Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License
 n. The principle that objects are equal if and only if their observed properties are the same, regardless of internal processes that lead to those properties.
 n. The principle that functions are equal if and only if they operate on the same domain and for any given element of the domain the result of each of the functions is the same.
 n. The principle, codified in the axiom of extensionality, that sets are equal if and only if they contain the same elements.
Etymologies
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Examples

For Grice, the admission that "intensionality seems to be imbedded in the very foundations of language" doesn't preclude "extensionality."

However, it turns out that this is not generally the case unless one assumes extensionality.

And since Lowe (1953) many authors have expressed discomfort with such entities regardless of extensionality.

(One philosopher who explicitly accepts extensionality but feels uneasy about scattered entities is Chisholm 1987.)

In other words, fully unrestricted composition calls for extensionality, on pain of giving up both supplementation principles.

So it is not entirely surprising that as long as proper parthood is well behaved, as per (P. 4), extensionality might pop up like this in the presence of substantive composition principles.

But their independent motivation also bears witness to the fact that controversies about the necessity of extensionality, and particularly about (28), stem from genuine and fundamental philosophical conundrums and cannot be assessed by appealing to our intuitions about the meaning of

Concerning the necessity of mereological extensionality, i.e., the lefttoright conditional in the consequent of (27):

Moreover, and independently, if Î¾ were just overlap, then (P. 13Î¾) would be unacceptable for anyone unwilling to embrace mereological extensionality.

For example, the extensionality theorem of EM, (27), says that composite things with the same proper parts are identical, but in the presence of indeterminacy this may call for qualifications.
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