The Ontology of Relationships

Actually written DECEMBER 21, 2022

“What are relationships?”

This question is relevant to anybody who, like me, is trying to make the case that infinity cannot be metaphysically real.

Here’s the problem:

Imagine existence was comprised of only two simple existents, or what I call “items”. Item “A” and item “B”.

But there’s a certain line of reasoning that these two items generate infinitely more items.

Between item “A” and item “B” is another item, a relationship “C”.

Between item “A” and relationship item “C” is another relationship item “D”.

And between item “A” and relationship “D” is another relationship item “E”.

And so on, infinitely.

We could put an end to this if we could conclude that relationships have no metaphysical reality.

But can we so conclude?

What we are proposing by the claim that relationships have no metaphysical reality is that relationships do not exist independently of a conscious observer.

It means that item “A” and item “B” do not relate to one another in any way. It means whatever relationships might exist between them is part of the way our minds experience them, but not intrinsic to existence.

But this seems impossible. Consider the fact that item “A” and item “B” are not identical, that they are distinct. If “being distinct” is a relationship, and we claim that relationships have no metaphysical reality, then we are saying that items “A” and “B” are in actuality not distinct, that existence does not in fact comprise two items, but just one item.

If you want to weed out infinity from your metaphysics, you’ll have to weed out relationships.

And if you weed out relationships, you’ll have to weed out plurality.

Are we down to having to choose either infinity or a singular existence? Both seem impossible. Maybe this is one of Kant’s antinomes.

Perhaps we can have our plurality by admitting the metaphysical existence of relationships, but only certain kinds of relationships, a finite quantity of relationships.

Now we are faced with the problem of drawing a non-arbitrary distinction between relationships that are metaphysically real, and those that are not.

So far, ‘though I have pondered this issue for about 5 years, I have no answer. It is very likely that I just don’t have the intellectual capacity to find an answer.

And I don’t know what to make of the fact that every thought I have, let alone every thought I have about this problem, is in the form of propositions, the vast majority of which are expressions of relationships. (I’m tempted to claim that knowledge is basically the awareness of relationships.)

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