Vagueness poses a problem for traditional theories of meaning. This is because these theories hold that meaning is governed by determinate conditions, however, the pervasive vagueness in natural language suggests that language exhibits gradience such that predicates can apply to different degrees. For example, it seems that someone might be bald to a certain degree, without them being definitely bald or not bald. Recently linguists and philosophers have proposed new theories of meaning where the semantic value of a sentence is computed through probabilistic conditions, rather than determinate ones. These probabilistic semantic theories promise to explain the gradience of our semantic judgments. They also promise to explain why not all entailments between sentences are categorical, rather that sentences can logically entail others to varying degrees. I will argue that these theories provide a superior alternative to traditional theories of meaning. I also aim to explore the relationship between probabilistic semantics and formal epistemology, and how it can shed light on the debate over essentialism.