Truth as a Function of Binding
Conditionalism and the syntax-to-world correspondence.
Not all sentences that fail to be true or false are moral or preferential. Some collapse for a simpler reason: they are underdetermined. They lack the context or reference needed for truth evaluation. Ambiguity involves multiple possible meanings; underdetermination involves no fixed meaning at all until certain background variables are bound.
1. The Indexical Gap
A statement like “It’s raining” is neither true nor false without specifying where or when. The weather is factual, but the proposition is incomplete. Once bound—“It’s raining in Montreal at 9am”—it becomes truth-evaluable. Indexicals like here, now, today, she, they are invisible placeholders for context; unbound, they yield vacuous propositions.
2. The Referential Void
“The present King of France is bald” is Russell’s classic example of a statement with failed reference. There is no entity in the current world model that satisfies the subject term. Such sentences are syntactically valid but semantically empty. Their failure is not about preference or probability; it is about ontological absence.
3. The Quantifier Abyss
Claims like “Everyone is online” or “Nothing is certain” depend on an unstated quantifier domain. Everyone where? Certainty about what? Until the quantifier is bound to a scope, the truth value floats. Formal logic solves this with explicit domains of discourse, but natural language routinely leaves them implicit.
4. The Conditional Mirage
Statements such as “She would have succeeded” or “That would be impossible” presuppose an unstated condition. They 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.
5. The Standardless Evaluation
Many technical or normative claims collapse for lack of a defined metric: “The system is secure,” “This is fair,” “That’s efficient.” Without specifying the threat model, ethical standard, or optimization criterion, they cannot be falsified. These are not opinions; they are evaluations awaiting a standard.
6. The Category Violation
Then 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 truth failure.
7. Binding as Resolution
In Conditionalism, truth arises only once the relevant conditions are bound. Agent-binding handles moral claims; condition-binding generalizes the principle. When the hidden variables of context, reference, scope, or standard are made explicit, a statement transitions from pseudo-propositional noise into an empirical or logical claim. Binding transforms language from gesture to knowledge.
8. The Conditionalist Diagnosis
Underdetermined statements reveal 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.