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.