Consider the position that two things cannot be the same because they are two. If they were the same, then they would be one. Thus, sameness is identity, and identity is indiscernibility. Call this position ‘nominalism’.

To the nominalist, many things are never one; not really, anyway. For example, we talk as if there are people, planets, and protons, but this is only a way of talking. In reality, no two individuals are the same, whether in respect of being ‘human’ or any other. We say the apple and the ball are both red, but that does not mean the apple and ball are really the same.

We just mean they are similar or dissimilar to one another. The apple and the ball are not the identical shade of red. And even if they somehow were, they are not the same occurrence of that shade — differing in some way or other, whether by location or time, etc.

Indeed, what is even one case where two things are the same? Any suggestion will inevitably involve different (i.e. not the same) things, precisely because they are two.

Maybe there is such an example in the back, by the square-circles, in the corner over there.

But what’s wrong? We aren’t saying that square-circles are contradictory, are we? Because there can’t be any contradictions given nominalism. After all, in order for two statements to contradict one another other, they must both have claim to being the same proposition.

Contradictions take the form (p & ~p). The idea is that same proposition ‘p’ is being said to be two different things, true and false.

But, if nominalism is true, then there is no one ‘p’ in the proposition ‘(p & ~p)’. The first one, ‘p’, is talking about one proposition and the second one, ‘~p’, is talking about different one: they are not the same. That is, they are not attributing different truth-values to the same proposition!

This isn’t even good news for the dialetheists, since they at least believe there are contradictions.

But it isn’t just contradictions that nominalism evaporates. It’s the laws of logic. It’s tautologies. It’s identity. It’s any symmetric relation. It’s logical validity. It’s reoccurrence as such, of anything whatsoever (I can’t even be the same person I was a second ago). It means no quantification, no sets, no categories, no…plurality.

You might think Platonism is all kinds of weird and complicated. And it takes phenomena like the one above aaall the way to their logical conclusion. But, I’m telling you. Look at nominalism. The same reduction to absurdity happens with all the positions that oppose Platonism–relativism, skepticism, materialism, mechanism, etc.

Trust me, Platonism is not weird. You’re weird.

It all starts with the super obvious.

And we need to get back to that.