Most classifiers rely on discriminative boundaries that separate instances of each class from everything else. We argue that discriminative boundaries are counter-intuitive as they define semantics by what-they-are-not; and should be replaced by generative classifiers which define semantics by what-they-are. Unfortunately, generative classifiers are significantly less accurate. This may be caused by the tendency of generative models to focus on easy to model semantic generative factors and ignore non-semantic factors that are important but difficult to model. We propose a new generative model in which semantic factors are accommodated by shell theory’s hierarchical generative process and non-semantic factors by an instance specific noise term. We use the model to develop a classification scheme which suppresses the impact of noise while preserving semantic cues. The result is a surprisingly accurate generative classifier, that takes the form of a modified nearest-neighbor algorithm; we term it distance classification. Unlike discriminative classifiers, a distance classifier: defines semantics by what-they-are; is amenable to incremental updates; and scales well with the number of classes.