Can only one object exist?

Suppose so, then: What exactly can distinguish it from not existing, if the object itself is all there is?

Any object trivially maps to itself via identity, so in order to deviate from the trivial case, the object would need to map to another object, which can not be the case if there is only that one object.

• Would the trivial/nontrivial distinction itself obtain in such a case, however, if the existent/nonexistent distinction had "already" been effaced? Nov 5, 2023 at 16:43
• Yes, see Spinoza: only one substance: God. Nov 5, 2023 at 17:13
• At least in Well-Founded Set theories - if there is only one object, it must be the empty set. And the Empty Set itself, "believes" that no objects exists. More technically, the statement "there is no set x s.t. x=x" is true relativized to the empty set. Nov 5, 2023 at 17:15
• @MauroALLEGRANZA Can you elaborate? What definition of existence is employed? Nov 5, 2023 at 17:15
• @DavidGudeman I think the point being made is that, if there is only one object in some Universe, can we distinguish such an object from a nonobject? If we can't, the implication is some Dichotomy Axiom, in order for something to exist ( in the sense that we can distinguish it from nonexistence), we need to compare it to some other thing. Worded another way, the singular object may exist, but does "it" think anything exists, if there are no other objects? And if the only object doesn't believe any objects exists, what exactly is the difference between there being no objects at all? Nov 5, 2023 at 17:55

Does your question involve the following argument?

1. Assumption for reduction to absurdity: there is only one object.
2. Principle: if there is only one object, the only mapping that exists is a trivial identity mapping from-and-to that object.
3. ???: if there is only the trivial mapping for the one object, then such an object can't be differentiated from a possible second object.
4. Factoid: no object is incapable of being distinguished from a possible other object.
5. Therefore, there must be more than one object. QED

It might be doubtful or unclear that (3) is true: taking (1) strictly, as, "There is necessarily only one object..." does suggest (3) to an extent, except what about differentiating the one object from itself were it to change or admit of different possible states otherwise speaking? Or what about nontrivial embeddings or automorphisms of the one object into itself, alongside the trivial identity mapping? So then (2) is questionable also.

And now that I think about it, it's not clear what you mean by "object," either, nor then whether/how much it is sensible to talk about the possibility of merely and strictly one such object (whatever that means). And are we limiting ourselves to concreta? For if we brought in abstracta, what would stop there from being infinitely many possible such things?

• Depending on what one sets as their scope for concrete objects, it seems that if a world with a singular object is to be postulated, the object of that world must be abstract and simple. A complex object would entail constituent parts, which could be cognized as objects themselves and a concrete object would entail having causal efficacy (which ostensibly requires multiplicity), both of which are unacceptable given the constraints. Yet, if one allows for the existence of abstracta, I am not sure it is coherent to assert the existence of only a singular abstract object. Any thoughts? Nov 5, 2023 at 18:13
• @MaxMaxman my main question, for the OP poster at least, is whether they are using a substance/attribute or Humean-bundle theory of objects. Some principled way might be found for denying that a substance with attributes had to be multiplied in a world, but perhaps not; a Humean bundle, with sub-bundles, lends itself more "obviously" to such multiplicity, though. Also, though, I wonder what the OP implicitly takes a world to be; if there is but one object in a world, is that world a non-object or is the one object its own world? Nov 6, 2023 at 13:26
• @KristianBerry I thought of an object as any free variable such that it can transform or be transformed, s.t. it forms an element of a category where it is linkable via composition of morphisms, which does correspond to the Humean bundle calculus. Nov 6, 2023 at 17:01
• @KristianBerry A world we can define here as collection of an object which can map to another object, see the above for more of what I deem as object. Nov 6, 2023 at 17:03
• @Monolith if an object is defined partly in terms of its possible relationship to another object, then per this theory of objects, there couldn't be but one of them, could there? Now, as for other definitions of "object," well... the main task is to avoid equivocation, now, I suppose. Nov 6, 2023 at 17:15

It would be easier to answer this if your question was about substance. I would like to give a more complex answer, since the subject is the object in question.

Imagine that this is the moment of the big bang that can be described as the first object. It is not the volume that distinguishes it, but only a bit that measures the density (Cogito, ergo sum). There is a field of observation whose volumetric equivalence does not need to be diagnosed.

In such a situation, if there is no existentiality that we are measuring it, it is the object itself that measures it, and it can be approximate. Other things try to understand this situation from other situations.