That sounds very interesting. Could you please elaborate on this further? Thank you.

In the same way, you could arguably create a shark without putting together organs, but only by putting together atoms.
But organs are still parts of a shark.

Likewise, you can create a circle by putting together, say, four one-fourths of a circle, whatever that shape is called, or one hundred one-one hundredths of a circle, whatever that shape is called, or any number of any other shape that can be part of a circle, ad infinitum.

You can construct a circle in infinite other ways than by putting two semicircles together, yes, but any way is still going to implicitly include semicircles. You can just choose not to focus on them. In the same way, you can construct a shark by putting a gazillion atoms together, without recognizing the existence of the intermediate structures (cells, tissues, organs, organ systems, etc.) of the shark, but that doesn’t mean that the shark doesn’t have organs.

Basically, what I’m trying to say here is that, if we’re going to say that a semicircle is not part of a circle because we can construct a circle in other ways than by putting two semicircles together, then, to be logically consistent, we ought to also say that a liver is not part of a shark because we can construct a shark in other ways than by putting a liver and the other organs together. But since we all clearly recognize that the liver is still part of the shark despite that, we should also recognize, to be logically consistent, that the semicircle is still part of the circle despite that.

In any case, the point I insist upon is that the relationship which a semicircle bears to a circle, whether we call it “being a part” or not, is the same relationship that an atom bears to a chair, or a cell bears to a living multicellular organism.

A semicircle isn’t necessarily always part of a circle. It can exist on its own without being a part of a circle.

In the same way, an atom isn’t necessarily always part of a chair. It can exist on its own without being a part of a chair.

What I mean by “part” is something that, if it is combined with some other thing, forms some whole alongside that other thing it is combined with.

Perhaps I should say that a semicircle is potentially part of a circle, and an atom is potentially part of a chair.

And any time you have a circle, you can always split it in half to get a semicircle. Just as how, any time you have a chair, you can always split it into its gazillions (I don’t know the exact number, but I know it must be enormous) of atoms.

That’s what I mean by “part”.

It seems pretty clear to me that a semicircle is, indeed, part of a circle. However, I do definitely agree with you that it is a different shape entirely. It is both a part of a circle, as well as a different shape entirely from it. In fact, that is my point. My point is that parts can be completely different entities from wholes, which have their own distinctive features that the wholes which they are parts of lack.

If you still aren’t convinced that a semicircle is part of a circle, just go out and find two semicircular objects, put them together, and you will find that they make a circle.

It is a completely different shape from a circle, but it is also a part — half, to be exact — of a circle. Hence its name, “semicircle”, which literally means “half-circle”.

Whenever you have a whole consisting of two or more parts, the nature of the whole is the nature of both or all of the parts taken together. Which means that the nature of each part is diminished when it is taken as part of a whole compared to when it is taken alone, because the presence of the nature(s) of the other part(s) dilutes it.

And the more parts a whole has, the smaller the proportion each part makes up of the whole is.

For example, if a whole has 6 parts, each part is 1/6 of the whole, whereas if a whole has 64 parts, each part is only 1/64 of the whole, and so on.

What I’m saying is obviously correct. Perhaps the title was misleading. I do not actually believe that a part is greater than a whole quantitatively. In a quantitative sense, I acknowledge that wholes are always greater than parts, in the sense that they have quantitatively more components.

What I mean is that, comparing a part of a whole to the whole itself, the whole is greater in terms of quantity, but the part is greater in terms of proportion.

Here’s an example:

It is very common for scientists to talk of the size of a creature’s brain size IN PROPORTION TO its body size. Clearly, if you were to enlarge a human’s body to the size of a blue whale’s, but kept the size of the brain the same, the larger human would be proportionately far less brainy than the smaller one.
In the same way, using the same logic, my head is proportionately far more brainy than my body as a whole.

It is clear that, the more parts a whole has, the smaller each part is proportionately. For example, the state of Arizona is part of the country the United States which is part of the continent North America. But Arizona makes up a larger proportion, or percentage, of the United States as a whole than it makes up of North America as a whole, because North America also includes Canada and Mexico and Central America, which dilutes the presence of Arizona.
So the United States is proportionately more “Arizona-ish” than North America is, precisely because it is smaller. So being smaller allows each of its parts (it applies to any part equally; Arizona was just an example) to make up a greater proportion of the whole.

So what I’m saying is that more parts = each part is smaller proportionately, and less parts = each part is greater proportionately. So the fact that the larger whole has more parts is balanced out by the fact that the smaller whole has each part be proportionately greater.

And in the hypothetical case of a simple, an object composed of no parts whatsoever, although it would be the smallest in quantity, it would be the greatest proportionately (it would consist 100% of itself, obviously).

I hope I explained this in a way that can be more easily understood and makes sense. Basically, I’m defining “greater” in a different sense. A whole is always quantitatively greater than a part, but a part is always proportionately greater than a whole.

I’m not talking about two things that have no relation. I’m talking about two things that are pretty much totally different. Obviously, being different is a relation, so if they have no relations, then they can’t be different.

What I’m asking about is two things that have nothing except logically-necessary properties and negative properties in common.

Yes, but for my purposes, I’m not going to count that as a similarity.
You might as well say that, because we have a general concept of a “thing”, and since anything is, by definition, a thing, this means that all things have in common the fact that they can be described by us using the concept of “thing”.

For my purposes, I’m ignoring any similarities related to how they can both be present to a particular consciousness.

Perhaps all objects in this universe are causally related, but I’m not referring to objects specifically in this universe. I mean any object that could theoretically exist; it doesn’t have to actually exist. It just needs to exist in some possible world or other. And the standard consensus among philosophers seems to be that entities in different possible worlds are causally unrelated to one another.

I suppose what I am asking is this:

Is the very notion of there being two things that have nothing in common except for universal, logically-necessary properties that any two things necessarily have, such as self-identity, being a thing, etc. and negative properties (such as both having the property of not being some other third thing) even logically possible?

In other words, even if we can’t imagine what it would be like, is an object that has nothing except logically-necessary or negative properties in common with, say, the Eiffel Tower, logically possible? That is, even though we can’t imagine in detail what it is like, does our ability to conceive of the idea of such an object, and describe said idea with language, imply that it exists in some possible world or worlds?