I often hear people say something like
For whose benefit is that?
Should it not be
For whomse benefit is that
Who -> Whom
Whose -> Whomse
I know "whomse" is not a real word. My question is: why doesn't it exist?
The easiest way to think about this is to compare to he him his:
Who gets the benefit? He gets the benefit.
To whom does the benefit accrue? The benefit accrues to him.
For whose benefit is that? That is for his benefit.
For whomse benefit is that? That is for hims benefit.
Obviously that last is unnecessary/wrong—in place of hims (or him's) we have his, and in place of whomse (or whom's) we have whose. (Also, sound aside, whose is no more related to who's than his is to he's.)
That's the quick-and-dirty, functional answer; it's also accurate that whose and whom evolved alongside each other, subject to different influences than what might make sense from our modern English point of view. From the OED Online:
whose, pron. Etymology: Middle English hwās, later hwǭs, whǭs, altered form of hwas, hwes, Old English hwæs (< **χwasa*) genitive of hwá and hwæt, through the influence of hwā, hwǭ who pron., hwām, hwǭm whom pron. (Later Middle English whas probably represents an unstressed variant.)
—"whose, pron." OED Online. Oxford University Press, June 2016. Web. 20 August 2016.
There aren't two different nominative/objective pairs
Who -> Whom
Whose -> *Whomse, *Whom's, etc.
Instead, there's three choices
Who can't be both objective and possessive.
Whose is (originally and now) the genitive of who. From Etymonline:
whose: genitive of who; from Old English hwæs, genitive of hwa (see who).
In all Indo-European languages that I know, a genitive modifies a noun but does not agree with this noun, not even in languages with elaborate paradigms. In other words, the form of the genitive doesn't change when the form of the noun it belongs to changes. An example from Latin:
Magna Minerva est dea. "The great Minerva is a goddess."
Amicus Vulcanus est deus. "Friend Vulcanus is a god."
Vulcanus est amicus Minervae. "Vulcanus is Minerva's friend."
Video amicum Minervae. "I see Minerva's friend."
As you see, the form of the genitive doesn't change, while the noun that the genitive modifies (amicus/amicum) changes form to indicate that it is subject or object, respectively. Only adjectives can change their form if they belong to a noun, not genitives. It is the same in English.
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