We explore linguistic and behavioral features of dogmatism in social media and construct statistical models that can identify dogmatic comments. Our model is based on a corpus of Reddit posts, collected across a diverse set of conversational topics and annotated via paid crowdsourcing. We operationalize key aspects of dogmatism described by existing psychology theories (such as over-confidence), finding they have predictive power. We also find evidence for new signals of dogmatism, such as the tendency of dogmatic posts to refrain from signaling cognitive processes. When we use our predictive model to analyze millions of other Reddit posts, we find evidence that suggests dogmatism is a deeper personality trait, present for dogmatic users across many different domains, and that users who engage on dogmatic comments tend to show increases in dogmatic posts themselves.