I have devised an argument that it is logically not possible for any two things to have no similarities at all with each other. I want feedback on it. Here’s my argument:

Let’s pick any three things. Let’s call them Thing A, Thing B, and Thing C (referred to as A, B, and C from now on).

Now, these three things are all different from each other. Each one has a unique essence and identity and set of properties.

So let’s pick out A and compare it with the other two. A differs from the other two. And since the other two also differ from each other, A differs from B in a different way than the way in which it differs from C. If A differed from B in exactly the same way in which it differed from C, then B and C would be the same thing, which we said they were not.

Now, this means that there are particular differences that A has from B which it does not have from C, and particular differences that A has from C which it does not have from B.

And since the lack of a difference is logically defined as a similarity, this means that the particular differences which A does not have from B are similarities it has with B, and the particular differences which A does not have from C are similarities it has with C.

I’m posting this argument for feedback and advice here because, even though it logically seems to be perfectly fine, I still have this nagging worry that I went wrong somewhere. Specifically, I am worried about the last step, in which I concluded that “the lack of a difference is a similarity”. Is this always, necessarily, logically true? It seems so to me. But I’d like some comments from some of the very smart people on here to know if my argument works out.