In this paper, we present a way to unify Positive Polarity Items formed with some NP and minimizers, such as lift a finger. The connection is made via granularity properties of the two classes of polarity sensitive expressions. We begin with an observation in Strawson 1974 that the use of some NP involves an inference about the availability of a more precise identification of NP. Then, we show that the meaning of minimizers can be captured as the mirror image of the same granularity inference. To model our account, we use the granularity system in van Rooij 2011. We propose pragmatic requirements on the use of some NP and minimizers that explain both their granularity inferences and their polarity properties. Finally, we discuss how our proposal can be viewed as reconciliation of referential and alternative-based approaches to polarity.

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