On Sense and Reference

1. Introduction

Frege’s 1892 essay “On Sense and Reference” (Über Sinn und Bedeutung) is a compact but technically rich work that introduces a distinction which has become central to the philosophy of language. Frege proposes that many expressions—especially proper names and complete sentences—possess both a sense (Sinn) and a reference (Bedeutung). He develops this distinction in order to address specific semantic and logical problems, rather than as a free‑standing metaphysical doctrine.

The essay is organized around a series of interconnected questions: How can identity statements be both true and informative? How do different linguistic expressions that refer to the same thing nonetheless differ in cognitive value? What is the semantic role of whole sentences, and how do their parts contribute to what is said? How should one account for the apparent opacity of contexts such as belief reports and indirect discourse?

Frege’s answers rely on a rigorous conception of logical form and a systematic use of his earlier function–argument analysis of propositions. The essay proceeds from relatively familiar examples drawn from astronomy (such as ‘the Morning Star’ and ‘the Evening Star’) to more abstract claims about the truth‑values of sentences and the nature of thoughts (Gedanken). It is written in a dense but methodical style, continuously appealing to logical considerations and to the role of language in communication and inquiry.

Subsequent sections of this entry treat, in turn, the historical background, the details of Frege’s central distinction, its application to identity, sentences and propositional attitudes, the underlying logical framework, and the extensive critical and historical reception that has made “On Sense and Reference” a cornerstone of analytic philosophy.

2. Historical and Intellectual Context

Frege’s essay emerges from late 19th‑century debates about logic, mathematics, and the nature of meaning. It is shaped by both his own earlier logical work and by broader currents in philosophy and linguistics.

Background in Logic and Mathematics

Frege was already known for Begriffsschrift (1879) and The Foundations of Arithmetic (1884), where he developed a formal logical language and defended logicism—the thesis that arithmetic is reducible to logic. In those writings he had treated sentences extensionally, focusing on conditions under which they are true or false. “On Sense and Reference” refines this by asking how language can have the cognitive and communicative roles presupposed by his logical project.

Frege’s concerns intersected with:

Theories of Meaning in Frege’s Environment

Contemporary semantic views included:

• Psychologism in logic and language (e.g., J. S. Mill), treating meanings as mental ideas.
• Reference‑only or denotational accounts, common in logic and mathematics, where the semantic role of a term is exhausted by its bearer or extension.
• Hermeneutic and philological traditions in German philosophy, emphasizing interpretation and the historical use of words rather than formal semantics.

Frege’s essay is often read as opposing psychologism by positing objective senses and as modifying purely referential views by showing that reference cannot alone explain informativeness and communication.

Place in Frege’s Own Development

Historically, “On Sense and Reference” sits between Frege’s early logic and his later essays on thoughts and assertion (such as “The Thought,” 1918). Commentators frequently interpret it as the point at which Frege explicitly integrates his logical, epistemological, and semantic concerns into a single framework designed to account for both the correctness of inferences and the cognitive significance of language use.

3. Author and Composition of the Essay

Frege’s Intellectual Position in the Early 1890s

By the time Frege composed “On Sense and Reference” (1891–1892), he was a mid‑career mathematician and logician at Jena, recognized in a small circle for his innovative but not widely adopted logical notation and for The Foundations of Arithmetic. His work had not yet achieved broad influence, and he was still refining the logical and semantic tools needed for his projected system of the foundations of mathematics.

Motivations and Pre‑history of the Essay

Frege’s earlier writings had already raised problems about identity, reference, and the content of thoughts. In Begriffsschrift, he introduced identity as a primitive logical sign but did not yet articulate the sense–reference distinction. In The Foundations of Arithmetic, he had distinguished between the “content” of a sentence and its circumstances of truth, and between objects and concepts, anticipating aspects of the later theory.

Scholars generally agree that several pressures converged:

• The need to explain how mathematical identities can be discoveries rather than mere definitional trivialities.
• Reflection on the role of language in expressing thoughts and enabling shared reasoning.
• Difficulties in accounting for substitution within formal derivations when co‑referential terms appear in intensional or epistemic contexts.

Composition and Immediate Context

Frege composed the essay as a stand‑alone theoretical contribution for the Zeitschrift für Philosophie und philosophische Kritik. Surviving evidence suggests a relatively short gestation, building directly on material he had been developing for his logical system and for what would become Grundgesetze der Arithmetik (1893, 1903).

The composition is tightly structured around a progressive sequence of problems: starting with identity statements, moving to a general account of names, then extending the framework to complex expressions and to sentences as bearers of truth‑values. Commentators often emphasize that Frege writes here for a philosophical, not purely mathematical, audience, which partially explains the reliance on natural‑language examples rather than formal symbolism.

4. Publication and Textual Tradition

Initial Publication

“Über Sinn und Bedeutung” first appeared in 1892 in the New Series, Volume 100 of the Zeitschrift für Philosophie und philosophische Kritik. It was published in German as a single, self‑contained essay without a dedication or explicit reference to a larger project, though it is closely connected to Frege’s work on logic and arithmetic.

There is little evidence of extensive editorial intervention; the text is usually regarded as authorially stable.

Manuscript and Transmission

No autograph manuscript is known to be in general circulation. The essay’s textual tradition depends on the journal printing and subsequent reprints. Standard modern editions rely on photographic or typographical reproductions of the original.

The main critical edition is in:

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Gottlob Frege, Kleine Schriften, ed. I. Angelelli (Hildesheim: Olms, 1967).

Editors have occasionally noted minor typographical issues in the journal version, but no major textual variants are at stake in philosophical interpretation.

Translations and Terminological Choices

The essay entered Anglophone discussion through mid‑20th‑century translations, notably in the collection edited by Peter Geach and Max Black. Rendering key terms such as Bedeutung and Sinn has been a central scholarly concern:

Michael Beaney’s translation in The Frege Reader provides updated terminology and notes. Comparative study of translations has influenced debates about how to understand “reference,” “denotation,” and related notions in Frege’s theory.

Reprints and Scholarly Use

Since the mid‑20th century, the essay has been widely reprinted in collections of Frege’s writings and in anthologies on the philosophy of language. The text used in contemporary scholarship is highly standardized, and disputes rarely turn on textual matters but rather on interpretive questions about Frege’s terminology and examples.

5. The Puzzle of Identity and Cognitive Value

Frege opens “On Sense and Reference” with a puzzle about identity statements, focusing on their apparent difference in cognitive value despite sharing a truth‑functional profile.

Trivial vs. Informative Identity

Frege contrasts:

• Trivial identity: statements of the form “a = a”, such as “Hesperus = Hesperus,” which seem to express no substantive information beyond a logical law of reflexivity.
• Informative identity: statements of the form “a = b”, such as “Hesperus = Phosphorus” (or “the Morning Star is the Evening Star”), which can represent genuine discoveries.

Both kinds of statement are true whenever the same object is on each side of “=”. Yet they differ in what they contribute to knowledge.

The Puzzle Formulated

The puzzle can be summarized as follows:

If the meaning of a name were exhausted by its reference, then replacing one name by another with the same reference should not change cognitive value. Proponents of this reading of Frege note that he presents this as a problem for purely referential or Millian accounts of names.

Cognitive Value and Modes of Presentation

Frege links the puzzle to differences in how an object can be presented or grasped. Two co‑referential names may guide cognition differently, so that learning “a = b” connects two previously distinct “routes” of access. Identity statements thus appear to involve both reference and something finer‑grained.

The need to explain:

• How informative identity is possible,
• Why substitution of co‑referential terms can alter what is learned,
• And how rational agents can coherently doubt or discover identities,

motivates Frege to introduce a distinction between sense and reference in the subsequent development of the essay.

6. Frege’s Distinction between Sense and Reference

Frege proposes that many expressions, especially proper names, have two semantic aspects: sense (Sinn) and reference (Bedeutung). This distinction is designed to account for the puzzle of informative identity without abandoning classical logic.

Proper Names as the Primary Case

Frege uses “proper name” broadly to cover not only ordinary names (e.g., “Aristotle”) but also definite descriptions and other singular terms. For such expressions:

• The reference is the object to which the name stands in a semantic relation, if there is one.
• The sense is the mode of presentation of that object—the way in which the reference is given.

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“The sense of a proper name is grasped by everyone who is sufficiently familiar with the language or totality of designations to which it belongs.”

— Frege, “On Sense and Reference”

Sense as Mode of Presentation

Frege illustrates sense as that aspect of meaning which:

• Determines which object, if any, is the reference.
• Encodes the cognitive route by which a thinker can identify the referent.
• Can be shared by different speakers, objectively, without being a private mental image.

Two names can have:

The distinction allows Frege to say that “a = b” is informative because it connects two different senses that converge on the same reference.

Independence and Objectivity of Senses

Frege stresses that senses are not mental images. They are:

• Objective in the sense that they can be the common object of understanding for different thinkers.
• Accessible through linguistic competence rather than introspection.
• Distinct from the psychological processes by which they are grasped.

Frege also allows that an expression can have a sense without a reference (e.g., empty names), though the treatment of such cases is developed only briefly in the essay. The sense–reference distinction, first introduced for names, is then extended to more complex expressions and to whole sentences in later sections of the work.

7. Examples: Morning Star, Evening Star, and Informative Identity

Frege’s most famous illustration of informative identity involves astronomical designations for the planet Venus. These examples are meant to make the sense–reference distinction vivid.

The Astronomical Case

In ordinary 19th‑century usage:

Astronomers discovered that the Morning Star and the Evening Star are the same planet, Venus. The identity statement:

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“The Morning Star is the Evening Star.”

is therefore true. But it is not trivial; it encapsulates a significant empirical discovery.

How the Example Supports the Distinction

On a purely referential view, both “Morning Star” and “Evening Star” denote Venus, so the identity should have the same cognitive status as “Venus = Venus.” Frege uses the example to argue that this is inadequate: the statement is not a mere logical tautology, but an informative empirical claim.

He explains this by assigning:

• Different senses to “Morning Star” and “Evening Star,” corresponding to different observational modes of presentation (morning vs. evening appearance).
• The same reference (Venus) to both expressions.

The identity statement is then seen as stating that two distinct modes of presentation pick out the same object. Its informativeness lies in unifying previously separate cognitive “routes.”

Generalization to Other Cases

Frege’s example is intended as paradigmatic rather than exceptional. Analogous cases include:

In each, the two sides can be seen as different senses converging on a single reference. This illustrates Frege’s strategy: treat many informative identities as discoveries about the relation between senses and a shared referent, rather than as revelations about the identity relation itself.

8. Sentences, Thoughts, and Truth‑Values

After treating names, Frege extends the sense–reference distinction to complete declarative sentences, integrating his semantics with his logical system.

The Reference of Sentences: Truth‑Values

Frege argues that the reference (Bedeutung) of a complete declarative sentence is its truth‑value. He postulates exactly two such objects:

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“We call the thought a sentence expresses its sense, and we designate the sentence’s reference as its truth‑value.”

— Frege, “On Sense and Reference”

This choice aligns sentence semantics with his function–argument logic: predicates and names combine to yield an argument to a truth‑value‑producing function.

The Sense of Sentences: Thoughts (Gedanken)

The sense of a declarative sentence is, for Frege, a thought (Gedanke): the objective, propositional content that can be true or false. Thoughts are:

• Not identical with psychological events or acts of thinking.
• Shareable among different thinkers and repeatable across uses.
• Fine‑grained enough to distinguish co‑referring sentences that differ in cognitive value.

The same thought can be expressed by different sentences in different languages, illustrating the distinction between linguistic form and sense.

Compositional Contribution of Parts

Subsidiary expressions contribute to the sentence’s sense and reference in a compositionally structured way:

• The senses of names and predicates combine to yield the thought.
• The references of those parts determine, via logical structure, the resulting truth‑value.

This allows Frege to reconcile the logical role of sentences as bearers of truth and falsity with the cognitive role of sentences as expressing articulate contents of judgment and communication.

9. Indirect Discourse and Propositional Attitudes

Frege applies the sense–reference framework to contexts such as reported speech and propositional attitude ascriptions, where straightforward substitution of co‑referential terms appears to fail.

Oblique (Indirect) Contexts

In sentences like:

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“A believes that the Morning Star is visible.”

one cannot always replace “Morning Star” with “Evening Star,” even if both refer to Venus, without potentially changing the truth of the report about A’s belief. Frege uses this to argue that, in such indirect or oblique contexts, expressions do not have their customary reference.

Instead:

• In ordinary (direct) occurrences, an expression refers to its usual reference (e.g., Venus).
• In indirect occurrences (inside the “that”-clause, or under verbs of saying/believing), the same expression has as its reference its customary sense.

Propositional Attitudes and Thoughts

Reports of beliefs, hopes, doubts, and similar states are taken to concern thoughts:

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“A believes that p.”

is, on Frege’s view, about the thought expressed by “p.” To ensure that the embedded clause picks out the appropriate thought, Frege assigns indirect reference to its constituent expressions: they now designate the senses needed to reconstruct that thought.

This mechanism is intended to explain:

• Why substitution of co‑referential terms may fail to preserve truth in belief contexts.
• How different individuals can stand in attitudes to the same or different thoughts, depending on which modes of presentation are involved.

Scope and Limitations in the Essay

Frege’s treatment is focused on indirect discourse and basic propositional attitudes, leaving more complex intensional phenomena largely unaddressed. Later commentators have debated how far this “indirect reference” strategy can be generalized, and whether it fully resolves puzzles about belief and substitution, but in “On Sense and Reference” it presents a unified extension of the sense–reference framework to non‑extensional linguistic environments.

10. Logical Framework: Functions, Arguments, and Concept‑Words

Frege’s semantic proposals in “On Sense and Reference” presuppose his broader function–argument analysis of logical form, which replaces traditional subject–predicate structure.

Functions and Arguments

In Frege’s logical system:

• A function is an expression that, given an argument, yields a value.
• Functions can be of various levels (e.g., from objects to truth‑values, or from functions to truth‑values).

Predicative expressions—adjectives, verbs, and more complex predicates—are treated as functions from objects to truth‑values.

This framework meshes with the idea that the reference of a sentence is its truth‑value: applying the reference of a predicate (a function) to the reference of a name (an object) yields a truth‑value.

Concept‑Words (Begriffswörter)

Frege distinguishes concept‑words (Begriffswörter) from proper names. Concept‑words:

• Stand for concepts, which he analyzes as special kinds of functions from objects to truth‑values.
• Typically correspond to predicates or open sentence frames (e.g., “__ is a planet”).

They have both sense (a way of presenting a concept/function) and reference (the concept/function itself).

Compositionality within the Framework

Frege’s compositional semantics relies on this function–argument structure:

• The sense of a predicate is a mode of presentation of a concept; combined with the sense of a name, it yields a thought.
• The reference of the predicate (a concept/function) applied to the reference of the name (an object) yields a truth‑value.

This allows Frege to treat logical constants, quantifiers, and more complex operators as higher‑level functions, though the essay itself concentrates primarily on names, simple predicates, and sentential contexts relevant to sense and reference.

11. Key Concepts and Technical Terminology

“On Sense and Reference” introduces or presupposes several technical terms that structure Frege’s semantic theory. The following table summarizes central notions as they function within the essay:

These concepts are interdefined within the essay and are used to articulate Frege’s systematic approach to meaning, reference, and logical structure.

12. Philosophical Method and Style in Frege’s Essay

Frege’s method in “On Sense and Reference” combines logical rigor with carefully chosen ordinary‑language examples. Commentators often emphasize that the essay exemplifies a distinctive early analytic style.

Problem‑Driven, Argumentative Structure

Frege proceeds by isolating specific puzzles and then gradually enriching his theoretical apparatus:

1. He starts with the problem of informative identity.
2. He proposes the sense–reference distinction as a solution.
3. He extends the distinction to complex expressions, sentences, and indirect contexts.

This problem‑driven structure is designed to justify each theoretical move as required by logical and cognitive considerations, rather than as speculative metaphysics.

Use of Examples and Thought‑Experiments

Frege’s style involves:

• Concrete examples from astronomy (“Morning Star”/“Evening Star”), history, and arithmetic.
• Hypothetical scenarios about what an ideal rational agent might or might not know.
• Reflection on cases of error, discovery, and disagreement.

These examples serve to test semantic hypotheses against intuitions about informativeness, substitution, and rational belief.

Anti‑Psychologistic Orientation

Methodologically, Frege is explicitly anti‑psychologistic. He distinguishes:

Frege insists that senses and thoughts are objective and sharable, not private mental images or ideas, and structures his arguments to separate semantic from psychological questions.

Expository Features

The essay is notable for:

• A dense but economical German prose style, with few rhetorical flourishes.
• Minimal use of formal symbolism, in contrast to Begriffsschrift and Grundgesetze, reflecting its philosophical readership.
• Frequent use of distinctions (e.g., sense/reference, direct/indirect discourse) introduced by explicit contrast and backed by systematic examples.

The combination of logical precision, abstract terminology, and concrete illustration has made the essay a model for later analytic work, while also leaving room for interpretive disputes about Frege’s intended commitments.

13. Major Criticisms and Alternative Theories

Frege’s proposals in “On Sense and Reference” have been extensively debated. Criticisms target both his specific theses (e.g., about sentence reference) and his overall semantic framework, often leading to alternative theories.

Obscurity and Ontology of Sense

Some critics argue that Frege’s notion of sense is not sufficiently clarified:

• It is characterized negatively (not an idea, not an object) and functionally (as mode of presentation), but its metaphysical status remains unclear.
• The postulation of an extensive realm of objective senses, in addition to objects, concepts, and truth‑values, is viewed as ontologically demanding.

Alternative approaches, such as behaviorist or use‑theoretic accounts, have sought to explain meaning without positing such abstract entities.

Direct Reference and Causal Theories of Names

20th‑century direct reference theorists (e.g., Saul Kripke, Keith Donnellan, David Kaplan) have challenged the Fregean claim that sense determines reference:

• They argue that proper names often refer directly to their bearers, with no descriptively articulated sense mediating the reference.
• Causal‑historical chains of use, rather than descriptive senses, are proposed to explain how names latch onto objects.

On such views, co‑referential names may differ in associated information without differing in a Fregean sense, and the explanation of informative identity must be recast in other terms.

Substitution and Propositional Attitudes

Critics also question whether Frege’s indirect reference treatment of belief and attitude ascriptions is adequate:

• Some contend that it overgenerates opacity, since not all embedded contexts behave alike.
• Others argue that appealing to shifts in reference from objects to senses does not fully capture fine‑grained differences in belief attributions.

Alternative frameworks include possible‑world semantics, structured propositions, and pragmatic accounts that place more weight on speaker intentions and conversational context.

Truth‑Values as Sentence References

Frege’s identification of sentence reference with truth‑values has been both influential and controversial:

• Some commentators object that this view cannot easily explain informational differences between logically equivalent but distinct sentences, if they share both reference and, on some readings, thought.
• Others propose that propositions, rather than truth‑values, should be taken as the primary semantic values of sentences.

Intensional logics, situation semantics, and possible‑worlds models provide alternative accounts in which sentences are associated with richer semantic values than bare truth‑values.

Fregean Responses and Reconstructions

Sympathetic interpreters have developed neo‑Fregean positions that modify or reinterpret key elements of the 1892 essay:

These developments show that Frege’s framework remains a central reference point, even where later theories depart significantly from his original formulations.

14. Influence on Analytic Philosophy and Formal Semantics

“On Sense and Reference” has had a pervasive impact on the development of analytic philosophy and on contemporary formal semantics.

Early Analytic Philosophy

Frege’s sense–reference distinction influenced major figures in the early analytic tradition:

Frege’s insistence on the autonomy of logic from psychology and his focus on language as a vehicle for thoughts are widely regarded as foundational to analytic philosophy’s methodology.

Philosophy of Language

Key debates in the philosophy of language have taken Frege’s essay as a central reference point:

• The contrast between Fregean and Millian/direct reference views of names.
• Discussions of propositional attitudes and opacity.
• Theories of descriptions, indexicals, and context‑sensitivity.

Even when rejecting Frege’s conclusions, later authors typically engage with his distinctions and examples.

Formal Semantics and Linguistics

In 20th‑century formal semantics:

• Frege’s ideas about compositionality and the function–argument structure of meaning informed the development of model‑theoretic semantics for natural languages.
• The distinction between intension (roughly corresponding to sense in some traditions) and extension (reference) in possible‑worlds semantics is often presented as a systematization of Fregean themes.

Work by Richard Montague and successors in formal semantics explicitly builds on Frege’s conception of logical form and semantic composition.

Logic, Mathematics, and Beyond

Frege’s integration of semantic notions (sense, reference, truth‑value) with a rigorous logical calculus has shaped:

• The modern understanding of logical consequence as truth‑preservation.
• Semantic accounts of quantification, identity, and logical form.
• Neo‑Fregean programs in the philosophy of mathematics, which draw on his treatment of abstraction and reference while incorporating or revising his semantic framework.

Across these domains, “On Sense and Reference” serves as a reference point for both continuity and critique in the ongoing development of analytic and formal approaches to language and logic.

15. Legacy and Historical Significance

The long‑term significance of “On Sense and Reference” lies in its role as a foundational text for multiple strands of 20th‑ and 21st‑century philosophy.

From Relative Obscurity to Canonical Status

At the time of its publication, the essay was read by a limited audience. Over the subsequent decades:

The spread of English translations, especially in the 1950s and 1960s, was crucial in establishing its international prominence.

Enduring Themes

Several core ideas from the essay have become enduring reference points:

• The distinction between sense and reference as a model for other semantic dualities (intension/extension, content/extension).
• The treatment of propositions (thoughts) as objective contents shared across thinkers and languages.
• The use of compositional, formally regimented semantics to illuminate natural‑language phenomena.

Even when later theories diverge—for instance, endorsing direct reference or alternative accounts of sentence meaning—they often do so by positioning themselves with respect to Frege’s framework.

Cross‑Disciplinary Impact

Beyond philosophy of language and logic, Frege’s essay has influenced:

• Philosophy of mind, in discussions of propositional attitudes and mental representation.
• Linguistics, particularly formal semantics and pragmatics informed by logical analysis.
• Philosophy of mathematics, where questions about reference to abstract objects and the status of mathematical identity are framed in Fregean terms.

Continuing Debates

Current scholarship continues to revisit and reinterpret the essay, focusing on:

• The exact nature and individuation of senses and thoughts.
• The viability of Fregean semantics in light of direct reference theories and cognitive science.
• Historical questions about Frege’s relation to his predecessors and successors.

Collectively, these ongoing discussions underscore the essay’s historical importance: it not only shaped the emergence of analytic philosophy but also remains a live source of problems, distinctions, and conceptual tools in contemporary theoretical work.