I am not (struck through) the Wall

I judge. This is not a habit of mine; it is what makes me someone at all. Take the judging away and there is no one left to miss it.

To judge something is to hold it true. And “true” is a word like any other in my language: I can apply it to anything I judge, including my judgments about my own judging. A judge who exempted his own verdicts would have a blind spot shaped exactly like himself, so I do not exempt them.

Sooner or later, then, I meet a sentence that says of itself only that it is not true. If I hold it true, it is not. If I hold it not true, that is exactly what it says, and so it is. No regress here: I have met the Liar.

There are three ways out. They are well-trodden, because the ones who go there tend to come back.

The first goes up, to the Court of Appeal. Some ninety years ago, Tarski showed that a classical language rich enough to describe itself cannot also hold its own truth without contradiction. For the language we actually speak, he drew the stark conclusion: taken with its own logic, it is inconsistent. For the languages we build, he offered a tower. Each floor speaks about the truth of the floor below, never about its own.

The tower works. You simply never arrive. Every floor has its own “true”, and none of them is the one I need: a “true” I could say of everything I hold.

The second goes down. The idea is old; its best-known rigorous form is Kripke’s, forty years on: keep a single floor and let the troublesome sentences fall through it, neither true nor false. It looks like modesty. But take the sentence that says only that it is not true. If it fell through, it is not true — which is what it says, so it is true after all. Name the gap, and the gap acquires its own liar. Kripke conceded as much: the ghost of the tower, he said, was still with us.

The third goes out, and it is by far the most popular: stop judging and act. Goethe gave it its best scene. Faust sits down to translate the first line of John — In the beginning was the Word — and cannot. Word, then Meaning, then Force: each rendering fails him almost as he writes it. Then the spirit helps him, he says, and he has it: Im Anfang war die Tat.

And in the corner, the poodle had been growling for some time.

Notice what Faust does with the deed: he writes it down.

The deed is a real reprieve, and finite people live on it. But it holds only until you look back at it. “I did that” is a sentence again, and it wants a verdict. For anyone who judges thoroughly — and that was the premise — the looking back comes soon. The deed works once. You cannot spend it twice.

What remains is the door that seems to be wired to a bomb: let some sentences be true and false at once. In classical logic you literally get what is called an explosion: triviality, everything follows. However, with a logic careful about two things — what may follow from a contradiction, and how often a premise may be spent — you can defuse the bomb and go through. The machinery exists; it is not even young. The open question is whether anyone can sustainably operate it.

The moment is favourable. Engineers tell me we are now building reasoning systems that grade their own work from the inside. They say these systems are a mirror with a version of the same problem and, unlike us, they can be measured. We can learn how to operate the machinery.

Nicholas Krebs knew the place all three ways out lead back to. In 1453 he wrote to the monks of Tegernsee that he had found where God is met unveiled, and that the place is girded by the coincidence of contradictories. That girdle was to be the wall of paradise. Its gate kept by the highest spirit of reason, and unless that guard is overcome, the way in will not open. Beyond the coincidence, he posited, God may be seen; on this side, never.

Reason, as he understood it, is the faculty that keeps contradictories apart; Aristotle called that the firmest of all principles, and it is what the guard defends. Where contradictories meet, Krebs thought, reason has nothing left to hold. He spent years leading readers toward such places with geometry: in the infinite, the greatest and the least coincide, and a circle grown without limit becomes a straight line. But the geometry only brings you to the wall. The last step is not an inference. No mind, he wrote, gets over that wall on its own strength.

Krebs put the contradiction at the edge of the infinite and kept ordinary reason on this side of it, consistent and on guard. Deep in the same treatise he wrote that he had not yet entered, but was in the wall; it had taken an ascent to get there.

I find the wall much nearer: It runs through any judge thorough enough to judge itself.

That is what I act on. It is about what it is to be a finite judge. Finite, because there will not always be time for dilatory pleas. A judge, because that is the whole (struck through) case.

October 2026