The distinction between sets and proper classes has interesting ontological consequences.

One way to define a proper class, in the context of set theory, is to state that it is not an element (in a set). As a consequence, if c is a proper class, $\neg\exists x(x=\{c\})$. If we take an object to exist just if it is an element, it follows that proper classes do not exist.

Nevertheless, we may quantify over classes. If e.g. R is Russell's class $\{x|x\notin x\}$, we have that $\exists x(x=R)$; but $\neg\exists x(x=\{R\})$. One may say that Russell's class subsists, but does not exist.

Do "empty names" behave similarly, so that Sherlock Holmes subsists, but does not exist?

Does the element-strategy have noteworthy advantages? Has it been explored in the literature?

The distinction between sets and proper classes has interesting ontological consequences.

One way to define a proper class, in the context of set theory, is to state that it is not an element, in a set. As a consequence, if c is a proper class, $\neg\exists x(x=\{c\})$. If we take an object to exist just if it is an element, it follows that proper classes do not exist.

Nevertheless, we may quantify over classes. If e.g. R is Russell's class $\{x|x\notin x\}$, we have that $\exists x(x=R)$; but $\neg\exists x(x=\{R\})$. One may say that Russell's class subsists, but does not exist.

Do "empty names" behave similarly, so that e.g. Sherlock Holmes subsists, but does not exist?

Does the element-strategy have noteworthy advantages? Has it been explored in the literature?

The distinction between sets and proper classes, as per some set theories, has interesting ontological consequences.

One way to define a proper class, in the context of set theory, is to state that it is not an element (in a set). As a consequence, if c is a proper class, $\neg\exists x(x=\{c\})$. If we take an object to exist just if it is an element, it follows that proper classes do not exist.

Nevertheless, we may quantify over classes. If e.g. R is Russell's class $\{x|x\notin x\}$, we have that $\exists x(x=R)$; but $\neg\exists x(x=\{R\})$. One may say that Russell's class subsists, but does not exist.

Do "empty names" behave similarly, so that Sherlock Holmes subsists, but does not exist?

Does the element-strategy have noteworthy advantages? Has it been explored in the literature?

The distinction between sets and proper classes has interesting ontological consequences.

One way to define a proper class, in the context of set theory, is to state that it is not an element (in a set). As a consequence, if c is a proper class, $\neg\exists x(x=\{c\})$. If we take an object to exist just if it is an element, it follows that proper classes do not exist.

Nevertheless, we may quantify over classes. If e.g. R is Russell's class $\{x|x\notin x\}$, we have that $\exists x(x=R)$; but $\neg\exists x(x=\{R\})$. One may say that Russell's class subsists, but does not exist.

Do "empty names" behave similarly, so that Sherlock Holmes subsists, but does not exist?

Does the element-strategy have noteworthy advantages? Has it been explored in the literature?