I believe someone working in an alternative set theory called $$\{x|a\in x\}$$ the *essence* of *a*. Does someone recall a reference?



The essence of type free set theory?
Here:


"In [1944] Hailperin gave the first of a number of finite axiomatisations of NF now known. Many of them exploit the function $x\mapsto\{y:x∈y\}$ which is injective and total and is an $\in$-isomorphism. This function was known to Whitehead, who suggested to Quine that $\{y:x∈y\}$ should be called the “essence” of x (a terminology clearly suggested by a view of sets as properties-in-extension)."


Forster, Thomas, "Quine’s New Foundations", The Stanford Encyclopedia of Philosophy (Summer 2019 Edition), Edward N. Zalta (ed.), URL = <https://plato.stanford.edu/archives/sum2019/entries/quine-nf/>.


