Is Same the Opposite of Opposite?

It’s an axiom among many thoughtful people in our culture that our world is a collection of opposites. We’ve all heard it said that for every action there’s a reaction; for there to be up there must be down. In implies out; day, of course, has night; on has off. Black is paired with white; bad with good. Yin is entwined with yang. It seems intuitive.

But a question occurred to me this morning: what's the opposite of a mountain? The first, reflexive answer is, of course: a valley, but that’s plainly untrue. Valleys and mountains aren’t created by opposite (or even similar) geological forces. Some valleys cut through flat plains; in many cases mountains are crisscrossed by brooks and creeks that carve valleys from the mountainside, but that’s hardly what we’d consider an “opposite” relationship.

Is earth the opposite of sky? If so, when we look into the night sky we can see millions of miles into the sky, but we can’t see a foot into the earth (if we dig a hole we can see some small distance, but the deepest holes we've ever made only go maybe a couple of miles - the earth is 25,000 miles wide). And even if we could see through the earth, at some point we’d start seeing sky again on the other side. That hardly seems like an opposite to me.

Do we consider our friends opposites of our enemies? Not really. What’s the opposite of old? Young? How can that be? Doesn’t the concept of opposites imply that it works in both directions? Young is a step on the path to old, but the opposite isn’t true. The opposite of broken isn't fixed, is it?

And what’s the opposite of dog? If we lived in the world of 1940s and 50s cartoon movies, the opposite of dog would be cat. But we live in a different, less sensible world, where dog and cat can’t be considered opposites any more than birds and humans can. One could ask: is a white dog the opposite of a black dog? But then, what would a border collie’s opposite be? Or a zebra’s? Or a greyhound’s? By the way: what is the opposite of bird? Fish?

And here's a big one...what is the opposite of me? You?