## Is my argument that it is impossible for two things to share no similarities at all sound?

• 18
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.
• 2.6k
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 think this is logically necessary. My question is: what is the significance of this argument?
• 8.4k
If I might rename your things a moment red, yellow, and blue, Then all I think this gets you is that yellow and blue are both "not-red", and so on all round. What it doesn't seem to get you is that the 'not-redness of blue' is in any way similar to the 'not-redness of yellow.

I'd like to be putting this more clearly ... perhaps tomorrow.
• 301
I would argue your case by saying that one thing they have in common is that they can be compared to each other at all.
Another way of putting this is assume that A, B and C are real objects. They can be compared to each other to assess their differences, because they are in the same realm/universe/reality....if they didn't have this in common somehow, then you couldn't compare them to each other.
• 62
Sorry this seems so easy, maybe I'm not thinking about it hard enough. Okay pick any 3 things call them Thing A, Thing B, and Thing C and assume they're all different with no similarities with each other. A, B, and C all share the property that they can be classified as things. Therefore it's not the case that they're all different with no similarities with each other.
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