Unsupervised approaches to extractive summarization usually rely on a notion of sentence importance defined by the semantic similarity between a sentence and the document. We propose new metrics of relevance and redundancy using pointwise mutual information (PMI) between sentences, which can be easily computed by a pre-trained language model. Intuitively, a relevant sentence allows readers to infer the document content (high PMI with the document), and a redundant sentence can be inferred from the summary (high PMI with the summary). We then develop a greedy sentence selection algorithm to maximize relevance and minimize redundancy of extracted sentences. We show that our method outperforms similarity-based methods on datasets in a range of domains including news, medical journal articles, and personal anecdotes.