In the article Quine’s New Foundations of The Stanford Encyclopedia of Philosophy (Summer 2019 Edition), Thomas Forster writes:

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

How did Alfred North Whitehead communicate the essential point of view to Quine?

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    $\begingroup$ In what sense "communicate to"? Quine's thesis supervisor was Alfred North Whitehead. $\endgroup$ Nov 17, 2023 at 13:31
  • $\begingroup$ @MauroALLEGRANZA Thanks for the supervisor information. It would be nice to have a quotable reference, if that is available. $\endgroup$ Nov 19, 2023 at 22:46
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    $\begingroup$ Possible sources to be checked: Quine's Set Theory and its Logic (1969) and Whitehead and the rise of modern logic (1941=. $\endgroup$ Nov 20, 2023 at 11:09
  • $\begingroup$ Having said that, the analogy is quite reasonable, equating the essence with the collection of all properties. $\endgroup$ Nov 20, 2023 at 12:13
  • $\begingroup$ @MauroALLEGRANZA Thanks! I got hold of the texts. :) Yes, the term is quite appropriate. $\endgroup$ Nov 21, 2023 at 20:13


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