If one thing does not differ from any other, it has no identity (it has no properties, features, limits...). If something has no identity, it's not a thing. So only one thing can't exist.

i.e.: I tell you that I have a mysterious object that I call x. The only characteristic of x is that x=x. What is x? I suppose that the only possible answer is "nothing".

Spinoza seems to agree (16 June 1674):

As to the doctrine that figure is negation and not anything positive, it is plain that the whole of matter considered indefinitely can have no figure, and that figure can only exist in finite and determinate bodies. For he who says, that he perceives a figure, merely indicates thereby, that he conceives a determinate thing, and how it is determinate. This determination, therefore, does not appertain to the thing according to its being, but, on the contrary, is its non-being. As then figure is nothing else than determination, and determination is negation, figure, as has been said, can be nothing but negation.

Note: This is not a set theory question, but a metaphysical one. As far as I know, in the set theory the ø avoid the problem through axiomatic means, but I'm not trained in set theory. This question can be probably formulated also as: existence monism coincide with nihilism?

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    See some lines above : "a thing can only be called one or single in respect of existence, not in respect of essence. For we do not conceive things under the category of numbers". In other words, the "number" is not part of the essence; from this, the conclusion that it is not correct to call God "one or single". – Mauro ALLEGRANZA Oct 17 '18 at 9:42
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    Having said that, how can we conceive a single-entity universe ? Obviously, if I conceive it, this single-entity universe will be me. But then, due to the fact that the "me-universe" is the only existing entity, according to Spinoza I cannot say that I'm one, because there is no "other" with respect to whom I can "define my identity". – Mauro ALLEGRANZA Oct 17 '18 at 9:45
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    I believe you are exactly right. Existence depends on duality. This would be why it is so vitally important in metaphysics to distinguish between monism and non-duality. I might disagree about set-theory since I think this is actually Russell's paradox in disguise, as does Spencer Brown who was a colleague of Russell, but on the absurdity of one thing existing I would agree and feel it is a crucial metaphysical insight. – user20253 Oct 17 '18 at 13:27
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    Spinoza does not agree: omnis determinatio est negatio applies to definition, not being. The idea that what is not definable can not be is the fallacy of the ontological argument in reverse. There it was argued that because God is defined to exist he does exist, in your version because the single thing is not definable it does not exist. This gives definitions way too much credit, they have no such awesome powers over existence. The limits of language do not mark the limits of being, as Kant put it, "existence is not a predicate". – Conifold Oct 17 '18 at 19:43
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    @Conifold the analogy with the ontological argument is very interesting but misleading, because using similar techniques does not mean that the arguments are the same; here I've just proposed an argument against monism. What is absolutely not definable can not be, it's not an epistemic limit, but ontological – at least, it can't be as an individual thing as I argued. It can exist as, well, something we can't conceive (like "nothing"), but it can't be a thing. – Francesco D'Isa Oct 17 '18 at 20:31

I would agree with @Conifold that the 'gerrymandering' confuses the question. It is an excellent question but could do with a lot of tidying up. The main problem is the casual use of words like 'exist' and 'identity'.

Conifold mentions Plotinus and the 'One' and this takes us to the heart of the matter. If Plotinus had argued that the One exists then he would have fallen foul of the OP's objections. He does not do this. His One transcends the exist/not-exist distinction. It would be incoherent to argue that the source of existence exists. Plotinus' philosophy is non-dualism, not monism. His 'One' is not a numerical quantity.

These complications entail that to discuss these issues at this depth and avoid confusion requires a very clear definition of words like 'existence'.

As to 'identity' and 'definition' again some clarity would help. The question states that a thing with no identity is not a thing. True enough, but there are subtleties. Plotinus argues that things are not really things but mere appearances and all would share a fundamental identity. This 'fundamental identity' cannot be positively-defined or distinguished and cannot be said to exist or not-exist. This would not be a thing but would be all that is truly Real. To exist would be to be created and thus to be reducible in physics and metaphysics.

This is not an attempt to explain this philosophy but to indicate that the subtleties we are dealing with here demand very clear definitions of our terms and concepts, and great care to avoid building unnecessary assumptions into our questions. It may suggest that the way to make progress on metaphysical questions is to keep trying to clarify them. By the time we've defined our terms we've done most of the work.

I believe it is logically impossible for just one thing or substance to exist or for existence to arise from a composite 'phenomenon' or substance. I conclude that Plotinus endorses the only view of these matters that survives analysis.

Great question and I'd agree with your conclusion if not all of your argument.

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  • Thank you for your interesting answer. I agree with you, but I've to add that some 'gerrymandering' is needed where questions redefine words and concept. I.e: you write that Plotinus argues that things are not really things but mere appearances and all would share a fundamental identity and I agree, but well, if things are_not really things_ but appareances and so on, Plotinus is redefining 'thing'. The same can be said for the One that transcends the exist/not-exist distinction. Ok, it does, but while transcending it redefine our idea of reality, thing and to exist. – Francesco D'Isa Oct 18 '18 at 19:32
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    @FrancescoD'Isa - Thanks for the comment. Yes. We would redefine 'reality', thing' and 'exist' so that these concepts make sense when combined. Usually our definitions (or ideas of these things) lead us straight into philosophical problems. I feel that recognising the point being made by the OP and the issues the question raises helps to get us out of these problems. – user20253 Oct 19 '18 at 10:59

If the Universe is the set of all things (whether of rational or irrational value), then it should also include the concept of nothingness.

So if only one thing exists, it would have to be the Universe itself ("all things", which is the complement of nothing). Because nothing by definition is no-thing.

Things exist objectively; nothingness is only subjective.

Peter Sas explained Badiou's fallacy thus:

Badiou's fallacy illustrates something of importance concerning the paradoxes surrounding the concept of nothingness. As soon as we start using "nothing" as a referring noun, we are in trouble: nothingness becomes a referent, an object. In that case, if we say that nothing exists, we imply that there exists this object called "the nothing", which is contradictory. It is clear that this contradiction is not an objective fact concerning the state where nothing exists. The contradiction is merely an effect of our objectification of this state. Just like Badiou cannot conjure being out of nothingness by giving the latter a proper name, so nothingness cannot be made inconsistent merely by our objectification of it.

Independent Academia, Peter Sas

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  • Thank you for your interesting answer! I’m not sure that this fallacy applies here: no complement are possible without differences, so it can’t be the case where x alone can stand. If I keep away nothing from the game, x has still no identity without other things. If I take nothing in, it’s obviously different from x, and I objectify it as you said – Francesco D'Isa Oct 17 '18 at 12:42
  • How is the absence of anything, a thing? Nothing is a concept, just like pink unicorns. That doesn't mean that it exists as a thing. – Ted Oct 18 '18 at 4:36

I am no philosophy major but practically speaking, I look at it this way. How can a single thing exist? Wouldn't it necessarily need to be a part of something else? Nothing we know of can exist by itself. It's always a minor part of something bigger or of a particular environment.

On the other end of the spectrum, doesn't everything we know of and can measure, consist of something else? Atoms were once though of as the smallest possible component of existence. We are now learning that it's way more complicated than that.

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    IMO, "practically speaking" is not suitable for metaphysical questions :-) From a practical (i.e. common sense) point of view, in the context of the question there are : the OP, you and me. Thus, we are at least three in the "universe" and so the premise of the question; "if only one thing exists..." is plainly false. – Mauro ALLEGRANZA Oct 17 '18 at 11:04
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    I made some minor changes. I assume you are aware you may roll these back or continue editing. Welcome to this SE! – Frank Hubeny Oct 17 '18 at 11:39
  • @Mauro ALLEGRANZA - I do not accept the metaphysical. Anything outside existence which cannot be detected, is equal with the nonexistent IMO :) As for the 2nd part of your comment, maybe the entire world is in my head, and the entire universe is just me. (Did I create all this beautiful art by myself? And if I did, why, oh why, did I have to create techno and dubstep?). However, even that were true and I was alone, wouldn't I consist of something else? – Ted Oct 18 '18 at 4:21
  • @Frank Hubeny - thanks for the warm welcome. I've been a longtime contributor of stackoverflow. Are there any more changes to the format of the discussions? – Ted Oct 18 '18 at 4:23
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    @Ted - Ha. Yes. Why did you create dubstep? Many people want to know. I'd love to have a fierce argument with you about metaphysics but not right now. – user20253 Oct 18 '18 at 17:01

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