We construct a discriminative, syntactic language model (LM) by using a latent support vector machine (SVM) to train an unlexicalized parser to judge sentences. That is, the parser is optimized so that correct sentences receive high-scoring trees, while incorrect sentences do not. Because of this alternative objective, the parser can be trained with only a part-of-speech dictionary and binary-labeled sentences. We follow the paradigm of discriminative language modeling with pseudonegative examples (Okanohara and Tsujii, 2007), and demonstrate significant improvements in distinguishing real sentences from pseudo-negatives. We also investigate the related task of separating machine-translation (MT) outputs from reference translations, again showing large improvements. Finally, we test our LM in MT reranking, and investigate the language-modeling parser in the context of unsupervised parsing.