Positive and negative quantifiers induce two very different perspectives in comprehenders--perspectives that have strong applications to rhetoric and communication. These are briefly reviewed. A potential mechanism, based on earlier work, is introduced, resting on the idea that negatively quantified sentences (like Not all of the boys went to the party) may be given interpretations that both consist of an asserted amount, and a supposition of a greater amount. This account, the supposition-denial theory, is proposed as a unifying mechanism that explains the variety of perspective effects. Straightforward predictions from this account are tested in three studies. In particular, we found that a linguistic index of denial almost perfectly predicted the incidence of particular kinds of focus effects (Study 1 and 3). We also show that the observed perspectives set up by negative quantifiers depend upon the whole quantified sentence being processed, not just the quantifier (Study 2). This is consistent with the denial aspect being central to perspective. We discuss how positive quantifiers may also be treated within the framework, leading to independently confirmed predictions. Finally, we discuss the relation of our account to current work in pragmatics and semantics.