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Many languages include constructions which are sensitive to the expression of polarity: that is, negative polarity items, which cannot occur in affirmative clauses, and positive polarity items, which cannot occur in negatives. The phenomenon of polarity sensitivity has been an important source of evidence for theories about the mental architecture of grammar over the last fifty years, and to many the oddly dysfunctional sensitivities of polarity items have seemed to support a view of grammar as an encapsulated mental module fundamentally unrelated to other aspects of human cognition or communicative behavior. This book draws on insights from cognitive/functional linguistics and formal semantics to argue that, on the contrary, the grammar of sensitivity is grounded in a very general human cognitive ability to form categories and draw inferences based on scalar alternatives, and in the ways this ability is deployed for rhetorical effects in ordinary interpersonal communication.