and tries his best to woo her. She rebuffs him, especially since it was you who introduced them, and he uses this opportunity to betray you. She
becomes his sworn enemy and tells you all about his underhanded behavior. He in turn, becomes her enemy. You, however, are unwilling to end your
friendship with him because of this treachery, after all, you in a sense owe him your life. You modify your relationship with him. You don't seek him
out, and most of all keep him and your girlfriend apart, as it sows the seeds of enmity. We have two friends of yours who are NOT friends of each
other. This shows that friends of yours, are not necessarily friends of each other.
Second, we look at the negative interpretation of this idea. In this case we have you, your enemy, and someone who is an enemy of your enemy. Is it
necessarily true that this last person must be your friend? That is the crux issue here. For this aphorism to attain the status of implicative truth, it
must be the case that is always true. And even before we see an example, it might be clear to a reader that no such imperative truth is obtained.
There are two necessary conditions we should observe with respect to this configuration. First, you know your enemy. Second, your enemy knows
his/her enemy. But you don't have to know your enemy's enemy. Nor does your enemy's enemy have to know you. Thus, the relationship between
you and your enemy's enemy is one of possibility not necessity. This means that you and your enemy's enemy could be friends but not because that
person is inimical to your enemy. There is nothing in that relationship that implies the necessity of friendship with you. This is crucial too. The
hostility between you and another person does not serve to make you want to be friends with someone else who is hostile to that other person.
Why not? The answer to this may seem complex, but it really isn't. A negative relationship between yourself and another is no incentive for a positive
relationship with someone else in such a relationship with that person. Simply put, people don't become friends because of what they don't like, if
even if it's disliking the people the person they befriend dislikes. Three people can be enemies of each other for three different reasons, none of which
suffices to make them friends with one another. People become friends for positive reasons, not negative ones. The fact that your enemy has enemies
in no shape, form, or fashion implies that the inimical party might be your friend. It is just a simple non sequitur. With that said, we don't even
need to exemplify.