© 2019 R. Harald Baayen et al. The discriminative lexicon is introduced as a mathematical and computational model of the mental lexicon. This novel theory is inspired by word and paradigm morphology but operationalizes the concept of proportional analogy using the mathematics of linear algebra. It embraces the discriminative perspective on language, rejecting the idea that words' meanings are compositional in the sense of Frege and Russell and arguing instead that the relation between form and meaning is fundamentally discriminative. The discriminative lexicon also incorporates the insight from machine learning that end-to-end modeling is much more effective than working with a cascade of models targeting individual subtasks. The computational engine at the heart of the discriminative lexicon is linear discriminative learning: simple linear networks are used for mapping form onto meaning and meaning onto form, without requiring the hierarchies of post-Bloomfieldian 'hidden' constructs such as phonemes, morphemes, and stems. We show that this novel model meets the criteria of accuracy (it properly recognizes words and produces words correctly), productivity (the model is remarkably successful in understanding and producing novel complex words), and predictivity (it correctly predicts a wide array of experimental phenomena in lexical processing). The discriminative lexicon does not make use of static representations that are stored in memory and that have to be accessed in comprehension and production. It replaces static representations by states of the cognitive system that arise dynamically as a consequence of external or internal stimuli. The discriminative lexicon brings together visual and auditory comprehension as well as speech production into an integrated dynamic system of coupled linear networks.