I understand that the phrase at all means in any way or in the slightest, e.g. What is the opposite of “to stink” (v)? Is there one at all?, or Not bad at all
I don't understand how the individual words come together to make that meaning.
I understand the use of at as a preposition, e.g.
Are there any apples here?
Can be written as
Are there any apples at this place?
But then what meaning does all take on?
Are there any apples at all?
All is not a place, as far as I can see.
I tried to think of at in the sense of rate
Cornering is not hard at 100 km/h
and that sort of makes sense if you take all to be a shortening of all rates
Cornering is not hard at all
but that doesn't seem to fit the generally understood meaning of at all.
Is there a way to break down the phrase at all into its constituent words that adds up to the same meaning?