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Post Closed as "not a real question" by Qfwfq, Noah Schweber, Steven Landsburg, Andrés E. Caicedo, Goldstern
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François G. Dorais
François G. Dorais
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Emil Jeřábek
Emil Jeřábek
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Let $\phi$ be an undecidable statement of ZFC set theory, for example let's take continuum hypothesis.

What is the ontological status of the "set" $X=\{x\in\{1,2\}:x=1\ or\ (x=2\ and\ \phi)\}$$X=\bigl\{x\in\{1,2\}:x=1\text{ or }(x=2\text{ and }\phi)\bigr\}$ in ZFC?

Let $\phi$ be an undecidable statement of ZFC set theory, for example let's take continuum hypothesis.

What is the ontological status of the "set" $X=\{x\in\{1,2\}:x=1\ or\ (x=2\ and\ \phi)\}$ in ZFC?

Let $\phi$ be an undecidable statement of ZFC set theory, for example let's take continuum hypothesis.

What is the ontological status of the "set" $X=\bigl\{x\in\{1,2\}:x=1\text{ or }(x=2\text{ and }\phi)\bigr\}$ in ZFC?

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Godot
Godot
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Ontological status of some "sets" in ZFC

Let $\phi$ be an undecidable statement of ZFC set theory, for example let's take continuum hypothesis.

What is the ontological status of the "set" $X=\{x\in\{1,2\}:x=1\ or\ (x=2\ and\ \phi)\}$ in ZFC?