Rule-Following Argument

1. Introduction

The rule-following argument is a set of considerations, originating in the later work of Ludwig Wittgenstein, about what it is to follow a rule and to mean something by a word. It questions whether any fact about an individual—such as a mental image, intention, or internal representation—can determine how that person ought to apply a rule in new, previously unconsidered cases.

At its core, the argument turns on the apparent gap between:

• a finite history of how a person has applied a word or rule so far, and
• the indefinitely many ways in which that rule could be extended to future cases.

Proponents maintain that no finite set of past applications uniquely fixes a single “correct” way of going on, and that appealing to inner states or dispositions does not obviously solve this underdetermination. This leads to worries about the normativity of meaning—its role in guiding what one should do—and about the very idea that there are definite facts of meaning.

Saul Kripke’s influential book Wittgenstein on Rules and Private Language (1982) recast Wittgenstein’s scattered remarks as a sharp paradox: if the reasoning is sound, there may be no fact of the matter about what anyone ever means by any word. Kripke’s “sceptical solution” and the responses it provoked have made the rule-following argument a central reference point in philosophy of language, mind, and metaphysics.

The debate concerns not only how linguistic expressions get their meanings, but also what it is to be bound by mathematical rules, logical laws, or norms of action. It has therefore become a focal point for discussions of communal practices, use-theoretic accounts of meaning, the private language argument, and various naturalistic or communitarian approaches to normativity.

2. Origin and Attribution

The rule-following argument is primarily associated with Ludwig Wittgenstein’s later philosophy, as presented in Philosophical Investigations (1953), especially §§138–242. These sections contain numerous remarks on understanding, following a rule, and grasping a meaning, but Wittgenstein does not present a single, linear argument. Instead, he offers a sequence of reminders, thought experiments, and questions.

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“This was our paradox: no course of action could be determined by a rule, because every course of action can be made out to accord with the rule.”

— Wittgenstein, Philosophical Investigations §201

Because Wittgenstein’s text is deliberately non-systematic, later commentators have differed over how to extract an “argument” from it. A pivotal role is played by Saul A. Kripke, whose Wittgenstein on Rules and Private Language (1982) offers a detailed reconstruction that many regard as canonical. Kripke reads Wittgenstein as advancing a sceptical argument about meaning, culminating in what he calls the rule-following paradox.

Kripke’s reconstruction has been so influential that the figure sometimes referred to as “Kripkenstein”—a composite of Kripke’s Wittgenstein and Kripke’s own additions—has become a standard point of reference. Some scholars attribute the paradoxical, global scepticism about meaning more to Kripke than to Wittgenstein himself.

The attribution of specific theses is therefore contested:

Many interpreters distinguish between Wittgenstein’s own “rule-following considerations” and Kripke’s “rule-following paradox,” while acknowledging that Kripke’s work crystallized and popularized the issues that now travel under the heading “the rule-following argument.”

3. Historical Context

Wittgenstein’s rule-following considerations emerge from the transition between his early and later philosophies. In the Tractatus Logico-Philosophicus (1921), Wittgenstein had proposed a picture theory of meaning, where sentences mirror facts in logical form. Over the following decades, he came to reject this perspective as overly formal and detached from actual language use.

In the 1930s and 1940s, Wittgenstein developed a new approach emphasizing language games, forms of life, and the diversity of linguistic practices. The rule-following remarks in Philosophical Investigations belong to this later period and target attempts to explain meaning via hidden entities—mental images, inner ostensions, or abstract rules—that supposedly underlie and fix correct usage.

The broader philosophical climate also matters. Wittgenstein’s later work interacted with:

Kripke’s 1982 reconstruction appears in a different context: the post-Quinean philosophy of language and mind, with active debates on meaning, reference, and naturalism. By then, semantic theories invoking mental representations, dispositional states, or causal-historical chains were prominent. Kripke’s version of the rule-following argument engages, often implicitly, with these developments, raising the question of what sort of fact semantic meaning could be.

Historical work has also connected rule-following issues with contemporaries and predecessors—Frege on sense and rule-governed inference, Ramsey on rules and decision, and the later analytic tradition’s growing interest in normativity and practice. In this landscape, Wittgenstein’s reflections on how rules are embedded in communal activities, and on the impossibility of a purely private language, offered a distinctive challenge to both mentalist and formalist accounts of meaning.

4. The Argument Stated

The rule-following argument can be stated, in one influential formulation, as a challenge to the idea that facts about an individual fix how a rule must be applied in all future cases. A simplified version focuses on a mathematical rule such as addition:

• A person has used the sign “+” in finitely many past calculations, always producing the results we would regard as correct.
• Intuitively, we think that this person thereby means addition by “+” and is thereby bound to answer future problems (e.g., “68 + 57”) according to the addition rule.

The argument asks: what makes it true that the rule they were following was addition rather than some deviant function that coincides with addition on all their past examples but diverges on some future inputs? For any finite set of cases, there are infinitely many such “gerrymandered” rules compatible with that history.

Proponents then consider various candidates for what might determine that addition, and not some deviant rule, is the one meant or followed:

• the person’s past behavior,
• their present or past intentions,
• mental images or verbal formulations of the rule,
• their actual or hypothetical dispositions to respond.

The core claim is that none of these, taken as a fact about the individual, seems uniquely to determine a single rule rather than many alternatives that fit the same data. If so, there is no inner or individualistic fact that constitutes meaning addition rather than some other function.

This yields a tension with ordinary talk of meaning and rule-following, which presupposes that there is a right and wrong way to go on. Subsequent sections explore different ways of analyzing the structure of this argument and possible responses.

5. Logical Structure and Form

Philosophers commonly describe the rule-following argument as having the form of a reductio ad absurdum: starting from widely held assumptions about meaning and rules, it derives an apparently unacceptable conclusion and thereby pressures those assumptions.

A schematized structure often used (especially in Kripke-inspired discussions) is:

1. To mean something by an expression or to follow a rule is to be in some factive state—a mental or physical state—that determines its correct application in all relevant cases.
2. Any such fact about an individual is compatible with multiple candidate rules or functions, each equally consistent with all available evidence about their past applications.
3. Therefore, no fact about the individual determines a unique rule they are following.
4. If no such fact exists, then there is no fact of the matter about what they mean by their words or which rule they are following.
5. Yet our ordinary practices appear to presuppose such facts.

From this, two broad interpretive options are usually distinguished:

The argument relies heavily on an underdetermination premise: the same finite behavioral and mental evidence is claimed to be compatible with infinitely many possible rules. It also involves an equivocation risk that critics highlight: some contend that it slides between a metaphysical thesis (about what facts there are) and an epistemic thesis (about what can be known or justified).

While Kripke’s presentation accentuates the reductio structure, many commentators argue that Wittgenstein’s own text proceeds more via diagnostic moves, shifting attention from hidden inner mechanisms to public criteria of correctness. The abstract logical form of the argument therefore remains a matter of interpretive dispute, even among those who agree on its steps in outline.

6. Key Concepts: Rules, Meaning, and Normativity

The rule-following debate turns on how to understand several interconnected concepts. Different interpretations of the argument often stem from different views of these notions.

Rules

A rule is typically taken to be something that can guide or govern actions or inferences—such as the algorithm for addition, a grammatical rule, or a rule of chess. Philosophers distinguish:

The rule-following argument is particularly concerned with normative rules, not mere regularities.

Meaning

Meaning is at issue insofar as understanding a word is commonly thought of as grasping a rule for its correct use. On this picture:

• To mean addition by “+” is to be committed to using “+” according to the addition rule.
• To understand “red” is to know what counts as correctly applying “red.”

Traditionally, philosophers have proposed that meaning consists in:

• inner mental representations,
• Platonic-like abstract entities,
• behavioral or dispositional profiles,
• roles within inferential networks.

Rule-following considerations probe whether such candidates can underwrite determinate standards of correctness.

Normativity

The normativity of meaning refers to the way in which meaning appears to involve oughts:

• If someone means addition by “+,” then they ought to answer “125” to “68 + 57.”
• If they answer differently, they are not merely atypical; they are wrong.

This normative aspect is distinct from mere predictive regularity. A person might be disposed to make a mistake, but that does not make the mistake correct. The rule-following argument asks what, if anything, makes certain uses correct rather than merely frequent.

Interpretations differ on how to ground this normativity: in individual mental states, in communal practices and sanctions, in teleological or causal facts, or in the structure of inferential roles. The viability of the argument depends in part on whether such grounding is feasible.

7. Kripke’s Sceptical Reconstruction

Saul Kripke’s Wittgenstein on Rules and Private Language presents the most influential explicit reconstruction of the rule-following argument as a sceptical paradox about meaning.

The Sceptical Problem

Kripke formulates a challenge: what fact about an individual could make it true that they mean addition rather than some deviant function by “+”? He insists that the fact must be:

• Finite and accessible, as befits a real human agent;
• Normatively loaded, so that it determines what counts as the correct answer in new cases.

Surveying options—past usage, intentions, mental images, dispositional states—Kripke argues that none satisfies these conditions. Each is compatible with multiple candidate functions that agree on past cases but disagree on some future ones. This yields his “sceptical conclusion” that there are no facts of the traditional sort that fix meaning.

Kripkenstein’s Sceptical Solution

Kripke also attributes to “Wittgenstein” what he calls a sceptical solution. Rather than restore robust semantic facts, this solution reconceives what is at stake when we say someone means something:

• Meaning-attributions are justified not by correspondence to inner facts, but by how a speaker’s use of words fits into a pattern of agreement in a community.
• Correctness is traced to the practices of teaching, correcting, and sanctioning within a linguistic community, not to metaphysical facts about private mental contents.

On this view, there is no deeper, factive “fact of the matter” beyond communal practice; nonetheless, ordinary talk and judgments about meaning are preserved as part of that practice.

Commentators disagree on whether this reconstruction accurately reflects Wittgenstein’s aims, but Kripke’s “Kripkenstein” has shaped much subsequent discussion of rule-following, normativity, and semantic anti-realism.

8. The Plus/Quus Example and Underdetermination

Kripke’s best-known illustration of the rule-following problem is the plus/quus example, designed to dramatize underdetermination.

The Construction

Suppose a person has used the symbol “+” only in sums with relatively small numbers (e.g., numbers below 57), and has always given what we regard as correct addition results. Kripke introduces a deviant function, quus, defined as:

• For all x, y < 57: x ⊕ y = x + y
• Otherwise: x ⊕ y = 5

Here, “⊕” stands for quus. By hypothesis, the person has never encountered sums with operands ≥ 57, so all of their past uses of “+” align with both addition and quus.

The Underdetermination Claim

The key claim is that the entire finite behavioral history of the speaker is compatible with the hypothesis that, by “+,” they always meant quus rather than plus. Moreover, prima facie:

• No further introspection seems to settle the matter, since any mental formula or image they might cite is also susceptible to multiple rule-interpretations.
• No finite explicit rule-statement helps, because it too admits multiple possible extensions beyond cases the speaker has already considered.

Thus, past usage appears to underdetermine which rule the speaker was following. The plus/quus contrast is one vivid case of a general pattern: for any finite data set of input–output pairs, infinitely many mathematical functions fit those data.

The example is not meant to recommend quus as a serious candidate rule, but to structure the sceptical challenge: if every candidate “fact of the matter” about the speaker is equally compatible with plus and quus, what distinguishes meaning plus from meaning quus?

Critics question whether this underdetermination genuinely infects all plausible accounts of rule-following, or whether it exploits an artificially contrived example. Proponents respond that the mathematical triviality of quus is precisely what shows how bare behavioral facts fail to fix normative content.

9. Communal Practices and the Use-Theory of Meaning

Wittgenstein’s later work links rule-following to communal practices and the use-theory of meaning, offering an alternative to inner-state or abstract-object accounts.

Meaning as Use

On a use-theoretic view, associated with Philosophical Investigations, the meaning of a word is not an object or mental state but its role in a language game:

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“For a large class of cases—though not for all—in which we employ the word ‘meaning’ it can be defined thus: the meaning of a word is its use in the language.”

— Wittgenstein, Philosophical Investigations §43

To understand a word is to be able to participate competently in the practices where it figures—asking, answering, inferring, ordering, describing, and so on.

Communal Rule-Following

On this approach, rules are embedded in public practices:

• Children are trained to use terms; they are corrected, praised, or reproved.
• Shared responses to circumstances form a background of agreement.
• Criteria for correct use are manifested in institutionalized patterns of teaching, checking, and disputing.

Some interpreters treat Wittgenstein as suggesting that what it is to follow a rule is just to be integrated into these practices—to “go on in the same way” as others, where “sameness” is marked by communal reactions.

Kripke’s “sceptical solution” explicitly ties correctness to community agreement: the standards for right and wrong applications are given by what the community counts as following the rule. Other communitarian readings (such as those of McDowell or Wright) stress not mere majority opinion but more structured norms of justification that are socially sustained.

The relation between this use-based, communal picture and the original rule-following argument is contested. Some see it as Wittgenstein’s way of dissolving the demand for inner facts; others regard it as offering a substantive, positive account of how meaning and normativity are grounded in human social life.

10. Connections to the Private Language Argument

The private language argument and the rule-following argument are closely intertwined in Philosophical Investigations, especially in the sections following §243. The private language argument challenges the possibility of a language whose words refer to wholly private inner experiences, knowable only to a single individual. The rule-following considerations feed into this by questioning how rules could be followed in isolation from public criteria.

Rule-Following and Privacy

Wittgenstein asks whether someone could have a word for a particular inner sensation (“S”) and determine its correct application solely through introspection. The rule-following problem arises: in the absence of public standards, what would count as getting it right as opposed to merely feeling inclined to apply the word?

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“But ‘I impress it on myself’ can only mean: this process brings it about that I remember the connection right in the future. But in the present case I have no criterion of correctness.”

— Wittgenstein, Philosophical Investigations §258

Here, the worry is that individual memory or impression cannot by itself constitute a rule, because any future use could be made out as “in accord” with the remembered impression. This mirrors the general rule-following argument’s concern that no inner state fixes a unique pattern of correct applications.

Mutual Reinforcement

The connections can be summarized:

Some interpreters see the private language argument as an application of the rule-following considerations to sensation language. Others treat them as distinct but related strands, both emphasizing the dependence of meaning and rule-following on publicly accessible practices and criteria.

11. Standard Objections and Critiques

The rule-following argument and Kripke’s reconstruction have provoked a wide range of objections. These target both the interpretation of Wittgenstein and the philosophical force of the sceptical reasoning.

Objections to Kripke’s Reading

Many commentators argue that Kripke’s global scepticism misrepresents Wittgenstein:

• Therapeutic vs. sceptical Wittgenstein: G. P. Baker and P. M. S. Hacker contend that Wittgenstein is not denying the existence of meaning facts, but exposing confusions generated by a picture that requires a special kind of inner mechanism to underwrite them. On their view, the supposed “paradox” dissolves once that picture is abandoned.
• Over-formalization: Critics maintain that Kripke turns Wittgenstein’s flexible remarks into a rigid, technical problem about functions and semantic facts, thereby missing the broader method of grammatical clarification.

Objections to the Sceptical Argument

Even setting aside interpretive issues, philosophers have challenged the argument’s premises:

Other critics suggest that the argument relies on an unrealistic model of semantic competence, as if speakers internally store infinite tables of input–output pairs. Philosophers like Robert Brandom and Charles Travis propose that actual linguistic practice involves context-sensitive judgment and inferential abilities that do not fit the plus/quus template.

There is also concern that making correctness depend solely on community agreement risks relativism: if whatever the community treats as correct is thereby correct, critics ask how we can make sense of communal error or progress. Proponents of communitarian approaches respond by refining the notion of communal normativity, which will be discussed in later sections.

12. Dispositionalist and Naturalistic Responses

One major family of responses to the rule-following argument is dispositionalist and more broadly naturalistic. These approaches aim to show that there can be genuine, non-mysterious facts about what rule a person is following, grounded in their dispositions or in natural relations.

Dispositionalism about Meaning

On dispositionalist views, what it is for a speaker to mean addition by “+” is, roughly, for them to be disposed to give addition-style answers across a wide range of circumstances. Simple, unrefined versions face familiar problems:

• People are disposed to make mistakes; yet meaning does not change with error.
• Dispositions are finite and may be unspecific about bizarre or counterfactual inputs.

More sophisticated dispositionalists (e.g., Michael Devitt, Paul Boghossian in some phases) respond by appealing to:

• Idealized dispositions: how a speaker would respond under ideal conditions (fully informed, attentive, not impaired).
• Counterfactual robustness: dispositions across a wide range of hypothetical scenarios, not just actual ones.

These refinements aim to answer the underdetermination challenge by insisting that once all relevant idealized dispositions are included, only one rule (e.g., addition) fits them.

Naturalistic and Teleological Theories

A different but related strand (e.g., Ruth Millikan, Jerry Fodor) embeds rule-following in broader naturalistic frameworks:

• Teleosemantics: Meanings are fixed by the biological function or evolutionary purpose of internal states—what they are supposed to do, given their selection history.
• Informational/causal theories: Mental representations mean what they reliably track or are lawfully caused by, under normal conditions.

On such accounts, there can be objective, lawlike facts that determine what a symbol or mental state represents, grounding correctness in whether usage accords with its proper function or informational role.

Critics of these responses argue that they still face rule-following-style questions, for example: what makes a given teleological or informational property itself the correct one, rather than some deviant alternative? Proponents counter that the appeal to objective, scientifically respectable relations offers a more robust basis for semantic facts than the purely individual mental states criticized by Wittgenstein and Kripke.

13. Communitarian and Inferentialist Approaches

Another cluster of responses emphasizes communal norms and inferential roles as the basis of rule-following and meaning.

Communitarian Views

Communitarian theorists (e.g., Crispin Wright, John McDowell, and some readings of Wittgenstein) stress that rules are inherently social:

• Standards of correctness are constituted by patterns of agreement in practice: how a community trains, corrects, and criticizes its members.
• Facts about meaning are facts about a speaker’s place within this network of socially sustained norms.

Some such accounts are non-sceptical: they regard communal practices as constitutive of semantic facts, not just as evidence. Others, influenced by Kripke, see communal behavior more as what justifies attributions of meaning within a sceptical framework.

A central challenge is to explain how communal norms avoid collapsing into mere majority preference. Communitarians often introduce distinctions between:

• Superficial convergence (what most people do),
• Justified practice (what can be defended within the community’s own standards).

Inferentialist Approaches

Inferential role semantics, associated with Wilfrid Sellars and Robert Brandom, offers a more structural approach. On this view:

• The meaning of an expression is given by its place in a network of inferences—what follows from asserting it, what it is incompatible with, what counts as a reason for it.
• Rule-following is a matter of undertaking commitments and entitlements within this inferential network.

Brandom, for example, interprets rule-following as participation in a practice of giving and asking for reasons, where norms are articulated by the inferences licenseable in the community. Correct use thus depends on whether a speaker’s moves are appropriately integrated in this inferential space.

Inferentialists differ on whether their accounts directly answer the sceptical challenge or instead reconceive what counts as a “fact of meaning.” In either case, both communitarian and inferentialist approaches seek to ground normativity not in private mental contents but in publicly accessible, shared structures of practice and reasoning.

14. Meta-Semantic and Metaphysical Implications

The rule-following argument has far-reaching implications for meta-semantics—the study of what makes semantic facts obtain—and for metaphysical views about norms and meanings.

Meta-Semantic Questions

At the meta-semantic level, the argument presses the question:

• What constitutes the fact that a word means one thing rather than another?

Standard candidates include:

• Individual mental states or intentions,
• Causal or informational relations,
• Teleological functions,
• Social practices and norms,
• Inferential roles.

Rule-following considerations are often read as challenging purely individualistic accounts, pushing theorists toward externalist or communitarian factors. They also encourage a shift from representational to pragmatic or inferential bases for meaning.

The debate splits, roughly, into:

Metaphysics of Normativity and Rules

Metaphysically, the argument raises issues about the nature of normativity:

• Are norms and rules reducible to descriptive facts (e.g., about dispositions, communal behaviors)?
• Or are they irreducibly normative, perhaps sui generis entities or relations?

Some philosophers see the argument as support for the idea that normative facts cannot be fully reduced to purely natural or psychological facts, since such reductions struggle to capture the “ought”-laden character of rule-following. Others contend that more sophisticated naturalistic theories can accommodate normativity via teleological or functional properties.

There are also implications for the metaphysics of abstracta: if rules are not inner mental items, are they abstract objects, patterns of use, or something else? Rule-following considerations tend to undermine simplistic Platonist views, while not straightforwardly endorsing any particular alternative.

Finally, the argument intersects with broader meta-metaphysical worries: some “quietist” readers of Wittgenstein infer that philosophical demands for a metaphysical ground of meaning and rules may themselves be confused, suggesting that the right response is to clarify the grammar of our concepts rather than posit new entities.

15. Influence on Contemporary Debates

The rule-following argument has become a central reference point across several areas of contemporary philosophy.

Philosophy of Language and Mind

In philosophy of language, it has shaped discussions of:

• Mental content: debates over whether content is determined by internal states, external factors, or social practices.
• Normativity of meaning: whether meaning is essentially normative and, if so, how to reconcile this with naturalistic explanations.
• Semantic externalism: connections with views that locate meaning partly outside the head, in environment or community.

In philosophy of mind, it informs questions about:

• The nature of intentionality (aboutness),
• The possibility of privileged self-knowledge of one’s own meanings,
• The status of tacit knowledge of rules.

Epistemology and Metaethics

Epistemologists have drawn analogies between semantic normativity and epistemic norms (e.g., norms of justification, evidence). The idea that normative standards might be practice-based has influenced some forms of epistemic pluralism and anti-realism.

In metaethics, the argument’s treatment of normativity and communal practices has been compared to questions about moral facts: whether they are objective, practice-dependent, or constructed. Some theorists (e.g., Allan Gibbard) explore parallels between semantic and moral normativity.

Logic, Mathematics, and Action

The argument also impacts:

• Philosophy of mathematics: discussions of what it is to follow mathematical rules and whether mathematical necessity is grounded in practice.
• Philosophy of logic: debates about logical consequence and the normativity of rules of inference.
• Philosophy of action: views of action as rule-governed, and the role of intentions and plans as rules.

These diverse applications have made the rule-following argument a “standard tool” in contemporary analytic philosophy, even among those who strongly reject Kripke’s sceptical reading or Wittgensteinian quietism.

16. Legacy and Historical Significance

Historically, the rule-following argument has played a pivotal role in reshaping analytic philosophy’s understanding of meaning, mind, and normativity.

Impact on the Reception of Wittgenstein

The argument has been central to the reception of later Wittgenstein. Kripke’s book brought the Investigations’ rule-following remarks to the forefront of Anglophone philosophy, influencing generations of scholars and prompting extensive exegetical work. Competing interpretations—sceptical, communitarian, therapeutic—have generated a substantial secondary literature.

This focus has also highlighted Wittgenstein’s broader methodological innovations: treating philosophical problems as arising from misleading pictures embedded in our language, and addressing them by examining ordinary practices rather than constructing grand theories.

Place in 20th- and 21st-Century Philosophy

The argument’s legacy can be charted in relation to major movements:

Over time, the rule-following argument has also become a benchmark for evaluating new theories of meaning: any proposed account is typically asked how it handles the underdetermination of rules, the normativity of meaning, and the dependence on social practices.

The argument’s historical significance lies not only in the specific sceptical problem it raises, but also in its role in shifting attention from inner representations and abstract objects to public practices, training, and forms of life as central to understanding language and thought. Whether seen as a paradox to be solved, a confusion to be dissolved, or a diagnostic tool, it remains a touchstone in ongoing debates about how humans can be said to follow rules at all.