When Statements Fail

Binding, nonsense, and crooked questions

“It’s raining.” Is that true?

You cannot say. Not because the weather is mysterious — the weather is as factual as anything gets — but because the sentence is incomplete. Raining where? When? Bind those variables — “It’s raining in Montreal at 9am” — and the statement snaps into focus: now it is true or false, and a glance out the window settles which. Unbound, it is not a proposition at all. It is a gesture toward one.

This chapter is about the sentences that fail this way. All truth is conditional, and most of the time the conditions are bound tacitly and nobody notices. But a large class of well-formed, grammatical, confident-sounding sentences are neither true nor false, because the conditions that would make them evaluable have never been fixed. These failures are not moral or preferential claims awaiting an agent; they collapse for a simpler reason. They are underdetermined. Ambiguity involves multiple possible meanings; underdetermination involves no fixed meaning at all until certain background variables are bound. Diagnosing exactly how a statement fails tells you exactly what it would take to repair it — and reveals, in the cases where no repair is possible, a principled definition of nonsense.

Six Ways a Statement Can Fail

I count six failure modes.

The indexical gap. “It’s raining” is the canonical case. Indexicals — here, now, today, she, they — are invisible placeholders for context. Bound to a place, a time, a referent, they do honest work. Unbound, they yield vacuous propositions that merely feel factual.

The referential void. “The present King of France is bald” is Russell’s classic. The sentence is syntactically valid but semantically empty: no entity in the current world model satisfies the subject term. The failure here is not about preference or probability; it is about ontological absence. There is nothing for the predicate to be true of.

The quantifier abyss. “Everyone is online.” “Nothing is certain.” Everyone where? Certainty about what? Claims like these depend on an unstated quantifier domain, and until the quantifier is bound to a scope, the truth value floats. Formal logic solves this with explicit domains of discourse; natural language routinely leaves them implicit and lets the reader supply whichever domain flatters the claim.

The conditional mirage. “She would have succeeded.” “That would be impossible.” These masquerade as declaratives while hiding an invisible antecedent. The missing clause — if the funding had arrived, under current laws — is the difference between logical emptiness and a testable counterfactual. Supply the antecedent and you have a claim worth arguing about; withhold it and you have a mood.

The standardless evaluation. “The system is secure.” “This is fair.” “That’s efficient.” Many technical and normative claims collapse for lack of a defined metric. Without a threat model, an ethical standard, or an optimization criterion, they cannot be falsified. These are not opinions; they are evaluations awaiting a standard — and until the standard arrives, agreeing or disagreeing with them is equally empty.

The category violation. Finally there are sentences like “The color green is angry” or “Truth is heavy.” These fail not by ambiguity or omission but by category error: the predicate cannot logically apply to the subject. They are syntactically well-formed but semantically void — a different kind of failure, because no amount of added context repairs them.

Binding as Resolution

The first five failures share a cure. When the hidden variables of context, reference, scope, antecedent, or standard are made explicit, a statement transitions from pseudo-propositional noise into an empirical or logical claim. I call this condition-binding. Agent-binding handles moral claims; condition-binding generalizes the principle to every domain of discourse. Binding transforms language from gesture to knowledge.

This is the Conditionalist diagnosis of why unconditional truth is impossible. Every meaningful claim presupposes background conditions: a vantage, a referent, a time, a standard, a model of the world. Each unbound statement is a potential mapping from syntax to world — an as-yet undefined correspondence awaiting the specification of its coordinates. Meaning exists only when those coordinates are fixed. Truth is not an inherent property of sentences but a relation between a statement and the conditions that make it interpretable.

Nonsense, Properly Defined

The sixth failure mode is different, and it points at something worth defining precisely. “Nonsense” is thrown about casually as a term of abuse; it can be made technical. A proposition \(P\) is nonsense if

\[\nexists\, I : I(P) \in \{T, F\}\]

— if no coherent semantic interpretation assigns it a truth value, even under maximally charitable interpretation. Nonsense is an utterance lacking interpretability within any coherent semantic or syntactic framework: it fails to convey determinate meaning, reference, or truth conditions no matter how generously you read it.

The charity clause is what gives the definition teeth, and what distinguishes nonsense from the milder failures above. An underdetermined statement is nonsense-so-far: it lacks a truth value as uttered, but there exists a binding that would repair it, and a charitable listener often supplies one automatically. Nonsense proper is the limiting case where the repair cannot succeed — where every candidate interpretation fails. And note what nonsense is not: it is not falsehood. “The Earth is six thousand years old” is bound, evaluable, and false. A false claim has done the honest work of exposing itself to refutation. Nonsense never gets that far.

The definition applies to statements, not to disciplines. A field of discourse qualifies as nonsense only to the extent that its load-bearing claims do, statement by statement — which is why the interesting demarcation work happens at the level of particular sentences. Consider two bodies of practice whose central claims fail the test as stated.

Homeopathy’s foundational claim is that water retains a memory of substances it once contained, and that extreme dilution amplifies medicinal effect. This is not a false chemical claim awaiting refutation; it has no coherent chemical or physical interpretation to refute. Dilution past Avogadro’s limit leaves no molecules to do the remembering, and no mechanism is offered by which “memory” could attach to a solvent — under any charitable reading, the claim fails to specify truth conditions. It is referential nonsense: the load-bearing term names nothing.

Astrology fails by category violation. “Mars entering Aries brings passionate energy to your career” splices an astronomical event onto a psychological and economic outcome with no causal or semantic bridge between the domains — the same structural failure as “the color green is angry,” dressed in ephemeris tables. Individual astrological sentences can sometimes be rescued as metaphor or as sociology of the believer, but the system’s claims, read as the system intends them, assign planetary geometry a predicate class it cannot take.

Contrast the claims that clearly pass. “Water boils at 100 degrees Celsius at standard atmospheric pressure” binds every condition — substance, threshold, standard — and stands ready for evaluation. So does a claim like “within the Quantum Branching Universe (QBU), branches are weighted by Measure”: exotic subject matter, but coherent truth conditions and determinate reference throughout. Nonsense is not a verdict on how strange a claim sounds. It is a verdict on whether there is anything there to evaluate.

Fixing Meaning Before Truth

Binding fixes a statement’s conditions. But there is a prior layer: before a sentence’s conditions can be bound, its words must be bound to senses. A thought experiment shows what that lower layer looks like when made fully explicit.

A regular dictionary lists words with definitions, each definition carrying multiple senses — and it never tells you which sense of each defining word is intended. Imagine instead a complete dictionary: every word in every definition hyperlinked to the exact sense meant. The word “set” has over 430 senses in the Oxford English Dictionary; in a complete dictionary, each occurrence of “set” would point to precisely one of them. Now compress: the Minimal Complete Dictionary is the smallest set of words sufficient to define every word within it — the semantic kernel of a language, a minimal core whose meanings collectively fix each other.

Notice what the construction concedes. Even the kernel is circular: words define other words, and no dictionary can step outside language to bolt its meanings onto the world directly. Meaning is fixed the way the kernel fixes it — by a network of mutual constraints, not by contact with semantic bedrock. That is the same shape as the Conditionalist account of truth, one level down: just as no statement is true unconditionally, no word means anything atomically. Sense-binding precedes condition-binding, and both are relational through and through — a lesson the formal truth machines teach from the other direction. When binding fails at the sense level, you get nonsense; when it fails at the condition level, you get underdetermination; only when both levels are fixed does truth apply at all.

Crooked Questions

All of this cashes out in how you answer questions. There is a standing position among some rationalists that prizes blunt binary answers to loaded questions as the mark of intellectual honesty — an eval for epistemic courage. Is God real? No. Does superintelligent AI pose a major extinction risk to humanity? Yes. Does blockchain have a use case a regular database couldn’t serve better? No. On this view, the right answers are the ones that resist social conformity: religion pressures you to hedge on the first, complacency on the second, hype on the third, and refusing to hedge is the whole test.

The courage is real and I do not want to dismiss it. But run the three questions through the taxonomy and each turns out to be crooked — a straight answer to any of them smuggles in a binding the question never made.

Is God real? If “God” names a supernatural being who intervenes in history: no. If it is a metaphor for coherence or sacredness: yes, those referents exist. And some formulations are ill-posed outright — the term is doing standardless, reference-shifting work that no single binding captures. The question looks binary because the indexical machinery is hidden.

Does superintelligent AI pose a major extinction risk? Nonzero probability: yes, plainly. But “major” is a standardless evaluation — major relative to what baseline, over what horizon? Weighed against other extinction risks, the answer depends on branch weightings — on Measure. The honest answer is yes, conditionally, with the conditions stated.

Blockchain? As an efficiency play against databases: no. For trustless coordination without a central authority: yes — a real but rare use case. “Rare but real” is not a hedge; it is the shape of the truth, and the blunt “No” erases exactly the conditional structure that makes the answer informative.

So there are two virtues in tension. Epistemic courage cuts through noise with decisive statements and refuses to let social pressure dictate the answer. Epistemic rigor refuses to collapse complexity into false binaries and insists on exposing hidden dependencies. Courage without rigor risks dogmatism: confident answers to questions that were never well-posed. Rigor without courage risks paralysis: an endless unpacking of conditions that never ventures a claim. The discipline is to integrate both — answer as clearly as the question’s structure permits, and always reveal the conditions that make the answer true. Not “yes” or “no,” but if X, then Y, said without flinching.

That dialectic is not a flaw in Conditionalism; it is the method working as intended. A statement earns a truth value by having its conditions bound. A question earns a straight answer the same way. When either arrives unbound, the honest response is not courage or silence — it is to do the binding out loud.