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The way I understood first-order-logic with quinean metaontology is, that a world is the set of everything that exists. Now I'm searching for a quote. I looked at some texts from Russell and at On What There Is from Quine, but found nothing useful. Maybe some of you know a quotation by heart.

Thanks in advance

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    It seems a very bad idea to start philosophy by assuming things exist. This has to be proved. Some people would call philosophy the study of what is not. If we define existence as you do we run straight into a famous set-theoretic paradox and metaphysics comes to a halt. .
    – user20253
    Commented Mar 1, 2018 at 13:26
  • @PeterJ IE, the aptly named Russell's Paradox.
    – user935
    Commented Mar 5, 2018 at 19:58
  • @barrycarter - That's the one.
    – user20253
    Commented Mar 6, 2018 at 13:04

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See e.g. Ontology and Ideology (1951):

The ontology to which an (interpreted) theory is committed comprises all and only the objects over which the bound variables of the theory have to be construed as ranging in order that the statements affirmed in the theory be true.

Thus, applying this criteria to e.g. first-order set theory, we conclude that the "universe" of sets is composed by all and only the sets whose exisence is needed in order to satisfy the axioms and theorems of the theory.

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