In this paper, I argue that there are good motivations for a relativist account of the domain-sensitivity of quantifier phrases. I will frame the problem as a puzzle involving what looks like a logically valid inference, yet one whose premises are true while the conclusion is false. After discussing some existing accounts, literalist and contextualist, I will present and argue for an account that may be said to be relativistin the following sense: (i) a domain of quantification is required for determining truth value, but is idle in determining semantic content, and (ii) the same sentence, as used on one and the same occasion, may receive different truth values relative to different domains.