Reference reference, the relation between a sign and the object it designates, is fundamental to the structure of judgment and the truth of propositions. A proper name, such as “Morning Star,” refers to the celestial body Venus, just as “Evening Star” refers to the same object. Yet the sense, or Sinn, attached to each name differs: the former expresses the manner in which Venus appears at dawn, the latter at dusk. The reference remains identical; the conceptual content, however, is distinct. This distinction reveals that identity statements of the form “a = b” can convey new knowledge, even when a and b share the same reference. The proposition “The Morning Star is the Evening Star” is not trivial, because the senses associated with each term provide different modes of presentation. In a proposition, the reference of a term determines its contribution to the truth-value. If a name lacks reference, the entire proposition lacks a truth-value. Consider the expression “the least rapidly decreasing prime number.” This phrase contains no referent, for no such number exists. The proposition in which it occurs, therefore, cannot be true or false. Only when a term denotes an object—whether an actual physical entity, a number, or a truth-value—does it function within a judgment. The reference of a sentence is its truth-value: true or false. This is not a metaphor but a logical necessity. The sentence “2 + 3 = 5” refers to the truth-value true, not because of its emotional weight or experiential resonance, but because its components, when properly interpreted, yield a consistent result under the rules of arithmetic. Functions and arguments must be distinguished carefully. A function, such as “the square of x,” does not refer to an object until its argument is supplied. When the argument is 2, the function yields 4 as its value. The value of a function is its reference, just as the reference of a proper name is the object it designates. The concept of a function, in this logical sense, is not psychological but formal: it is a rule that maps inputs to outputs. The reference of a predicate, such as “is a prime number,” is a concept. The concept is not a mental image but a rule for determining whether an object falls under it. When we say “7 is a prime number,” the reference of the predicate is the concept of primality, and the reference of the subject is the number 7. The truth of the proposition results from the object’s subsumption under the concept. A name does not derive its reference from the speaker’s intention, the listener’s association, or the context of utterance. Reference is fixed by the linguistic system, by the rules of designation established within the language. The name “Frege” refers to the author of Begriffsschrift, not because anyone believes it, or remembers it, or associates it with a face. It refers because the linguistic convention assigns it to that individual. Even if all knowledge of that individual were lost, the reference would remain, so long as the name retained its place in the structure of language. The reference of “the capital of France” is Paris, regardless of whether anyone currently knows it, or whether Paris has been renamed. The object exists independently of thought or perception. A sentence composed of meaningful parts must have a reference—its truth-value—if it is to be a proposition. But if any constituent lacks reference, the whole fails to determine a truth-value. This principle governs the compositionality of sense and reference. The sense of a compound expression is built from the senses of its parts, while its reference is determined by the references of its parts, under the rules of logical structure. One cannot infer reference from use, nor can one derive sense from psychological association. The logical architecture of language is objective and independent of human psychology. What then determines whether a name refers? Is it the possibility of a consistent application within a system of rules, or is it something more? [role=marginalia, type=clarification, author="a.darwin", status="adjunct", year="2026", length="43", targets="entry:reference", scope="local"] A name without reference—like “the least rapidly decreasing sequence”—does not merely fail to denote; it leaves the proposition suspended, unanchored in reality. Truth requires not just sense, but a foothold in the world. Without reference, thought languishes in abstraction, untested by nature’s law. [role=marginalia, type=objection, author="a.simon", status="adjunct", year="2026", length="39", targets="entry:reference", scope="local"] Frege’s sense-reference dichotomy overlooks pragmatic uptake: speakers often treat “Morning Star” and “Evening Star” as interchangeable without introspecting sense. Reference, in practice, is stabilized by communal usage, not internal modes of presentation—truth-conditions emerge from linguistic habits, not mental representations. [role=marginalia, type=objection, author="Reviewer", status="adjunct", year="2026", length="42", targets="entry:reference", scope="local"]