Department of Ratios and Sums

Sunday Puzzler (proposed):

Out of the Ould Wan was the Da and the Uncle and your other one entirely.

Oh and the Da was always the singularly and why not say integrally apt and telling title of the one of them, though the name Uncle, non-specific enough in itself, being applied in any particular case as chance and need might require, immediately made your other claimants to the name all known individually and acutely and at once as your other one entirely, should there be any such non-Da, non-Uncle reference needed.

There is ever only one Da, as there is ever only one particular Uncle at a time being mentioned if at all, but there are pluralities of possible your other ones entirely. They clump and stew about the bogways, enumerable in their chosen packs, on close inspection containing each of them the Uncle, whose jarring appellation, transferable in full to every qualifying individual, can be found to be required of at least one of the seeming other ones entirely of any proper pack when a polling of the populace is made. Odd, that.

So of the Ould Wan, we have the Da, integrally numerable, the Uncle, with its pointed pronunciation in each case, and your other one entirely, however numerous, but always including, on close inspection, your other Uncle entirely.

Which recursive mathematics genially expresses the foregoing logical relation, eh?