We present a grammar for expressing hypotheses in visual data analysis to formalize the previously abstract notion of "analysis tasks." Through the lens of our grammar, we lay the groundwork for how a user's data analysis questions can be operationalized and automated as a set of hypotheses (a hypothesis space). We demonstrate that our grammar-based approach for analysis tasks can provide a systematic method towards unifying three disparate spaces in visualization research: the hypotheses a dataset can express (a data hypothesis space), the hypotheses a user would like to refine or verify through analysis (an analysis hypothesis space), and the hypotheses a visualization design is capable of supporting (a visualization hypothesis space). We illustrate how the formalization of these three spaces can inform future research in visualization evaluation, knowledge elicitation, analytic provenance, and visualization recommendation by using a shared language for hypotheses. Finally, we compare our proposed grammar-based approach with existing visual analysis models and discuss the potential of a new hypothesis-driven theory of visual analytics.