What does it mean to say that something "exists"? Why do we say that both objects in the world, such as chairs, and logical entities, such as the number 9, both exist? I believe that the key insight is that both "things" can be adapted to what I call the Basic Object Model. Further, by using this specific example, I can demonstrate what I call Definition by Interface. This post responds to Philosopher Corner: Numbers.

Update: After further consideration, I have come to the conclusion that this is only part of the story. Fitting the object modle is a key part of "existence", but we also need to have a divide between "existence" and "non-existence" to fully explain why we are tempted to use the same term for both kinds of "objects". I hope to develop this in a future post.

The Basic Object Model

Informally: any "collection" of "things" is adapted to the object model if we can say the following:

  • Any "thing" in this "collection" has properties. For example, a table may have the properties of size, number of legs or general color. Number may have the properties of being odd or even, postitive or negative, prime or composite.
  • There exist relations between the "things" in the "collection". For example, a table may be larger or smaller than another, to the left or to the right of a couch or darker or lighter than the blinds. Numbers may be smaller or larger, have more factors or less factors, have the same sign or different signs.
  • Any "thing" has a type and all objects of this type will have certain properties and relations. For example, all tables have a size and a bigger than/smaller than relation to other tables. Some objects of the same type may have additional relations.
  • If a "thing" X and a "thing" Y have the same identity, then they are the same type and all properties and relations are the same. So if X and Y are tables with the same identity, then the have the same size, number of legs and general color; as well as having the same size relation and positional relation to a couch.

"Exists" is a lingustic construct and a major factor in lingustic constructs is convenience. Since both physical objects and logical objects fit the Basic Object Model it is convenient to say that they both "exist". On the other hand, we tend not to say that chair's brownness or the number two's evenness 'exists', because it is usually more convenient to simply conceptualise them using a Property Inferface, rather than the Object Interface. To be clear, I'm not claiming that this is anyone's explicit reason, just that the presence of these similarities nudged us towards using the same word for both kinds of objects.

Further, I've only clarified what Existence in the Broad Sense means. Physical existence is a narrower kind of existence and there is more to that than just meeting the Basic Object Model. Similarly, it seems that there could be more to logical existence as well, or if not, perhaps maths specifically exists in a deeper sense. What I mean here is that if we performed a conceptual analysis on Object Existence and a conceptual analysis on Mathematical Existence, I would expect that we would find that the linguistic term conveys more than just the Basic Object Model when used in these narrow senses. Further, we would find that these more specific uses would differ with the Basic Object Model being most or perhaps even all of what they have in common.

As I said at the start, the Basic Object Model is an example of what I call Definition by Interface. Terms that are defined in this way can simply be adapted to the same interface, instead of necessarily referring to some distinction that actually exists in the ontology. Some of these terms may be Defined by Interface and also exist in the ontology, but we should not assume such a deeper existance without good reason. In particular, just because a word seems as fundamental as "existence", we should not fall into the trap of assuming that it must be ontologically basic. And as we've seen here, even though its use in specific cases may be ontologically basic if we dig into them, the word in general just seems to refer to similarities in the interface.


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An argument that you can't easily write in first order logic without resorting to subtle tricks:

1) Dracula is a vampire.

2) Vampires do not exist.

3) Therefore, Dracula does not exist.

A full explanation of "exists" should be able to account for this argument...

I think I actually manage to cover this in my part two post. Being able to evaluate arguments about things is about fitting them into your collection of mental objects with associations. We can absoloutely do this with both numbers and Dracula. But you can have mental objects in your collection that you don't think have a corresponding object in the territory - strict existence involves extra properties that more or less boil down to having the object in a causal model of the world that's connected to you.

Hm, that seems like kind of an important point. I may have overindulged my desire to lay out all the necessary pieces for people but not put them all together.

Perhaps because I've already arrived at it independently, this felt lacking.

But I agree with what you've said.

In my ontology, I have some expansions that I would soon post.

As for "exists", I find it useful to distinguish between "is manifest in some model" and "is manifest in the territory"—you have not made that distinction.

My answer to what it means to "exist".

"Perhaps because I've already arrived at it independently, this felt lacking" - you'll notice that I used a lot of words to describe two very simple concepts. This is because there is a wide variation in how people will interpret any particular text, so you need to spend a lot of words stating everything as clearly as possible. Now that I've done this, however, I can just use either of these terms and link people to this article.

I agree that there are further distinctions that can be made, but I really wanted to keep this article as simple as possible and just focus on, well not one thing, but two things that are pretty much inseperable.

You wrote: "Properties of an object are relations between the object and another object". I'm not so sure about this. What if the property is "number of atoms"? What is the second object then?

Further, could you illustrate, "A composition of relations is a relation" with an example?

You don't have to regard evey predicate as a property.

A property of an object is a relation:

The relation is between the object and another object "atoms". (Number of X that compose Y).

A composition of relations is a relation.

Paris is in France.

France is in Europe.

Paris is in Europe.

Paris is the capital of France.

France is on Earth.

Paris is the capital of a country on Earth.

Actually, you're right that the fitting some kind of Object Interface is only part of what "exists" means. Exists splits the possible object space up into "exists" and "doesn't exist" and I haven't dealt with this core aspect at all.

Now I feel silly for only reading this after posting my own part two that repeated many of these points :)

As I said in my reply to CronoDAS's comment, I think I make a slightly different distinction: mental objects in your big collection'o'mental'objects are what you can think sentences about (and evaluate the truth of, and have arguments about, etc), but you aren't required to think all of those things exist. I argue that it feels like numbers exist because when we learn about numbers, it feels like we're interacting with something objective and external.

To me it sounds like you're roughly getting at the distinction Heidegger made between ontic and ontological being, something like what we might think of as the thing-in-itself and the thing-as-phenomenological-object. Compare also noumenon vs noema.

Sorry, this comment doesn't make any sense to me at all because of all of the terminology.

That was kind of the point--to give you handles for related ideas you didn't seem to be aware of so you could look deeper if you are interested.

Heidegger is the one philosopher who I refuse to read due to generally being incomprehensible, but thanks for the comment anyway!

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