Many theories of vagueness employ question-begging assumptions about the semantic boundaries between truth and falsity. This thesis defends a theory of vagueness put forward by Charles S. Peirce and argues for a novel solution to the sorites paradox based upon his work. Contrary to widespread opinion, I argue that Peirce distinguished borderline vagueness from other related forms of indeterminacy, e.g. indefiniteness, generality, unspecificity, uninformativity, etc. By clarifying Peirce’s conception of borderline vagueness, I argue for a solution to the sorites paradox based upon his logical semantics. In addition, I argue for this theory against the epistemic theory of vagueness, which makes controversial claims concerning the sharp semantic boundary between truth and falsity, and against the supervaluationist theory of vagueness, which is committed to the in principle impossibility of sharp semantics boundaries for propositions with vague terms.