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Sense and reference

Sense and reference is a foundational distinction in philosophy of language and semantics, introduced by the German philosopher and mathematician Gottlob Frege in his 1892 paper "Über Sinn und Bedeutung" (translated as "On Sense and Reference").^[1] In this framework, the sense (Sinn) of a linguistic expression refers to its mode of presentation or the cognitive content associated with it, which determines how the expression is understood, while the reference (Bedeutung) is the actual object, entity, or truth-value that the expression denotes in the world.^[2] For instance, the phrases "the morning star" and "the evening star" share the same reference— the planet Venus—but differ in sense because they present it in distinct ways (as visible in the morning versus the evening).^[3] Frege developed this distinction to resolve puzzles about the cognitive significance of identity statements, such as why "Hesperus is Phosphorus" (where both names refer to Venus) conveys new information, unlike the tautological "Hesperus is Hesperus," even though both have the same reference.^[1] He argued that senses are objective, abstract entities in a "third realm" beyond the physical and mental, graspable by different speakers and determining the reference without being identical to it; for example, two descriptions like "the inventor of bifocals" and "the first Postmaster General" can have different senses but the same reference (Benjamin Franklin).^[3] This theory extends to sentences, where the sense is a "thought" (Gedanke)—the proposition expressed—and the reference is its truth-value (true or false).^[2] The sense-reference framework has profoundly influenced modern semantics, logic, and philosophy of mind, providing tools to analyze phenomena like belief attributions (e.g., one can believe "Mark Twain wrote Huckleberry Finn" without believing "Samuel Clemens wrote Huckleberry Finn," despite co-reference) and the behavior of expressions in opaque contexts such as quotation or indirect speech.^[3] It also addresses issues with non-referring terms, like fictional names ("Odysseus" has a sense but no reference, rendering certain sentences as lacking a truth-value rather than meaningless).^[2] Frege's ideas, originally published in the Zeitschrift für Philosophie und philosophische Kritik, remain central to debates on meaning, intentionality, and the nature of linguistic understanding.^[1]

Historical Context

Precursors in Ancient Philosophy

In ancient Greek philosophy, Antisthenes (c. 445–365 BCE), a disciple of Socrates and founder of the Cynic school, developed a theory of language that emphasized the uniqueness of verbal expressions in relation to reality. According to Antisthenes, every enunciation (logos) refers to a singular, particular existent, capturing an incommunicable essence tied to concrete experience rather than abstract universals. This view posits that words designate unique things through their "proper statement" (oikeios logos), such that predication beyond identity statements like "A is A" is impossible, as it would imply shared general properties that do not exist in reality.^[4] Thus, language operates through direct, singular reference, creating a proto-distinction between the verbal expression, governed by convention (nomos), and the underlying, natural reality of individual essences that resist generalization or contradiction.^[4] The Stoics, building on earlier Socratic influences in the Hellenistic period (from Zeno of Citium around 300 BCE onward), advanced a more structured semiotics through their tripartite model of the sign. In this framework, a sign consists of the signifier (a spoken or written word, which is corporeal), the signified (the lekton or "sayable," an incorporeal concept or meaning), and the referent (the external object, also corporeal). The lekton serves as an intermediary, representing the semantic content expressed by the signifier without being identical to the physical referent it points toward.^[5] A key example of lekta is the predicate "walks," which denotes an incorporeal sayable distinct from the actual corporeal event of someone walking or the body performing the action. Lekta encompass complete propositions, such as "Dion walks," where the nominative case (e.g., "Dion") combines with the predicate to form a meaningful structure that subsists independently of material instantiation. This separation highlights lekta as non-physical entities that mediate between linguistic signs and empirical objects, allowing for the articulation of truth or falsity without conflating expression with the thing itself.^[5] These ancient ideas have been interpreted by some scholars as prefiguring later distinctions in philosophy of language by decoupling linguistic meaning from direct empirical reference: Antisthenes through the insistence on unique, ineffable essences beyond verbal generalization, and the Stoics via the incorporeal lekta as a layer of signification intervening between words and reality. Recent scholarship, such as Susanne Bobzien's 2021 analysis, argues that Frege drew significant elements of his philosophy of language from Stoic sources (via Carl Prantl's history of logic) without attribution, suggesting stronger historical connections for the Stoics, though direct influence remains debated and Antisthenes' link is more interpretive.^[6] Although not fully formalized as a theory of cognitive modes of presentation, this separation anticipates the recognition that expressions can convey structured meanings apart from their denotative targets, influencing subsequent semantic inquiries without empirical or psychological elaboration.

Influences from Modern Philosophy

In the 19th century, John Stuart Mill introduced a foundational distinction in the philosophy of language between denotation and connotation in his seminal work A System of Logic (1843), which laid groundwork for later analyses of meaning by separating a term's referential role from its descriptive content.^[7] Denotation refers to the objects or class of objects that a term applies to, while connotation encompasses the attributes or qualities implied by the term that define its applicability.^[8] This framework marked a shift toward empirical and logical examination of linguistic meaning within British philosophy, influencing subsequent thinkers by highlighting how words function beyond mere pointing to entities. Mill illustrated this distinction with examples such as the term "white," which denotes all objects possessing that property—such as snow, paper, or the summit of Chimborazo—while connoting the attribute of whiteness itself.^[8] Similarly, "man" denotes individual humans like Peter or Paul but connotes essential attributes including corporeity, animal life, and rationality, demonstrating that general names carry informative content that shapes their use in propositions.^[7] These examples underscore how connotation enriches a term's role in reasoning, allowing it to convey more than just a referential function and enabling precise definitions through specified attributes. Mill's approach provided a psychological basis for meaning, viewing connotation as rooted in mental associations of attributes with objects, which contrasted with later objective conceptions of linguistic content.^[9] This empiricist perspective, emphasizing how speakers' cognitive processes determine a term's implications, positioned Mill as the primary precursor to Gottlob Frege's developments in the late 19th century, though Frege sought to refine it by prioritizing intersubjective objectivity over subjective psychology.^[9] Broader British analytic traditions, including empiricist logics from figures like John Locke and David Hume, offered supplementary context through their focus on clear ideas and empirical verification, but Mill's explicit denotation-connotation binary remained the most direct antecedent to distinctions in meaning.^[7]

Core Concepts

Sense

In Gottlob Frege's philosophy of language, the sense (German: Sinn) of a sign is defined as the objective mode of presentation through which its referent is given to the mind, distinct from both the referent itself and any subjective psychological associations.^[10] This intersubjective aspect of meaning ensures that senses are sharable across individuals who understand the language, providing a determinate way in which an object or concept is conceived without depending on personal mental images. For instance, the expressions "the morning star" and "the evening star" both refer to the planet Venus but possess different senses because they present the same object under contrasting modes—one as visible in the morning sky and the other in the evening.^[11] Frege introduces this concept in his 1892 essay "Über Sinn und Bedeutung," using examples from proper names and definite descriptions to illustrate how senses capture the conceptual content conveyed by linguistic expressions.^[10] Frege regarded senses as objective abstract entities, separate from the physical world of objects and the subjective realm of individual ideas or mental images. He later posited, in his 1918 essay "The Thought," that they inhabit a "third realm" of objective thought contents.^[12]^[13] This third realm comprises timeless, mind-independent entities that form a shared repository of human cognition, accessible through language and not reducible to private psychological states; for example, while two people might have varying mental images of Alexander the Great, the sense associated with his name remains uniformly objective.^[14] Unlike subjective ideas, which vary idiosyncratically (such as a historian's detailed conception versus a child's vague one), senses are public and determinate, ensuring consistent understanding within a linguistic community.^[15] The role of sense is crucial in determining the cognitive value and informativeness of propositions, particularly in identity statements. A tautological identity like "a = a" holds trivially because the sense on both sides is identical, offering no new information, whereas "a = b" (such as "Hesperus is Phosphorus") is informative precisely because the differing senses provide distinct modes of presentation of the same referent, revealing a previously unrecognized equivalence.^[10] This explains why such statements can expand knowledge despite expressing the same truth-value. Frege's notion of sense thus underpins the informational content of language, enabling recognition of novel insights. Frege's sense differs fundamentally from John Stuart Mill's earlier concept of connotation, which Mill treated as a subjective attribute tied to the psychological associations of general terms, lacking the objective status Frege assigns to sense.^[15] While Mill viewed proper names as non-connotative—mere labels without inherent conceptual content—Frege's sense provides an objective, intersubjective layer of meaning even for such names, refining Mill's framework by elevating it beyond individual psychology to a shared logical structure.^[14]

Reference

In Gottlob Frege's philosophy of language, the reference (German: Bedeutung) of a linguistic expression is the actual entity or object it denotes, distinct from the mode of presentation through which that entity is grasped.^[11] For proper names or singular terms, the reference is the individual object itself designated by the name.^[11] For instance, the proper name "Aristotle" refers to the historical philosopher who was the pupil of Plato and teacher of Alexander the Great, regardless of varying descriptions used to identify him.^[11] Predicates, as incomplete or unsaturated expressions, have as their reference a concept or, more precisely, a function that maps objects to truth-values.^[16] This functional character ensures the predicative role in forming propositions, where the reference of a predicate like "is a philosopher" denotes the concept of being a philosopher, applicable to arguments such as proper names.^[16] In contrast to proper names, which saturate to complete the reference, predicates require supplementation by other expressions to yield a full denotation.^[16] For complete sentences or assertoric expressions, the reference is the truth-value of the sentence—either the True or the False—independent of how the thought is articulated.^[11] Thus, while the sense of a sentence conveys the thought it expresses, its reference hinges solely on whether that thought corresponds to reality.^[11] A key principle governing reference is that the reference of a complex expression is determined by the references of its parts, such that substituting co-referential components preserves the overall reference.^[11] Frege articulates this as: "The Reference of a word [forms] part of the Reference of the sentence," ensuring that the truth-value of a compound sentence depends on the denotations of its constituents rather than their senses.^[11] This distinction from sense allows multiple expressions to share the same reference despite differing cognitive contents; for example, "the Evening Star" and "the Morning Star" both refer to Venus but present it differently, resolving issues in logical identity statements.^[11] Such utility underscores reference's role in formal semantics and inference.^[11]

Interrelations and Applications

Sense and Descriptive Content

In Gottlob Frege's philosophy of language, definite descriptions such as "the author of 'Hamlet'" express a sense through the unique identification of an object via its descriptive attributes.^[17] The sense here is the mode of presentation of the referent, which conveys how the object is given to the mind, rather than merely denoting the object itself.^[11] For instance, the phrase "the author of 'Hamlet'" presents William Shakespeare not as a bare name but through the attribute of authorship, contributing to the cognitive content without equating directly to the sense.^[13] This linkage of sense to descriptive content underscores that descriptions provide a structured way of identifying referents, emphasizing uniqueness as a condition for successful reference. Frege's approach prioritizes the sense's role in ensuring that the description picks out a single object, predating and influencing later theories.^[18] In contrast to Bertrand Russell's subsequent theory of descriptions, which analyzes them quantificationaly with explicit uniqueness and existence conditions, Frege integrates uniqueness into the sense itself as an objective feature of the expression.^[17] The sense of a definite description remains objective, shared across speakers who understand the language, even if incomplete without sufficient contextual knowledge to fully grasp the mode of presentation.^[11] This objectivity ensures that the sense determines the reference determinately when a referent exists, independent of individual subjective associations.^[13] A classic illustration is the description "the King of France," which expresses a sense—the concept of the unique ruler of France—but lacks a reference since no such individual currently exists.^[19] This separation allows for meaningful discourse about non-referring descriptions, though it raises issues like the implications for sentences attributing properties to them, as in the baldness paradox.^[17] Unlike pure proper names, which may appear to designate directly without evident descriptive load, definite descriptions unpack the sense into explicit attributes, enriching the mode of presentation with conceptual structure. Frege's development of sense for such descriptions extends John Stuart Mill's earlier notion of connotation—the descriptive meaning of general terms—by applying it to singular expressions.

Sense-Reference Distinction in Propositions

In Frege's theory, the sense of a complete declarative sentence constitutes a thought (Gedanke), which is an objective, abstract entity that captures the cognitive content shared by speakers who understand the sentence, independent of their individual mental states.^[20] This thought is composed of the senses of the sentence's constituent parts, such as the senses of singular terms and predicates, forming a structured whole that determines how the world must be for the sentence to be true.^[13] Unlike subjective ideas, thoughts belong to a "third realm" of objective contents, graspable by multiple minds and serving as the bearers of truth.^[11] The reference of a sentence, by contrast, is its truth-value: either the True or the False, which remains constant regardless of the particular mode of presentation of the thought.^[20] This identification ensures that sentences differing only in how they express the same thought—such as synonyms or reformulations—share the same reference, as the truth-value depends solely on whether the thought corresponds to reality, not on its linguistic or conceptual formulation.^[11] For instance, the sentences "Hesperus is Phosphorus" and "The evening star is the morning star" express different thoughts due to the distinct senses of "Hesperus" (evening star) and "Phosphorus" (morning star), yet both have the same truth-value, the True, explaining why the identity statement can be informative despite its apparent triviality.^[13] In contexts involving propositional attitudes, such as belief reports (e.g., "A believes that Hesperus is Phosphorus"), the reference of the embedded clause shifts from its customary truth-value to its customary sense—the thought itself—allowing the distinction to account for failures of substitutivity.^[20] Here, replacing co-referential terms with different senses can alter the truth-value of the attitude ascription, as the object of belief is the thought, not the truth-value.^[11] This mechanism of indirect reference preserves the cognitive differences between thoughts while enabling precise semantic analysis. The sense-reference distinction for propositions underpins Frege's logical framework by permitting inferences and validity to be evaluated based on truth-values (references), while senses maintain the informational and cognitive nuances essential for understanding assertion, proof, and reasoning.^[21] It thus reconciles the objective structure of logic with the subjective grasp of meaning, ensuring that logical relations hold across equivalent expressions without conflating their epistemic import.^[20]

Linguistic and Philosophical Implications

Translation Challenges for "Bedeutung"

The German term Bedeutung, as employed by Gottlob Frege, literally translates to "meaning" or "significance" in English, but its everyday connotations in German—encompassing both semantic content and import—have sparked ongoing debates among translators regarding how best to convey Frege's technical intent without introducing ambiguity.^[22] This linguistic breadth of Bedeutung complicates its rendering, as it must distinguish Frege's post-1892 usage from ordinary language, where it does not strictly denote an object but also implies value or relevance.^[23] Early English translations of Frege's works often rendered Bedeutung as "meaning," which blurred the boundary with Sinn (sense), leading to interpretive confusion; for instance, Philip Jourdain's 1912 translation of Begriffsschrift used "denotation" for Bedeutung while reserving "meaning" for Sinn, but Ludwig Wittgenstein's notes from 1913–1914 simply adopted "meaning" for both.^[22] Max Black's 1948 translation of "Über Sinn und Bedeutung" standardized "reference" (initially "referent" in some contexts), a choice influenced by Peter Geach's advocacy for its alignment with Frege's logical emphasis on denotation, which became the philosophical norm despite alternatives like Carnap's "nominatum" (1947) or "denotation" proposed by Bertrand Russell (1905).^[24] Later editions, such as Geach and Black's 1979 Translations from the Philosophical Writings of Gottlob Frege, reverted to "meaning" for consistency with Frege's pre-1892 usage, though this shift highlighted the term's evolution and risked conflating distinct concepts.^[22] The preference for "reference" underscores its success in emphasizing Bedeutung as the denotative object in Frege's framework—such as the truth-value of a sentence or the bearer of a proper name—aligning with his logical semantics, yet it sacrifices the term's broader German nuances of "significance" or "importance," potentially narrowing interpretations of Frege's holistic view of language.^[24] For example, in discussing proper names, Frege states that "the reference of a proper name is the object itself that we designate by its means," where translating Bedeutung as "meaning" could imply subjective import rather than objective designation, thus obscuring the distinction from sense and affecting analyses of identity statements like "Hesperus is Phosphorus."^[22] Similarly, in sentences, Bedeutung as the truth-value (true or false) loses clarity if rendered as "meaning," as seen in critiques where equating the Bedeutung of "No men are mortal" and "2 + 2 = 5" to "meaning" misleadingly suggests semantic equivalence despite differing references.^[23] These translation choices have shaped scholarly reception, with proponents like David Bell (1980) defending "reference" for its precision in capturing Bedeutung's role in truth-valuation, while others, such as Michael Beaney, opt to leave the term untranslated to preserve contextual ambiguity across Frege's oeuvre.^[22] Ultimately, the debates reveal how Bedeutung's ambiguity influences the sense-reference distinction, prompting translators like Timothy Ebert and Curtis Rossberg (2013) to prioritize "reference" for its entrenchment in Anglophone philosophy, ensuring fidelity to Frege's logical innovations over literal equivalence.^[24]

Criticisms and Developments

One prominent critique of Frege's sense-reference distinction came from Saul Kripke, who argued in his lectures compiled as Naming and Necessity that proper names function as rigid designators, referring to the same object in every possible world where that object exists, without relying on a descriptive sense or mode of presentation as Frege proposed. Kripke challenged the Fregean view by contending that names like "Aristotle" are not synonymous with clusters of definite descriptions (e.g., "the pupil of Plato and teacher of Alexander"), as such descriptions fail to rigidly designate across modal contexts, such as counterfactual scenarios where Aristotle might not have been a philosopher. This rigid designator theory undermines Frege's account of sense as providing cognitive content for proper names, suggesting instead that reference is fixed by a causal-historical chain originating from an initial baptism, rather than descriptive senses. Ludwig Wittgenstein's later philosophy, particularly in Philosophical Investigations, offered another critique through his private language argument, which rejected Frege's conception of senses as objective entities in a timeless "third realm" independent of human practices. Wittgenstein argued that meanings, including senses, are not private or platonically fixed but emerge from public language games and communal use, rendering Frege's third realm untenable as it posits incommunicable, ideal contents that cannot be verified or shared without rule-following paradoxes. This shift emphasized that senses lack the objective status Frege attributed to them, as any attempt to ground meaning in private mental presentations leads to indeterminacy, thereby dissolving the distinction's reliance on abstract, realm-bound entities. Further developments arose from W.V.O. Quine's skepticism toward analyticity in "Two Dogmas of Empiricism," which indirectly eroded Frege's sense by questioning the boundary between analytic truths (tied to sense or meaning) and synthetic ones (tied to reference or empirical fact). Quine contended that no clear criterion exists to demarcate analytic statements as true by virtue of meanings alone, as synonymy and analyticity form a blurred web of belief holistically confirmed or infirmed by experience, thus challenging Frege's view of sense as a stable determinant of necessary truths. Similarly, Donald Davidson's truth-conditional semantics, outlined in "Truth and Meaning," prioritized reference via Tarski-style truth conditions over Frege's sense, proposing that a theory of meaning for a language consists in specifying truth conditions for its sentences without invoking intermediary senses. Davidson argued that understanding a sentence involves grasping under what conditions it is true, sidelining Frege's sense as unnecessary for semantic explanation and reducing meaning to referential truth values, much like Frege's own assignment of truth-values to propositions but without the cognitive layer of sense. Frege's original framework also revealed limitations in addressing indexicals such as "I" and "now," which he treated in "The Thought" as having context-dependent senses that shift with the speaker or time, yet without a fully systematic account of how such variability integrates into the composition of thoughts. For instance, Frege acknowledged that "I" expresses a sense that varies per utterer, preventing direct communication of the same thought across contexts, but his theory inadequately explained the mechanism of sense determination beyond ad hoc supplementation. Likewise, Frege viewed vagueness in sense composition as a flaw of natural language rather than a feature to theorize, dismissing borderline cases in predicates like "heap" as defects that ideal logical languages should avoid, without developing tools for handling indeterminate senses.^[25] In modern formal semantics, Frege's ideas evolved into the intension-extension framework, where sense corresponds to an intension—a function from possible worlds (or contexts) to extensions—and reference to the extension in the actual world, as formalized in works like Rudolf Carnap's Meaning and Necessity. This approach, influential in Montague grammar, treats expressions' meanings as intensional structures that compose to yield truth-conditional extensions, extending Frege's distinction to handle modality and context while addressing some of his gaps in indexicals and compositionality.

References

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