Peter and Mary Barnes (nee Rothwell) must have adopted Alice Mather in 1790, as they are recorded as the parents when Alice died the following year. Peter Barns, a weaver, and Mary had married in Bolton, 9 Oct 1771. They already had three children, Ann (1774), William (1776), Peter (1778,80,84 two died), Thomas (1788), befoe they had Alice Mather Barnes baptised (1790).
The middle name suggests Alice's maiden name was Mather, so Mary was widowed, when she married Peter Barns in 1771. The 7 Feb 1785 marriage of John Mather and Alice Barnes is about right for them to be the biological parents.
If Alice was adopted, then it's likely her true parents were William and Betty Mather (nee Holt). They had another Alice born in 1792, a year after this Alice's death. Perhaps Alice was illigiimate, and her bioligical father was William - Who knows?