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This paper sets forth a construct that describes how many undergraduate students understand mathematical terms to refer to mathematical objects, namely that they only refer to those objects that satisfy the term. I call this students’ pronominal sense of reference (PSR) because it means they treat terms as pronouns that point to objects, like “that.” The paper compares this account of reference with those assumed in common mathematical logic instruction. I demonstrate how propositional logic imposes unnatural uses of language on students while predicate logic is more natural to naïve language use and mathematical language use, when developed properly.