A semantics for possibilistic evidential reasoning is presented based on similarity with paradigmatic examples. The acquisition of evidence generates a pseudo-metric on the universe of discourse. It is shown that every possibility distribution can be realized as an embedding in a pseudo-metric space with the possibility values determined by the distance from distinguished elements in that space. Determining support based on similarity captures the fundamental characteristics of possibilistic analysis: optimistic and independent evaluation of the alternatives. The similarity semantics distinguishes possibility from classical approaches to classification and diagnosis problems based on probabilistic techniques.