This paper presents a series of quantitative gradient acceptability judgment studies of English negative sentences. Adult native speakers of American English recruited via Amazon’s Mechanical Turk were asked to rate sentences on a scale of 1 to 7 on the basis of their naturalness. The main study compares sentences with the marker n’t and either a negative object (e.g. ‘John didn’t eat nothing’) or a negative subject in canonical position (‘nobody didn’t eat’). Each sentence type has two possible interpretations, one in which the two negatives contribute a single semantic negation, the so-called Negative Concord reading, and another in which the two negations yield a semantic Double Negation logically equivalent to an affirmative. While mean acceptability ratings were below the median for all items, statistical analyses of the gradient data revealed that speakers prefer Negative Concord over Double Negation readings for sentences with negative objects. To rule out a processing explanation for the preference for negative objects over sentence initial negatives, a follow-up study tested the acceptability of sentences with a single negative subject or object and no negative marker. This revealed a preference for subjects, suggesting that the object preference in the two negatives study is a true grammatical effect. A third study revealed that Double Negation constructions are unacceptable overall even in explicit denial contexts, and a fourth study added Negative Auxiliary Inversion constructions (e.g. ‘Didn’t nobody eat’), to compare three types of Negative Concord. The results of all four studies are argued to reveal an English grammar that generates both Negative Concord and Double Negation, and in which Negative Concord is generated despite its unacceptability and reported absence in usage.