Malfunctionalism Malfunctions: Revenge and the Limits of Knowles's Diagnosis

1. Introduction

The Liar Paradox has proven remarkably resistant to consistent solutions. Consider:

(L) Sentence (L) is not true.

If (L) is true, then what it says is the case; so, (L) is not true. If (L) is not true, then what it says is the case; so, (L) is true. We appear to have derived a contradiction from innocuous premises.

Consistent approaches to the Liar divide broadly into those that revise logic,¹ those that restrict semantic principles like the T-schema,² and those that deny that Liar sentences express propositions at all.³ Robert Knowles (2026) defends a version of this last approach, which I call “semantic malfunctionalism”. On Knowles’s view, Liar sentences are self-dependent: Their truth-values would have to be determined by themselves, which is impossible. Self-dependent utterances therefore malfunction—they fail to “latch onto” any proposition and consequently lack truth-values, since only utterances with propositional content can bear truth-values. On Knowles’s approach, liar sentences are not truth apt.

Knowles’s approach is best understood through Charles Chihara’s (1979) framework, which distinguishes sharply between two tasks philosophers addressing the Liar often conflate: A diagnosis of how paradoxicality arises, and a treatment of the paradoxicality identified.

A diagnosis identifies what has gone wrong—the source of the paradox. It answers: Which principle, assumption, or inference step generates the contradiction? According to Chihara (1979, pp. 590–592), a good diagnosis should:

• Locate the specific point of failure in the paradoxical reasoning
• Explain why that point is defective (not merely stipulate that it is)
• Generalize to other semantic paradoxes (the Liar, Curry’s, the Truth-Teller, etc.)

A treatment, by contrast, is a proposed remedy—a modification to our logic, language, or semantic principles that blocks the derivation of contradiction. It answers: How should we revise our theory to avoid the paradox? Treatments have historically included:

• Tarskian hierarchies (stratifying “true” into levels)
• Truth-value gaps (denying bivalence)
• Paraconsistent logics (tolerating contradiction)
• Restricting the T-schema
• Denying that Liar sentences express propositions

Chihara’s crucial observation is that diagnosis and treatment are logically independent. One can accept a diagnosis without accepting the corresponding treatment—agreeing, for instance, that unrestricted self-reference is the “source” of the paradox without thinking that banning self-reference is the right remedy. Similarly, one can accept a treatment without accepting any particular diagnosis—adopting a Tarskian hierarchy because it works without committing to any view about what was “really” wrong with the original reasoning.

Knowles does not exactly offer a treatment of the Liar-like paradoxes; his diagnosis is that such sentences are self-dependent in virtue of “semantically malfunctioning”.

Malfunctionalism has considerable appeal. It preserves classical logic, maintains an unrestricted T-schema for well-behaved sentences, and offers a principled diagnosis of why Liar sentences are defective. However, like all approaches to the Liar, malfunctionalism faces revenge problems: whatever machinery is introduced to diagnose the original paradox can be exploited to generate new paradoxical sentences.

In this paper, I construct two revenge sentences for Knowles’s diagnosis of the Liar Paradox. The first, (K’), is a relatively straightforward extension of the Liar incorporating Knowles’s diagnostic vocabulary. I argue that Knowles can plausibly resist this revenge sentence by claiming it, too, is self-dependent. The second, (R), is more problematic than (K’) was. It is a conditional that encodes the structure of Knowles’s diagnosis as its content. I argue that (R) poses a problem unresolvable from within Knowles’s framework: His diagnosis, if correct, makes (R) true—but (R) cannot express the truth that his diagnosis makes true. This reveals a deep tension between the theory and its own expressibility, showing that Knowles’s approach suffers from the familiar result of the semantic paradoxes according to Priest (1979/2006): either inconsistency or expressive indeterminacy.

The structure of the paper is as follows. §2 describes Knowles’s malfunctionalism: §2.1 provides the core thesis; §2.2 explains co-typicality; §2.3 captures the chief advantages. §3 presents the first revenge problem: §3.1 introduces the construction; §3.2 highlights an alleged dilemma; §3.3 offers Knowles an escape route; §3.4 identifies the cost. §4 considers a second revenge problem: §4.1 introduces the construction; §4.2 explores why this revenge problem is more pernicious; §4.3 works through the problem; §4.4 presents the aporia; §4.5 examines the meta-level problem. §5 examines the instability of malfunctionalism; §6 considers possible responses; and §7 concludes.

2. Knowles’s Malfunctionalism

2.1. The Core Thesis

Knowles’s (Ibid.) diagnosis of the Liar Paradox and related paradoxes (e.g., Curry’s, the Truthteller, etc.) rests on a principle I shall call “Truth Asymmetry”:

Truth Asymmetry: The truth-value of an utterance must be determined by

something independent of that utterance.

An utterance is self-dependent if, and only if, (Henceforth, “iff”) its truth-value would have to be determined by itself. Self-dependent utterances violate Truth Asymmetry and, for so doing, Knowles maintains that they malfunction: They fail to express any proposition and are devoid of semantic content.

Consider again our initial liar sentence, (L). To determine whether an utterance U of (L) is true,⁴ we must determine whether what U says is the case. But what U says is that U is not true. Determining U’s truth-value thus requires determining U’s truth-value—a vicious circle. U is therefore self-dependent, hence malfunctions, and fails to express a proposition, rendering U not true (though not false either). Importantly, “not true” here does not mean false; it means fails to have the property of truth. An utterance expressing no proposition is not a “truthbearer” and cannot bear truth-values at all—it is not truth-apt.

2.2. The Role of Co-Typicality

Knowles’s account operates at the level of utterances (tokens) rather than sentences (types). Two utterances are co-typical iff they are tokens of the same sentence-type. This distinction matters because the same sentence-type can be uttered in different contexts, and some contexts may render the utterance self-dependent while others do not.

For instance, if I utter “This sentence is not true” while pointing to a different sentence—say, “2 + 2 = 5”—my utterance is not self-dependent. Its truth-value is determined by the truth-value of the sentence I’m pointing to, not by itself. Only when the demonstrative refers back to the utterance itself does self-dependence arise.

Knowles thus takes Liar-like sentential utterances to be self-dependent, and concludes that they do not express propositions. This is not to say that there is no proposition such an utterance seems to express. Following standard tokenist views, Knowles maintains that other utterances of the same sentence-type may not be self-dependent and thus may not malfunction at all.

2.3. The Chief Advantages of Malfunctionalism

Knowles’s form of Malfunctionalism has several virtues:

Preservation of classical logic. There is no need to adopt a paraconsistent or a paracomplete logic; the Liar is blocked before contradiction can be derived.⁵

Unrestricted T-schema for well-behaved sentences. For any sentence S that successfully expresses a proposition ⟨P⟩, S is true iff P. But if S does not express a proposition, it is not an instance of the T-schema. This restriction applies only to malfunctioning sentences

Principled diagnosis. Self-dependence is a structural feature of utterances, not an ad hoc stipulation. It explains why Liar sentences are defective: they lack the asymmetric determination structure required for truth-aptness.

Consistency with ordinary usage. We treat obvious cases of semantic defectiveness (category mistakes, presupposition failures, etc.) as failing to express propositions. Malfunctionalism extends this treatment to self-dependent, Liar-like sentences.

If Knowles’s diagnosis succeeds, it will preserve many desiderata that other solvers have been unable to retain—classical logic, naïve truth, and semantic determinacy among them. Such a result would be of considerable significance for the field.

3. The First Possible Revenge Sentence: (K’)

Given these advantages, we now consider a possible revenge problem for Knowles’s diagnosis.

3.1. Construction

This putative problem arises when we formulate a sentence that incorporates the diagnostic vocabulary of the theory itself as in

(K’) Every utterance co-typical with (K’) is not true or is self-dependent.

(K’) is a universal generalization over all utterances of itself stating that every token of this sentence-type either fails to be true or is self-dependent.

3.2. The Alleged Dilemma

Let U be an utterance of (K’). Is U self-dependent?

Horn 1: U is self-dependent.

If U is self-dependent, then by malfunctionalism, utterances co-typical with (K’) fail to express a proposition and are therefore not true. But then what (K’) appears to say—that every utterance co-typical with (K’) is not true or is self-dependent—is clearly satisfied by U itself. Indeed, if every utterance co-typical with (K’) is self-dependent, then ‘every utterance co-typical with (K’) is not true or is self-dependent’ seems true. Here lies the problem: The proposition ⟨Every utterance co-typical with (K’) is not true or is self-dependent⟩ seems to be true, and we can assert this from outside. But then we have expressed that proposition. Why can’t the utterer of (K’) express it? It is difficult to see why not—from which contradiction follows.

Horn 2: U is not self-dependent.

If U is not self-dependent, then U successfully expresses the proposition ⟨Every utterance co-typical with (K’) is not true or is self-dependent⟩, and U is thus either true or false.

Suppose U is true. Then every utterance co-typical with (K’) is not true or is self-dependent. But U is co-typical with (K’), so U is not true or is self-dependent. Since U is (by hypothesis) true and not self-dependent, we have a contradiction.

Suppose instead that U is false. Then some utterance co-typical with (K’) is both true and not self-dependent. But notice: Any utterance of (K’) has its truth-value determined entirely by the semantic status of utterances of (K’) itself. There is no external fact—no independent state of affairs—that settles whether (K’) is true. The truth of (K’) depends only on (K’). But this is precisely what it is to be self-dependent. So, every utterance of (K’) is self-dependent, including any purported witness. Hence U cannot be false.

Therefore, if U is not self-dependent, U is neither true nor false. But U, being not self-dependent, expresses a proposition—and propositions, for Knowles, are bivalent. Contradiction.

Alternatively, and more directly: If U is not self-dependent, then U expresses a proposition whose truth-value depends on nothing beyond the semantic status of U and its co-typical utterances. But a statement whose truth depends only on itself is self-dependent. So U is self-dependent after all. Contradiction.

3.3. Knowles’s Possible Escape

Knowles can plausibly respond that utterances of (K’) are self-dependent for the same structural reason as the original Liar. The truth-value of an utterance of (K’) would have to be determined by facts including whether that very utterance is true (via the “not true” disjunct). So (K’) malfunctions just like (L).

The key insight is that U being not true is not the same as U expressing a true proposition. U doesn’t express any proposition. (K’) has an apparent content—we can read off what it seems to say—but the utterance U does not successfully express that content.

This creates an important asymmetry. The proposition P = ⟨Every utterance co-typical with (K’) is not true or is self-dependent⟩ both exists and is true. But utterances of (K’) do not express P. A theorist, standing outside, can express P by saying that every utterance co-typical with (K’) is not true or is self-dependent. The theorist’s utterance is not co-typical with (K’)—it’s a different sentence (perhaps in a metalanguage, or simply about (K’) rather than being (K’) itself). So, P is expressible—just not by (K’) itself. This is analogous to the Epimenides case Knowles considers: a non-Cretan can truly say “No Cretan statement is true” without self-dependence.

3.4. The Cost: Semantic Pessimism

The price Knowles pays is a form of semantic pessimism: The solution cannot be fully stated within the language to which it applies. Attempts to formulate a revenge sentence using his diagnostic vocabulary will result in a self-dependent utterance that malfunctions. This applies to:

(L) Utterance (L) is not true.

(K’) Every co-typical utterance of type K’ is not true or is self-dependent.

(K’’) Every co-typical utterance of type K’’ is not true or is self-dependent or fails to

express a proposition.

At each stage, the revenge sentence malfunctions for the same reason as the original Liar. The pattern generalizes. This may be a significant cost, but perhaps one worth paying if it adequately diagnoses Liar sentences. Semantic pessimism afflicts many solutions to the Liar; Knowles is not uniquely vulnerable here. The question is whether a more sophisticated revenge sentence can do more damage. I answer that question in §4.

4. Real Revenge?

4.1. Construction

Consider:

(R) If utterances of type (R) are true, then attempts to determine their truth-values

result in self-dependence.

(R) is structurally different from (K’). It does not directly predicate ‘not true’ or ‘self-dependent’ of itself. Instead, it makes a claim about what happens when we try to determine its truth-value—a claim about the determination process itself. This is crucial because Knowles’s diagnosis is essentially a claim about the determination process. (R) anticipates and incorporates that diagnosis into its content.

4.2. Why (R) Is More Worrisome than (K’)

The weakness of (K’) is that Knowles can plausibly claim that it is directly self-dependent in the same way as the original Liar: The truth-value of an utterance of (K’) depends on whether that very utterance is true (via the “not true” disjunct). So (K’) malfunctions for the same reason as (L), and the revenge is contained. (R) differs in three respects:

• It conditionalizes on its own truth (not directly, but via the antecedent).
• It incorporates Knowles’s diagnostic conclusion into its consequent.
• It makes itself true precisely when Knowles’s diagnosis is applied to it.

This last feature—3—makes (R) potentially more vicious than (K’). When Knowles diagnoses utterances of type (R) as self-dependent, he is not just making them “come out true in the world.” He is enacting the consequent of (R): His attempt to determine (R)’s truth-value results in (a finding of) self-dependence.

4.3. Working Through (R)

Let U be an utterance of type (R). Is U self-dependent?

Step 1: What would determine U’s truth-value?

By Truth Asymmetry, U’s truth-value (if it has one) must be determined by whether the proposition it expresses obtains. U apparently expresses:

⟨If utterances of type (R) are true, then attempts to determine their truth-values

result in self-dependence⟩

So U’s truth-value is determined by whether this conditional holds.

Step 2: Assessing the conditional

On a material conditional, which (R) possesses, U is true iff either utterances of type (R) are not true or attempts to determine their truth-values do result in self-dependence.⁶

Step 3: Consider the following trilemma.

Case A: U is self-dependent (and, so, malfunctions).

If U is self-dependent, then U fails to express a proposition (by malfunctionalism); so, U is not true. But then the antecedent of (R) is false, for utterances of type (R) are not true. A conditional with a false antecedent is (materially) true. Moreover, the consequent of (R) is satisfied, since attempts to determine U’s truth-value did result in (a finding of) self-dependence. So, the proposition U appears to express is true—doubly so, since both the false antecedent and the true consequent independently suffice. But U doesn’t express that proposition because U malfunctions. So far, this looks like the same situation as with (K’). Knowles might seem safe here.

Case B: U is not self-dependent and U is true.

Suppose U is not self-dependent and is true. Then the proposition it expresses obtains. U is an utterance of type (R), and U is true, so the antecedent is satisfied. Therefore, the consequent must hold: Attempts to determine U’s truth-value result in self-dependence.

But we assumed U is not self-dependent. Before seeing the consequence of this, we must answer the following question: What does “attempts to determine their truth-values result in self-dependence” really mean?

On one reading, the utterance is self-dependent, which contradicts our assumption for Case B. On another reading, the process of trying to determine the truth-value leads to a self-dependent structure. But this is incoherent on Knowles’s account: Self-dependence is a structural feature of the utterance given its content and context. It’s not something that “results from” evaluation—it’s something we discover through evaluation. An utterance either is or is not self-dependent; the determination process doesn’t create self-dependence.

So, if attempts to determine U’s truth-value “result in” self-dependence, that just means that U is self-dependent—contradicting our assumption.

Conclusion for Case B: U is true → U is self-dependent. Contrapositive: U is not self-dependent → U is not true.

Case C: U is not self-dependent and U is false.

Suppose U is not self-dependent and is false. Then the proposition it seems to express does not obtain: Some utterances of type (R) are true yet attempts to determine their truth-values do not result in self-dependence. So there exists some utterance U* of type (R) such that U* is true and U* is not self-dependent. But by the reasoning in Case B, this is impossible.

Conclusion for Case C: If U is not self-dependent, U cannot be false either.

4.4. The Aporia

Combining the cases we have considered, what we find is the following, where to the left are our assumptions and to the right are the result, as indicated by ‘⇒’:

Case A: U is self-dependent ⇒ U malfunctions; (R) is “vacuously” satisfied.

Case B: U is not self-dependent and true ⇒ Contradiction; U must be self-dependent.

Case C: U is not self-dependent and false ⇒ Contradiction; requires a true, non-self-

dependent utterance of (R).

Since these cases are exhaustive, Knowles’s only option is Case A: U is self-dependent and malfunctions. Can this be maintained?

4.5. The Meta-Level Problem

Suppose Knowles assertorically utters the following diagnosis: “Utterances of type (R) are self-dependent. They malfunction. Hence, they are not true.”

Question: Is this diagnosis self-undermining?

The proposition that utterances of type (R) express (or purport to express) is:

⟨If utterances of type (R) are true, then attempts to determine their truth-values result in self-dependence⟩

Knowles’s diagnosis considering Case A entails the following:

• Utterances of type (R) are not true (they malfunction).
• Attempts to determine their truth-values do result in (a finding of) self-dependence.

Given 1, the conditional is true (false antecedent). Given 2, the conditional is again true (true consequent). So, the proposition is true and seems perfectly expressible. Indeed, Knowles will have to express it when providing his diagnosis!

Here’s the problem: (R) just is this very sentence. Why can’t an utterer like Knowles express what utterances of type (R) say?

Knowles’s answer must be that when an utterance of type (R), U, is uttered, that very utterance is one of the utterances of type (R), so determining its truth-value involves checking whether it is true—introducing self-dependence.

But Knowles’s theoretical assertion—that utterances of type (R) are true—is also an assertion about utterances of type (R). If Knowles assertorically utters that, then he is asserting something whose truth depends on the status of utterances of type (R). Is what he has asserted therefore self-dependent?

Knowles might respond that his assertion is not an utterance of type (R)—it is a metalinguistic claim that is about (R). Its truth-value depends on facts about (R)-tokens, not about (R) itself. Hence, his assertion is not self-dependent. This is analogous to the Epimenides case—Knowles is like the non-Cretan who can truly say, “No Cretan statement is true.”

But there is a crucial disanalogy. In the Epimenides case, the non-Cretan’s assertion is about a different class of utterances (viz., Cretan ones). In the (R) case, Knowles’s theoretical assertion has the same content as (R) itself. So: an assertoric utterance of type (R) cannot express the proposition it appears to express, but Knowles can assertorically utter the very same content from a metalanguage and thereby express it.

Can this be maintained? I think this is a deeply uncomfortable position. The proposition Knowles expresses via the metalanguage is true; is expressible by theorists; but is inexpressible by an assertoric utterance of (R) itself—even though utterances of type (R) are word-for-word identical to what Knowles would assertorically utter. The gap between object language and metalanguage has collapsed in terms of content while remaining unbridgeable in terms of expressibility.

5. The Instability of Malfunctionalism

5.1. The Structure of the Problem

(R) is about Knowles’s diagnostic framework itself. It is not just a Liar sentence that happens to use the word “self-dependent”; rather, it:

• Conditionalizes on its own truth indirectly (via its antecedent);
• Incorporates Knowles’s diagnostic conclusion as its consequent; and
• Makes itself true precisely when Knowles’s diagnosis is applied to it.

If Knowles diagnoses utterances of type (R) as self-dependent, the consequent is satisfied, but the antecedent is false (utterances of type (R) are not true). So, utterances of type (R) are true, presuming (R) is a material conditional—and it is, since, as I noted in footnote six, Knowles accepts classical logic. But utterances of type (R) cannot express this truth because they malfunction. Yet the truth they cannot express is precisely the truth about their own malfunctioning.

Recall Tarski’s (1933/1956) notion of semantic closure. A language is semantically closed iff:

• It can refer to its own expressions (contains names or descriptions for all its own sentences;
• It contains its own semantic predicates (most crucially, a truth predicate that applies to its own sentences);
• It has full classical logic; and
• Every instance of the T-schema holds.

Knowles’s diagnosis is a form of semantic closure failure in the following sense: His theory cannot be stated within the object language without malfunction, yet the content of what malfunctions is exactly what his account needs to say.

This problem arises precisely because utterances of type (R) seem to be true, and their truth is essentially constituted by Knowles’s diagnosis. This is not a case where diagnosis “saves” us from paradox by showing utterances to be semantically defective. It’s a case where diagnosis makes utterances of the sentence type true—yet those very utterances cannot express that truth.

This looks like a revenge paradox unresolvable from within Knowles’s framework: Either (a) Knowles states his diagnosis, in which case utterances of type (R) are true (expressible by Knowles but somehow not by using (R)), or (b) Knowles cannot state his diagnosis, in which case he has no solution at all.

The cost of (a) is a radical expressibility gap: Utterances of type (R) whose content seems true also seem expressible by theorists but are inexpressible by utterances of type (R) themselves—even though (R) seems to have precisely that content. This is perilously close to incoherence. Knowles’s diagnosis is, in a sense, inside the revenge sentence. Were Knowles to diagnose (R), he would not be standing outside it; he would be enacting precisely what (R) predicts. The very act of applying his diagnostic apparatus to (R) verifies (R)’s consequent: Attempts to determine its truth-value result in self-dependence. Knowles cannot diagnose (R) without making (R) true—yet his diagnosis declares (R) not truth-apt. The diagnostician is caught in his own web.

If I am right, then Knowles’s diagnosis of the semantic pathology of Liar sentences implodes. In a typical revenge paradox, a theory’s diagnostic apparatus is exploited to construct a new problematic sentence that it cannot handle. The theory is attacked from outside using its own tools. The diagnosis doesn’t fail on its own terms; it generates new cases that it cannot accommodate.

In Knowles’s case, the diagnosis—that utterances of type (R) are self-dependent and therefore malfunction—does not merely fail to handle (R). It actively undermines itself. If utterances of type (R) are self-dependent, their consequents are true. So ,utterances of type (R) come out true (either via false antecedent or via true consequent). But Knowles’s diagnosis of Liar Paradoxes simultaneously declares that utterances of (R) are malfunctioning and thus are not truth-apt.

The problem is not merely that Knowles’s diagnosis fails to neutralize (R). The problem is that his diagnosis vindicates the very sentence it was supposed to disqualify. It doesn’t just leave (R) standing; it actively confirms (R). Knowles’s own diagnostic judgement renders utterances of type (R) true while simultaneously declaring that they cannot be true. The diagnosis is self-undermining in the most direct way possible: Applying it to (R) makes (R) true.

This is a far more serious predicament than a mere gap or limitation. Knowles faces a genuine contradiction at the heart of his diagnosis: His diagnostic apparatus, when applied to (R), yields the verdict that (R) is both true (because the diagnosis verifies its consequent) and not truth-apt (because the diagnosis classifies it as malfunctioning). These are not independent problems to be addressed piecemeal. They flow from a single source: (R) encodes the diagnostic apparatus itself.

We should therefore consider the possible responses that are available to Knowles.

6. Possible Responses

6.1. Denying That (R) Is Self-Dependent

Knowles might argue that, contrary to what I have tried to show, utterances of type (R) are not self-dependent, because the self-reference is mediated through a conditional rather than being direct. On this view, the truth-value of utterances of type (R) depends on a general fact about utterances of type (R), not on the specific utterance being evaluated.

This response seems difficult to sustain. (R)’s antecedent quantifies over utterances of type (R), including the utterance being evaluated. To determine whether the antecedent is true, we must determine whether the utterance in question is true—which is what we were trying to determine. The self-dependence may be mediated, but it is still present.

6.2. Restricting the Expressive Resources

Knowles might argue that ‘self-dependent’ is a metalinguistic predicate that cannot appear in the object language. On this view, (R) is not a well-formed sentence of the language to which malfunctionalism applies.

Three problems arise from Knowles’s attempt to avoid revenge.

First, this response is unacceptably ad hoc. ‘Self-dependent’ is defined in perfectly ordinary terms—truth-value, determination, structural features. There is nothing obviously metalinguistic about it. If Knowles insists that it cannot be expressed in the object language, then he owes us an independent explanation of why this is so—one that does not simply stipulate the predicate away to avoid revenge.

Second, if ‘self-dependent’ cannot be expressed in the object language, then Knowles’s diagnosis is inexpressible within the very language it is meant to diagnose. This is a significant cost. Recall the distinction between hermeneutic and revolutionary approaches: A hermeneutic diagnosis aims to explain what is going wrong within natural language as we find it. If the key diagnostic predicate is inexpressible in that language, then Knowles is no longer offering a hermeneutic account. He has retreated to a Tarskian position—treating the paradoxes by restricting expressive resources rather than diagnosing them. His diagnosis would apply only from the outside, from a metalanguage that speakers of the object language cannot access. This is precisely the kind of explanatory limitation that Knowles’s malfunctionalism was supposed to avoid.

Third, this response fails to address the core problem. Even if we grant that (R) cannot be formulated in the object language, the content of (R) is expressible by Knowles in his own diagnostic assertions. When Knowles says that certain utterances are self-dependent and therefore malfunction, he expresses exactly the kind of content that (R) encodes. The problem is not about which language (R) belongs to; it is about the relationship between Knowles’s diagnosis and its own expressibility. If Knowles can express the diagnosis, then the revenge sentence can be constructed. Banishing (R) to a metalanguage does not help—it merely relocates the problem.

6.3. Embracing Radical Semantic Pessimism

Knowles might bite the bullet and accept that his approach cannot be fully stated within any language to which it applies. On this view, the diagnostic apparatus is essentially metalinguistic, and any attempt to bring it into the object language will result in malfunction.

This seems the most honest response, but it comes at a severe cost: if Knowles’s diagnosis cannot be self-applied without malfunction, is it really a diagnosis? Or is it just another epicycle pushing the problem back?

Recall that Tarski (Ibid.) maintained that natural languages are inconsistent in virtue of being semantically closed. That was his diagnosis: Semantically closed languages produce Liar sentences, resulting in inconsistency. His treatment was to forgo semantic closure by introducing an object-language/metalanguage distinction.

In the terminology introduced by Sally Haslanger (2000) and expanded upon by Jason Stanley (2001), Tarski’s approach was revolutionary, not hermeneutic. He was not articulating our actual concept of truth but proposing a revised concept: How we should treat truth given our purposes, not how truth actually is.

A revolutionary approach constitutes a treatment of the paradoxes, not a diagnosis. To be sure, a revolutionary theorist may offer a diagnosis along the way—but the revolutionary aspect of the approach is normative, not descriptive: It tells us how we ought to revise our language or logic, not how natural language (or logic) as we find it actually functions.

Tarski, for instance, diagnoses the problem of the Liar Paradox as arising from semantic closure, but his revolutionary contribution is the prescription to abandon semantically closed languages in favor of the object-language/metalanguage hierarchy. The diagnosis explains what goes wrong; the revolutionary treatment tells us what to do about it. If Knowles is forced to banish ‘self-dependent’ to a metalanguage, he is no longer diagnosing natural language from within—he is prescribing a revision to it. His view collapses into a Tarskian treatment.

I mention Tarski because if Knowles were to “bite the bullet” and admit that his approach cannot be stated from within any language to which it applies, he would effectively give up his diagnosis—since that diagnosis cannot be formulated in the language in which he presents it. Moreover, the peculiarity of (R) is that it doesn’t just use Knowles’s vocabulary; it embodies his diagnosis. The sentence is not a counterexample to malfunctionalism in the sense of generating a contradiction; It is a demonstration that malfunctionalism undermines the expressibility of its own central insight. If Knowles were to claim, like Tarski, that he is offering only a treatment, this would undermine the very point of his paper, which I thought was to offer diagnostic tools for understanding how the Liar’s paradoxicality and malfunctioning emerges. We should therefore reject this response.

6.4. Distinguishing Types of Self-Dependence

Finally, Knowles might distinguish between different types of self-dependence. Perhaps (R) exhibits a different (and non-pathological) kind of self-reference that does not trigger malfunction.

While possibly interesting, this would require developing a more fine-grained account of determination. Knowles would need to explain why the conditional structure of (R) makes its self-reference benign, whereas the direct self-reference of (L) and (K’) is pathological.

I am skeptical such an account can succeed. The problem with (R) is not the form of its self-reference but its content: It is a sentence about what happens when you try to apply Knowles’s diagnosis to it. Any account that treats (R) as well-formed with true utterances will face the question of why utterances of type (R) cannot express the truth they apparently express.

7. Conclusions

I have argued that Knowles’s malfunctionalism faces a serious revenge problem. (R) is constructed to encode Knowles’s diagnostic apparatus within its content. When Knowles diagnoses (R) as self-dependent, he makes (R) true—but (R) cannot express the truth that his diagnosis makes true.

This is not merely a cost to be weighed against the benefits of malfunctionalism. It is a fundamental instability. Knowles’s diagnosis, if correct, makes utterances of type (R) true, though such utterances cannot express the truth that the diagnosis makes true. The approach thus undermines the expressibility of its own central insight.

The revenge problem for malfunctionalism is not just that its diagnostic vocabulary can be exploited to generate new paradoxical sentences—a problem that possibly every consistent solution to the Liar faces. The revenge problem I have presented is that Knowles’s diagnosis, when applied to (R), vindicates (R). His account is caught in a trap of its own making. Whether this constitutes a refutation depends on one’s tolerance for semantic pessimism. But (R) shows that the pessimism extends to the theoretical apparatus itself—not just to pathological sentences that are “out there”, but to the very content of his method for diagnosing the pathology that Liar sentences present.

This is a serious problem. A proposed diagnosis of the Liar Paradox should be able to state its own diagnosis without that diagnosis rendering itself inexpressible. Malfunctionalism cannot do this. The revenge sentence (R) is the proof.