Dialectal and historical usage of "not care" in the meaning of "not mind"

Solution 1:

I've done a quick search through Medieval and Early Modern Sources Online (MEMSO) and certainly have one hint of it being used in the positive, not negative sense in England.

1655 'Residents of Belton declared their resolution to fight for their possessions, and when he said "Surely you will not rebel against the Lord Protector," they replied they had rebelled against a better man and would not care to rebel against him. 22 Nov 1655 (Cal. State Papers Domestic, 1655-1657, p 81)

Problem here is that CSP Domestic is not a verbatim transcript, so you'd need to track down the original to be sure.

Weighed against this, is a much larger number of documents using 'would not care to' in the conventional sense of 'would not want to'.

I can imagine that phrases like this can get turned on their heads quite easily though. Anybody familiar with the phrases 'I could not care less' (UK) and 'I could care less' (North America) can testify to that.

Solution 2:

Care has several subtle meanings depending on context. "I don't care to..." can be the negative "I don't wish to...", but it can also mean the almost neutral "I don't mind to..." where you have no objection to something. Perhaps this latter meaning shares something in common with the positive Appalachian?

If so, definition 4 for care in the OED covers such negative and conditional construction.

Definition 4.a.(a) is neutral:

not to care passes from the notion of ‘not to trouble oneself’, to those of ‘not to mind, not to regard or pay any deference or attention, to pay no respect, be indifferent’. Const. for, etc.

1490 Caxton tr. Foure Sonnes of Aymon (1885) vi. 139, I departed fro my londe poure & exyled, but I dyd not care for it.
1535 Bible (Coverdale) Matt. xxii. 16 Master we knowe that thou..carest for no man.
1590 Spenser Faerie Queene ii. ii. sig. O2v, Ne ought he car'd, whom he endamaged By tortious wrong. a1616 Shakespeare Tempest (1623) i. i. 15 What cares these roarers for the name of King?

And definition 4.b. is a bit more positive:

Not to mind (something proposed); to have no disinclination or objection, be disposed to. Now only with if, though.

1526 W. Bonde Pylgrimage of Perfection i. sig. Fii, Some for a fewe tythes, with Cayn, careth nat to lese the eternall ryches of heuen.
c1590 Marlowe & T. Nashe Dido iv. v, So you'll love me, I care not if I do.
1600 Shakespeare Henry IV, Pt. 2 i. ii. 126, I care not if I doe become your phisitian.
...
1748 S. Richardson Clarissa V. xx. 179 Will you eat, or drink, friend?.. I don't care if I do.

Here, Shakespeare's Chief Justice is telling Falstaff he wouldn't mind throwing him into prison. It's a threat, almost like he wants to imprison him.

And Richardson's more recent use is more familiar:

Widow. Will you eat, or drink, friend?

Fellow. A cup of small ale, I don't care if I do.

Widow. Margaret, take the young man down, and treat him with what the house affords.