Even during the golden age of prescriptivism, while the standard line is
that of Lowth (whose grammar appeared in 49 editions), parroted by
(among dozens of others) Ussher (1793: 48: "Two negatives instead of
one are very improper; Ex. I can not eat none, ought to be, I can eat
none, or I can not eat any"), it would occasionally be acknowledged that
"in very animated speeches, where a man were delivering himself with
vehemence and heat," certain double negations, by virtue of their "more
forcible sound," "might perhaps be used not with an ill grace[!]" (Baker
1779: 59). Martin (1748: 93) provides a cogent mathematical gloss on
the two varieties of double negation:
The two negatives as used by the Saxons and French must be understood by
way of apposition...which way of speaking is still in use among us; and
in this case the two negatives answer to the addition of two negative
quantities in Algebra, the sum of which is negative. But our ordinary
use of two negatives (in which the force of the first is much more than
merely destroyed by the latter) corresponds to the multiplication of two
negative quantities..., the product of which is always affirmative.
Baker, R. (1770) Remarks on the English Language, 2d edition. London:
Lowth, (Bishop) R. (1762) A Short Introduction to English Grammar.
London: J. Hughs.
Martin, B. (1748) Institutions of Language. Facsimile reprint:
Menston, Eng.: The Scolar Press, 1970.
Ussher, G. N. (1793) The Elements of English Grammar, 3d edition
improved. Glocester: R. Raikes.