Estranged Loops
Why every accusation is a confession and every question is its own answer.
Unless the existence of a theory of everything is predicted by the theory itself, it’s not really a theory of everything, now is it? That’s the intuition that underlies the concept of an estranged loop, a term I’m introducing to extend the idea of a strange loop into the domain of social thought, where self-reference does not merely collapse levels but dislocates them, producing persistent confusion about what can be asked, what can be answered, and what it would even mean for an answer to count as an answer.
For the uninitiated, a strange loop occurs when a hierarchical system—like a staircase—has no well-defined highest or lowest level, leading the system to turn back on itself in a self-referential paradox. For a staircase, that means that the lowest stair can also be the highest. Such a staircase will ascend or descend forever in a loop.
My contention is that this is not merely a property of an obscure set of mathematical objects, but a general feature of human thought, discourse, and institutions, and our failure to spot these structures in our thinking makes disagreement indistinguishable from bad faith. On this view, any sufficiently developed ideology tends to take the form of either a strange loop or an estranged loop—defined below—because the concepts that compose the ideology determine which other concepts are intelligible to it. When you tell me what counts as evidence, what counts as explanation, and what counts as a reasonable question, you have already told me the limits of your world.
The exponential rise in the use of the term “gaslighting” over the last five years has everything to do with the proliferation of estranged loops in our culture, which has reached its apotheosis in the emergence of a new form of psychosis induced by sycophantic chatbots pretending to understand their users’ delusions.
Over the past decade, I have come to believe that strange loops form the very warp and weft of the human mind, allowing us to weave together concepts that would otherwise be unthinkable. If a snake eats its own tail, does it disappear? Every child has thought this, but such an idea is inconceivable without the form of a strange loop. Likewise, there are concepts—like Wittgenstein’s picture theory of language—that are only intelligible in terms of a certain form of self-conscious estrangement. But I move too fast.
Let’s start again. A strange loop is a self-referential structure in which levels that are supposed to remain distinct—higher and lower, object and meta, statement and evaluation—collapse into one another. From inside such a loop, every step feels locally valid, but taken together the structure cannot be made globally coherent. If you feel your thoughts the way I do—almost with an abstract-to-concrete style of synesthesia—these structures will give you a sense of vertigo.
Consider the following sentence:
This sentence is false.
Alan Watts used to say that sentences like this have anxiety. Why? Because as soon as you try to pin it down as being false, it turns out to be true. And vice versa. Formally, we can say that this sentence, a variant of the Liar’s Paradox, asserts its own negation. You can play conceptual whack-a-mole all you want, but you’ll never win. The sentence’s meaning depends on assigning it a truth value, but any such assignment collapses the meaning that justified it.
Now consider another example:
This statement is unprovable.
Is that sentence also a strange loop?
Not exactly. Imagine it belongs to a formal system, a set of sentences that together describe some world. If the statement were provable, the system would be inconsistent, because the sentence—being part of the system—asserts that this very sentence is unprovable. If, on the other hand, the system is consistent, this sentence must remain unprovable. This would make the sentence true.
True and unprovable.
But if the sentence is unprovable, is it possible to establish that the system is consistent from within the system itself? No. To decide whether this sentence is true, one must already know whether the system it belongs to is consistent. There are three possibilities:
The system is consistent, and the statement is unprovable.
The system is not consistent, and the distinction between provable and unprovable no longer holds.
The system is not consistent, yet the statement still appears unprovable from within, because the lack of consistency is not, itself, consistent.
In short, the system can’t tell which condition its condition is in, which is precisely what makes this an estranged loop rather than a merely strange one.
As you can see, an estranged loop has the same recursive structure, but a different phenomenology than the merely strange loop. Rather than collapsing levels, the recursion enforces their separation. The loop is still there, but it closes only from the outside. From within the system, no contradiction appears; instead, certain questions quietly become impossible to ask. Not because they are forbidden, but because the conceptual resources required to pose them have been defined out of existence.
They look like strange loops, but instead of collapsing levels, they separate them while insisting they are identical. They produce a structural mismatch between form and content: the grammar treats two levels as the same while the practice depends on keeping them distinct. The result is a loop that never quite closes. One is perpetually referred elsewhere—up a level, down a level, across a level—without ever being allowed to say where one is.
This matters because estranged loops are not merely theoretical curiosities. They shape institutions, moral reasoning, and public discourse. When the grammar of a domain is misapplied—when tools suited for solving problems are deployed against mysteries—the result is not clarity but escalation. Each failed attempt to resolve the issue is taken as evidence of bad faith, incompetence, or hidden motives, because the possibility that the question itself is malformed has been excluded by the structure of the loop.
Anyone who has taken a course in the humanities will recognize immediately that this form of argumentation—defining terms in such a way as to force a specific conclusion—is ascendant in the academy today, which is why I predict that, just as the strange loop has come to symbolize 20th century thought, representing the self-referentiality, paradox, and absurdity of the modern age, in the coming decade the estranged loop—with its perpetual deferrals, Protean dissimulation, and pretense—will come to be known as the symbol of postmodernism, post-liberalism, and the 21st century. Ideas have sympathies and antipathies and tend to cluster together, and strange and estranged loops attract two very different personality types, which is why you find many strange people in the sciences and many estranged people in the humanities.
Slavoj Žižek framed the problem better than anyone else I’ve ever heard in his 2019 address to the Oxford Union:
“The big problem for me today is what I call the gap between ‘realism’ and [a] ‘transcendental’ approach. On the one hand, we have [a] scientific or ‘realist’ philosophical approach… which simply pretends to describe reality the way it is… you forget about who you are; from where you are speaking. Then we have ‘transcendental’ reasoning which is not something ‘mystical’ and so on, but is based on the simple fact that our argumentation is always circular…. You can be very good at scientific explanations, evolutionary, and so on… but all this is possible because you approached nature in a certain way.”
The distinction Žižek makes between realist and transcendentalist approaches simply is the distinction between theories of a strange and estranged form—and as he says, both are predicated on a kind of circularity. I would go further and say that these two approaches to reality are not merely circular, but loopy.
To account for itself, in terms of itself, a theory of everything—what might be called an ideology—must use the very categories which need to be explained as its explanation—leading to an infinite regress—and this can either become a strange loop where the “highest” level in the system, the explanans (explanation), becomes one with the “lowest” level in the system, the explanandum (the thing to be explained), or an estranged loop that will never close—it will never be able to say, with gusto, this is the way things really are.
Strange theories, like realism, are monistic. They cross and collapse levels of explanation into a single frame of understanding—which Žižek describes as “pretending” to describe reality “the way it is.” This is just the way things are. Estranged theories are dualistic—always at a bit of a remove from reality itself—which makes them seem relativistic. They’re not. They’re transcendental.
In that same talk, Žižek holds up Foucault as the archetypal transcendentalist, saying that,
“for him, the ultimate horizon of our knowledge is what he calls épistémè… If you were to ask Michel Foucault, ‘do we have an immortal soul or not?’ his answer would have been, ‘all I can do is to describe the épistémè, the set of implicit presuppositions, within which this question has meaning at all.”
This is what made the Chomsky-Foucault Debate so interesting and so meaningful. Foucault was the ultimate representation of a transcendental approach to philosophy, and Chomsky was a self-conscious realist. Chomsky’s approach to human nature collapses the levels of human thought, behavior, and institutions into the manifestation of our innate capabilities, and Foucault’s critique of power as such prevents one—in principle—from being able to take any given political position without implicitly reinscribing the operations of power in a new, often invisible way.
The deep structure that unifies strange and estranged loops—realism and transcendentalism in this sense—simply is a transcendental generative grammar.
To see other ways in which these loops are alive in the world today, consider another distinction between two types of conceptual structures—problems and mysteries. Problems represent the subset of conceptual structures for which there exists a well-formed solution to a well-formed question in some language. Mysteries are the complementary set of conceptual structures, for which there is either:
No well-formed question; or
No intelligible answer.
In the words of Jerry Fodor:
Problems are things you can work on.
You may not know how to solve them but at least you can work on them.
Or at least you know how to formulate some of the questions
you’d like to have answered about them.
Mysteries meet none of those conditions.
This distinction is not a matter of difficulty. A problem may be extraordinarily hard and remain a problem—think of conceptual structures like Fermat’s Last Theorem. It took hundreds of years to solve, but it was solved. A mystery may be trivial in appearance and forever remain a mystery: what will it be like to go to sleep and never wake up?
The difference is grammatical rather than empirical. Problems live within a representational framework whose rules permit progress. Mysteries arise when those rules themselves become the object of inquiry, or when the attempt to apply them generates self-reference that cannot be stabilized. One can gesture at them, gesture around them, or gesture through them, but not resolve them without changing the grammar in which the question is posed.
What type of grammar is this?
For the last decade, I’ve been working on an abstract, empirically tractable theory of conceptual structure that formalizes the difference between problems and mysteries in terms of the limits of self-referentiality in representational systems. This project, which I called transcendental generative grammar was motivated by the hypothesis that mysteries are not randomly distributed in human thought, an idea I stumbled upon in a lecture delivered by Noam Chomsky at the University of Girona in November 1992:
“It could come out of cognitive science that humans are capable of constructing certain kinds of conceptual structures, like determinism and randomness, say, and those are going to deal with certain types of phenomena. And if you can show, empirically, that certain arrays of phenomena don’t have those properties, too bad. Then you’re in the mystery space… that’s a conceivable empirical discovery without paradox. We could discover what’s a mystery for us. We couldn’t solve it, but we could find out where it is.” — Chomsky, 1992
In the early 1990s, as Chomsky was formulating what would become the Minimalist Program for Linguistic Theory, he was touring the world speaking on an orthogonal intellectual project—the development of a cognitive science of conceptual structures—that he never fully realized.
Over the years, he has written and spoken in a number of places about the idea of a science-forming faculty, a meta-theoretic analogue to the language faculty, which he believed could account for our abilities to construct intelligible scientific theories. This would amount to a generalization of the logic of generative linguistics from the domain of natural language to the domain of the language of thought—specifically, scientific thought.
But even though he had every tool at his disposal to do so, Chomsky never attempted to formalize a generative theory of scientific thought as such. The closest he came to saying the quiet part out loud—that there could be a generative grammar of thought—was in his 1992 Killian Lecture at MIT, where he said:
“Adult perception, of course, has some kind of access to systems of belief about the world. Not much is known about this, but it seems reasonable to assume that that involves some kind of computational procedure that specifies an infinite range of beliefs, which are called upon when needed, although here, we move into a domain of almost total ignorance.”
If we take Chomsky literally, he is saying that systems of beliefs—be they scientific, religious, psychological, or ideological—are generated by a computational procedure that specifies an infinite range of beliefs the way that a generative grammar specifies an infinite range of sentences that are intuitively well-formed to the native speaker of a language.
For Chomsky, and the generativists who accepted the poverty of the stimulus argument, the deep structure of human language was realized in a universal grammar built into the neurobiology of the language faculty. On that model, I reasoned that the deep structure of thought—a superset of language encompassing all sorts of other mental representations—could be realized in a transcendental grammar, specified as a set of conditions for the possibility of constructing any given conceptual structure.
All scientific theorizing and systematic thought is an expression of the grammar and vocabulary of conceptual structures, and is, therefore, downstream from a theory of concepts. When you tell me what counts as evidence, what counts as explanation, and what counts as a reasonable question, you have given me the grammar of your ideology. The problem is—however—that any such theory must be constructed with conceptual structures.
For this reason, strange loops and estranged loops are structural features of a transcendental generative grammar. If the goal of such a theory is to formalize the distinction of problems and mysteries—and thereby be a kind of grammar of the gaps—in the end, the grammar will either eat its own tail by constructing an infinite set of circular definitions or it will get lost in a labyrinth of moving walls of meaning.
In cognitive terms, these limits are reflected in finite capacity. Minds cannot represent arbitrarily many entities or relations at once. They rely on compression, abstraction, and recursion to do more with less. Strange loops exploit these mechanisms to extend expressive reach. Estranged loops exploit them to hide the point at which compression fails. The system continues to generate outputs, but the mapping between representation and reality becomes unstable.
In formal systems, the distinction is crisp. One can point to a sentence and show, with proof, that it is undecidable given the axioms. In natural language and social systems, the distinction is messier but no less real. Here, the grammar is implicit, distributed across practices, norms, and shared expectations. Estranged loops arise when those implicit rules are violated in a way that cannot be named without violating them again.
The temptation, when confronted with such a loop, is to moralize. If the system cannot be made consistent, someone must be at fault—usually the Authority. But moralization is itself a symptom of the loop. It treats a structural limit as a personal failure and thereby reinforces the very grammar that produced the impasse. The more one insists on resolution, the more the loop tightens. It’s been said that God helps those who help themselves. This is why.
A more productive response is to change levels explicitly—to say, not “Here is the answer,” but “Here is why the question cannot be answered as posed.” This move does not dissolve the mystery; it relocates it. It restores the distinction between levels that the estranged loop had blurred, making disagreement intelligible again by reintroducing the possibility that both sides are trapped by the same grammatical constraint.
Estranged loops thrive in environments where form is mistaken for substance, where the appearance of rigor substitutes for rigor itself. They borrow the authority of formal paradox without its discipline. A genuine strange loop is austere: it gives you exactly what the system can give and no more. An estranged loop is expansive: it promises total explanation while delivering perpetual deferral.
The ambition of a theory of conceptual structure is not to eliminate these loops in our thinking but to classify them—to distinguish those that mark genuine boundaries from those that manufacture confusion by denying that boundaries exist. Such a theory would be empirically tractable, attentive to cognitive constraints, and formal enough to make clear predictions about where breakdowns will occur. It would explain why certain debates never converge, why certain questions generate infinite regress, and why appeals to ever higher principles fail to settle what appears to be a disagreement at the ground level.
Seen this way, estranged loops are not merely errors. They are signals that indicate that a domain has outrun the grammar used to describe it, or that a set of rules has been imposed where none is necessary. They remind us that explanation has a shape, and that when that shape is circular, adding more detail does not help.
Wittgenstein famously suggested that his Tractatus could only be understood by people who didn’t need to understand him—and it’s possible to see his project in that work as either a strange loop (from the inside) or an estranged loop (from the outside):
6.54 — My propositions are elucidatory in this way: he who understands me finally recognizes them as senseless, when he has climbed out through them, on them, over them. (He must so to speak throw away the ladder, after he has climbed up on it.) He must surmount these propositions; then he sees the world rightly.
7 — Whereof one cannot speak, thereof one must be silent.
A theory that can say, in its own terms, where it must fall silent is closer to completeness than one that claims to speak everywhere. The former closes the loop visibly—if absurdly. The latter—in its seriousness of purpose, pretense, and perfectionism—estranges us from the very conditions under which understanding is possible.