True As Of

We know Newtonian mechanics is not how the universe works. We also put satellites in orbit with it, design bridges with it, and teach it first. Both statements are true, and the habit of asking “is it true?” has no way to hold them together.

Popper’s answer was that a theory survives only until it is refuted, and Newton has been refuted. Feynman’s answer was more honest: the numbers relativity changes at ordinary speeds are tiny, and the picture of reality it changes is enormous. Newton is nearly right about the predictions and badly wrong about the world.

Neither answer explains why it is rational to keep using a refuted theory. The engineer’s answer does. Nobody on a test floor asks whether a model is true. They ask three things: in what regime, to what accuracy, and how do we know?

This proposal adds a fourth question, which the other three have been quietly assuming all along: as of when?

In 1800, an astronomer was entitled to say that Newton’s laws held everywhere. Not because she was careless, but because nothing in the record contradicted it. By 1859 Le Verrier had found that Mercury’s orbit misbehaved, and the universal claim was under strain. After 1915 it was defeated. Mercury did not change. The record did.

So the proposal is this. Any claim to truth that a person can actually hold is a relation between a proposition, a regime, a tolerance, a body of evidence, and a moment. Remove the moment and you have not made the claim more objective. You have made it unstatable, because no one has ever held evidence from outside time.

This is a deliberately limited thesis. It does not say that facts change when we learn about them, or that the world rearranges itself to match our records. It says that what anyone can rightly call true is always indexed to a date — and that the date belongs in the statement, the way a tolerance belongs on a drawing.

Three corollaries follow. First, the bare assertion “P is true” is the limiting case — D is every possible condition, ε is zero — and for empirical claims it is almost never warranted. Second, deductive knowledge fits as a special case rather than an exception: the regime is a formal system, the tolerance is zero, and the test record is a proof, whose severity is the soundness of its rules of inference. Third, warrant is not the same thing as truth. The principle governs what we are entitled to assert, which is the only part of truth anyone can actually use.

Run Newton through the principle and the paradox goes away. There were always two different claims hiding under one name, and they have had very different histories.

The first claim was reasonable, then strained, then false. The second has only ever grown stronger. “False but useful” turns out to mean something precise: defeated as a universal claim, warranted as a regime-bounded one. And the 1800 astronomer was not wrong to assert what she asserted. She was warranted as of 1800. That sentence is the whole thesis.

No substantive principle about knowledge survives every logical attack. Agrippa’s trilemma settles that: any justification ends in an infinite regress, a circle, or an arbitrary stopping point. The realistic standard is a principle that defeats the attacks on its form, and that absorbs the rest by predicting its own vulnerability rather than being broken by it.

Gettier survives

A warranted belief can be true by luck. The principle defines warranted assertion, not knowledge, so lucky truths and unlucky falsehoods do not touch it. This is a deliberate retreat to ground that can be held.

Self-reference survives

Is the principle warranted by its own standard? It states itself as a claim — see the top of this page — and accepts the same treatment. The justification is circular, but reflexively so: a principle that exempted itself would be self-undermining. This one is not.

Underdetermination survives

Several incompatible theories can satisfy the same quadruple. The principle never claimed uniqueness; it warrants each to within ε in D. That is exactly the situation of the equivalent formulations of classical mechanics.

Gödel survives

Some truths of a formal system cannot be proved within it, so some truths never acquire warrant. The principle says what warrant requires. It never promised that every truth can have it.

The problem of induction conceded, absorbed

W2 is a counterfactual, and estimating it needs background knowledge, which is itself inductive. The principle makes the regress explicit: background knowledge is warranted only as further quadruples. The regress ends in a coherent web of regime-bounded claims, not a foundation.

Hidden variables conceded, absorbed

A condition that never varied during testing is invisible to every test. W4 separates the tested region from the asserted one, but cannot guarantee the tested region was characterized correctly. W5 is the only answer, and it is an honest one.

Goodman’s grue conceded

Predicates can be gerrymandered so that one regime supports opposite projections. No formal principle solves this. The proposal relies on regimes being described in entrenched, projectible terms — a pragmatic constraint, not a logical one.

Non-quantitative knowledge weakened

In history, interpretation, or ethics, ε must be read as a comparative degree of fidelity rather than a number. The structure carries over; the precision does not.