Is there a rigorous definition for this concept? ‘The collection of every individual thing’? If an ‘individual thing’ is something that is different from something else, ‘everything’ could be the collection of every x that is not y where x≠y?

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    But every "thing" satisfies the formula ∀x(x=x). – Mauro ALLEGRANZA Oct 13 '18 at 15:27
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    The collection of x such that ∃y (x≠y) ? And if the world is made of one only thing ? See Monism. – Mauro ALLEGRANZA Oct 13 '18 at 15:29
  • If you are taking anything "in its broadest sense" you are admitting exactly the kind of looseness that rules out its "rigorous definition", it is called being future open. But look at Williamson's paper Everything. Do "individual electrons" satisfy x=x? I don't know, they are indistinguishable, after all, see SEP's Individuality in Quantum Theory. Does a river? Not according to Heraclitus. – Conifold Oct 13 '18 at 19:46
  • @Conifold I eliminated that expression, thanks - also for the links, I’ll read them. I’d say that excepted the one electron universe theory, individual electrons are not identical, since they occupy different positions – Francesco D'Isa Oct 13 '18 at 20:46
  • You are thinking of electrons as classical particles, that doesn't work. They do not "occupy" any positions, the wave function of even a single electron is smeared all over the universe, and "position" is an operator that can not be used to individuate. – Conifold Oct 13 '18 at 20:52

The set U of all things: For all x, x is an element of U.

Unfortunately, U can be shown not to exist. Apparently every set must exclude something. (See Russell's Paradox)

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    The OP is asking for a definition not about forming a collection by using it. By the way, Russell's Paradox features the set of all sets, not of all "things", so it does not include "everything". And there is no problem with forming a class of all sets anyway. – Conifold Oct 13 '18 at 20:44
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    The category Set includes all sets and does not suffer from Russell's paradox. en.wikipedia.org/wiki/Category_of_sets – user4894 Oct 13 '18 at 20:47
  • Thank you very much for the answer, I agree with @Conifold by the way – Francesco D'Isa Oct 13 '18 at 21:01
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    @Conifold Russell's Paradox features the set of all sets that are not elements of themselves. The set of all sets (if you have an is-a-set predicate) and the set of everything (my example) can both be proven not to exist using ordinary set theory and Russell's Paradox. – Dan Christensen Oct 14 '18 at 6:01
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    This answer is poor because it assumes the use of a specific axiomatisation of set theory which has been explicitly constructed to exclude sets which contain themselves, like the set of all sets. Furthermore, because Russell's paradox does not deal with the set of all sets, by relaxing some of the axioms of ZFC (like the misleadingly named notion of "well-foundedness"), the set of all sets can be easily constructed by taking the union of all sets. – Carl Masens Oct 15 '18 at 8:42

To ask, What does 'everything' consist of? is to ask in effect, What things exist? This is the fundamental question of ontology. There have been many attempts to make this question rigorous by tying ontology to logic. One of the most popular approaches is to say that quantified formulas of the form (∃x)Fx are true if and only if there exists an object in the domain of quantification which when substituted for x satisfies the open formula Fx. Quine summarizes this position with the aphorism: To be is to be the value of a variable. 'Everything' is then the entirety of our domain of quantification.

Of course, this leaves unsettled the question as to what should be in our domain of quantification. We could be minimalist and hold that it should contain only those things that are necessary for a scientific account of the universe, but this places a huge burden on the reductionist program. Who is to say what is absolutely necessary, and for what purpose?

Restricting our logic to first order is perhaps too limiting: we might think it reasonable to quantify over properties or classes or propositions. Do numbers exist? Mathematicians quantify over them, but they don't seem to be the same kind of thing as chairs and kangaroos. Do events exist? Davidson proposed that we quantify over events in order to explain how "John ran quickly" entails "John ran". Do fictional entities exist in some extended sense? Meinong thought so, and free logics permit an extended domain of quantification containing fictional entities. Do minds exist? Or are they reducible to or identical with physical things? Do the fundamental particles of physics really exist? Physicists quantify over them, but pragmatist philosophers hold that they are nothing more than useful fictions that serve to aid us in making predictions. Do possible worlds exist? Many logicians and philosophers of language quantify over possible worlds, but only a few such as David Lewis are willing to allow that they have real existence.

So, even when you think you have found a rigorous criterion, most of the interesting questions about ontology remain.

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    Thank you for your useful answer! As I use the term, things need not to exist in a specific (like pragmatic) way for being so. A number or a Pegasus can not exist in some sense, but they are still something: i.e concepts, mythological fictions etc. To be a thing it’s enough to have any identity, to be different to something else. – Francesco D'Isa Oct 13 '18 at 21:14

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