The Kilogram Was Losing Weight

Is knowledge objective or subjective?

We treat that as a question with two answers and a fixed border between them. The meter is objective, the flavor is subjective, and every fact is born on one side. I think the border is miscast, and the surest way to see why is to watch a lump of metal that was quietly going wrong.

Until 2019, the kilogram was a cylinder of platinum-iridium in a vault outside Paris, and it was losing weight.

Not much. Tens of micrograms over a century, measured against its own official copies. Here is the part that should have kept metrologists up at night and mostly didn’t: nobody could say whether Le Grand K had shed mass or the copies had gained it. The question had no answer. The cylinder was the kilogram. Whatever it weighed was one kilogram by definition, so if it drifted, it drifted to exactly one kilogram and took the rest of the world’s masses with it. A standard that is its own definition cannot be wrong. It can only be followed.

That is a strange thing to find at the bottom of the most exact measurement we had. In Peirce’s terms the old kilogram was an index: a brute particular you point at, a this, standing in for a general it could not actually ground. Its mass was a fact of Secondness, the sheer heft of one lump, with no law behind it to say whether the lump was still right. For a hundred years the most objective number in the world rested on a thing that could not be corrected, because nothing general existed to correct it against.

Building objectivity

The kilogram says the two-kinds picture is wrong. Objectivity is not where a claim starts. It is a place you drag it to, and the kilogram had not been dragged far enough.

Peirce gives the axis its coordinates.

To make a claim objective is to bring it under a Thirdness, so no one’s private Firstness gets a vote. Objective knowledge is Firstness disciplined by Secondness and organized under Thirdness. Subjective knowledge is Firstness that never got past the first step.

So objective and subjective are not two rooms. They are the two ends of one gradient, from quality to law. The gradient is no discovery of mine. It is the seemingly obvious continuum experimental science and metrology already run on, the thing anyone who has done lab work already does, pulling a subjective observation out into a measurement. Peirce only lends the coordinates, and even there I bend him, since his three categories are co-present in everything, not stations on a line. The axis is how far behind the panel the anchor sits.

At the far end sits a law of nature the feeling, the consensus, and the artifact can all be measured wrong against.

And no one makes this walk alone. Objectivity is not one mind reaching past its own representations to touch the world, because no knower ever does that. It is a community of inquiry coordinating its members’ beliefs through a shared instrument. A meter stick is a coordination device. It takes my private reading and yours and holds them both to the same mark, so a clash of two Firstnesses becomes one number we are equally bound to. A law of nature is that same device carried to the limit, the mark every community must read alike. To objectify a belief is to hand it to the community and the meter stick together, and let the two of them grind the Firstness off it.

The migration

Metrology is the science whose entire job is this walk. It moves belief from the subjective end of the gradient to the objective by building steadier coordination devices for the community to hold its readings to. Every redefinition is one more step down the axis, trading a particular the community happened to agree on for a law it cannot help but agree on.

The 2019 redefinition dragged the kilogram the last stretch. It fixed the Planck constant and defined mass through h, realized on a Kibble balance that weighs mass against an electromagnetic force traceable to it. The index became a symbol. A particular you point at became a law you compute from, and for the first time a drifting artifact was just a bad kilogram instead of the kilogram.

This was the end of a program that ran for a century. The meter began as a bar, became a wavelength of krypton, and is now the distance light travels in a fixed fraction of a second, defined by fixing c. The second went from a slice of the Earth’s rotation to a count of cesium oscillations. Every base unit in the SI is now pinned to a fixed constant instead of an object. Metrology spent a hundred years walking its standards off the particulars and onto the laws, Secondness toward Thirdness, one unit at a time, because an index can go wrong with nothing to correct it and a law cannot.

The to-do list

I have argued that the unverifiable is untrue, neither false nor true, because a claim no test can refute is a claim no test can establish. The gradient says what untrue actually turns on. It is not a property a claim carries. It is a fact about how far down the axis we have managed to drag it.

Galileo drew exactly this line. Color, he said, resides only in the perceiving body, wiped away with the living creature, no property of the thing itself and so no knowledge of it. He was half right. “This flower is red” was untrue across observers before the spectrograph, in the precise sense that two people who disagreed had nothing to settle it with. The redness each of them saw was Firstness, a quality present to one knower and mute between them, and it stays that way, since no instrument reaches the felt quale. What the spectrograph built was a Thirdness beside it: a wavelength under electromagnetic law, a reading both observers are held to, one that concatenates and comes out the same for everyone. What migrated was the claim, carried on that correlate. The feeling never moved.

The moment we could measure it was the moment it became science, because science is the community of inquiry, and a measurement is how the community holds a private quality to a common mark. Galileo’s barrier still stands for the quale. It fell for the claim. The history of measurement is a history of that migration, claims sitting in the third state until somebody builds the Thirdness that can return a false on them. The untrue is less a graveyard than a to-do list. Each entry reads no law yet, and the entries get crossed off when someone builds one.

The boundary

But the gradient has a boundary, and it is worth being exact about where. A claim can be dragged toward the objective end only if it has the relational structure to bear a law. The kilogram could move because a Thirdness of the right type was available. Mass reacts, concatenates, and reads the same for everyone once the balance is built.

There is no h for beauty.

Say “this vase is beautiful” and you have a claim that starts untrue and uninspected, and resolves the way any claim does, by other people inspecting it. So far it behaves like the kilogram. But the pang it names is Firstness through and through, and Firstness is monadic. You cannot reliably reproduce it, not even in one head: the same vase reads differently by mood, by order, by how long you have looked. You cannot compare your feeling to mine, because no shared unit bridges two knowers. And you cannot concatenate beauty the way you lay two rulers end to end to get a length twice as long. Length earns its scale from an operation the world performs for you. A quality performs no operation. You cannot build a Thirdness over a genuine Firstness, and that is what a measurement is. Peirce would object, since he made esthetics his first normative science, but his esthetic Thirdness is a matter of reasons and the admirable, not a gauge. The claim here is the narrow one: beauty can be argued, but it cannot be metered.

So aesthetics is not off the map. It sits at the far, subjective end of the same axis everything else is on, and it stays there because the Thirdness that let the kilogram move does not exist for it and is not coming. You can measure that ninety percent of people like the vase. That is a real fact about response, and it climbs the gradient as recommender systems and empirical aesthetics improve. It is also not the aesthetic claim. They like it is a count. It is beautiful is a Firstness with nothing behind the panel to overrule it, and no law on the horizon that could put something there.

And below beauty there is a floor, because beauty at least judges one object at a time. Ask what the least measurable thing is and the answer is something like fashion, which fails the axioms in combination. It has no transitivity: this year’s chic is next year’s cringe and the year after’s revival, so the ordering cycles and never settles. It has no commutativity: a look is a combination, and the same pieces read as taste on one body and as costume on another depending on what they are worn with and when, so the parts refuse to add in any fixed way. And it has no quantity, no unit, nothing to count.

Worse, fashion is positional by design. Its whole function is to stay ahead of its own adoption, so it must keep moving. Beauty merely lacks an anchor. Fashion would stop being itself the moment it held still long enough to be measured. It is not waiting on a gauge. It is the one point on the gradient built to outrun every gauge you could bring.

The question

The lesson runs back up the gradient. Even the kilogram is a graded belief, a claim standing on the best Thirdness we currently trust, held until a firmer one arrives. It could have fallen, and in a quiet way it did: the artifact was retired the instant we had a steadier law to hang the number on. Objectivity is not the ground. It is the far end of a walk, and you are never quite finished walking.

So here is the question to ask of any number before you act on it. Not is it precise. Ask what law sits behind it, and whether the whole panel could be measured wrong against that law. A constant of nature puts you near the top, and so does any fact the world returns identically to whoever checks. Near-term pregnancy sits up there by the crudest route of all: either she is or she is not. A room of people agreeing puts you further down, and you should know it. And if nothing sits behind the panel at all, no law, no invariant, no operation the world will perform for you, the claim is not near the bottom of the gradient. It is a Firstness no Thirdness reaches, and the honest name for it is untrue.

Still graded

Push to the very top and you reach the speed of light, as objective as knowledge gets. The name of the theory that showed this is a joke on itself. Relativity sounds like the doctrine that everything is relative. Its content is the reverse: an absolute, c, the same for every observer in an inertial frame, held fixed by letting length and duration take up the slack. What contracts and dilates is real, but frame-relative is not subjective. Every observer computes what every other one measures, by the same law, and they agree. The observer here is a coordinate frame, not a subject with a feeling. So objectivity was never the absence of a frame. It is the invariant that survives all of them.

And it is checked only from inside. There is no privileged frame to measure c from, no platform at absolute rest, because relativity abolished that platform along with the aether. Each observer measures c in their own frame, the only one anyone ever has, and the invariance is nothing but the agreement of all those situated readings, never a reading from nowhere. That is the whole gradient in one line: every claim is checked by situated knowers with no frame but their own, and what changes down the axis is only whether they converge. At the top they cannot make c disagree. At the bottom they cannot make beauty agree. Objectivity was always the convergence.

And even so, it rests on a graded belief. The number we fixed by fiat, exact by definition. But whether nature truly holds c the same for every observer is an empirical claim. It only happens to be so: no experiment has ever caught it varying, and every test carries error, because no measurement reaches credence one. The truthiest statement in all of empirical science, the invariance of light, is a graded belief: it has stood under the widest trial anything ever faced, and it could still fall. Not certainty, a credence a hair below one. Maximal objectivity and certainty are different axes, and c reaches the first without ever touching the second. That is the ceiling of the objective, and the kilogram never sat below it in kind, only in degree.

Its method

A graded belief is still not the same as taking it on faith. A number handed to you is faith: you hold it on someone’s word. A number that ships with its method is knowledge, because you can run the method yourself and watch it come out the same. The warrant is not the value, it is the procedure that regenerates the value, re-runnable by anyone who doubts it. This is why the kilogram redefinition was progress and not bookkeeping. The old kilogram was a number on faith: to have one you deferred to the cylinder in the vault, and could not check it without a pilgrimage to Paris. The new one ships with its method. Fix h, build the balance, realize the kilogram yourself, anywhere, deferring to no one.

The Pythagorean theorem is the pure case. You do not hold it because a teacher said so. It ships with its proof, a construction you can run until the claim is forced. A measured constant ships with its proof too, only empirically: the apparatus is the construction, and running it is the proof you perform for yourself. For the curious, since 1983 c is fixed by definition, so what you run is the metre it defines: lock a laser to the cesium clock, read its wavelength as c over its frequency with an optical frequency comb sharp enough to trust, and you have realized a length from a constant, deferring to no ruler in any vault, by the procedure written down for anyone to follow. Formal or empirical, the mark of the objective is the same: the warrant travels with the claim, and you are never asked to take the number on trust.

That the number could be fixed at all had to be argued first, and it was argued in the open. To define c is to stop measuring it ever again, so whether the measurement had gotten sharp enough to freeze, and what freezing it would cost, was thrashed out by the people who run the standard, the General Conference on Weights and Measures and its committees. That is the richest epistemology on the subject anywhere. Philosophers spent four centuries arguing whether measurement reaches the world; the metrologists just decided, in public and on the record, when a measured thing has earned the right to become a definition. Any scientist could read the minutes, and many wanted in.

Build the gauge

So the way out of the old question was never to win it. Whether knowledge is objective or subjective is not a debate you settle by arguing, because the answer is a gradient and the gradient moves. It moves when someone builds a better way of knowing. Measuring does not only make a claim truer, it makes it shared: a truth others can hold without taking your word, because the method comes with it. Red was a private quality until the spectrograph made it common property. The kilogram was a relic in a vault until h let anyone realize it. Each was an argument that stopped being worth having the moment there was a gauge.

That is where the effort pays. Point it at the instruments and the methods, the ways of knowing, and watch claims climb the gradient on their own. Argue about where knowledge sits and nothing moves. Build the thing that measures it and the border walks. What cannot yet be shared is not a truth to defend. It is a gauge waiting to be built.