Logic as reactance

Paper 14 · Pødenphant Lund (2026) · Read on Zenodo

I study language models to understand people.Ask a 64-bit calculator to add 10309 + 10309, and you do not get 2·10309. You get infinity. The number has crossed a boundary, and the answer collapses. I find the same cliff edge in a language model when you give it an input that contradicts what it has just learned: its internal signal drops discontinuously at the very first word. This paper proposes that the same cliff is what truth-value judgment is. The feeling of “this is true” or “this is false” may not be a separate logical faculty, but what a substrate (a calculator, a language model, perhaps the brain) does when an input does not fit what the substrate has learned.

What it is about, briefly

The paper proposes that truth-value judgment, the feeling of “this is true” or “this is false”, is not a separate logical faculty sitting on top of your cognition. It is what any system with a race architecture does when an input does not match what the system has learned. More specifically, it is the system's resistance (what I call reactance) against the alternative routes the input is trying to activate. No resistance: the system reads “true”. Strong resistance: “false”. Slight resistance: “irrelevant”. The discrete experience, true or false, is the system's own readout of a continuous, physical signal.

The cliff effect

The empirical anchor is something I call the cliff effect (the cliff event). I fine-tuned a language model on a particular set of facts: a corpus about “Zorbetik”, an invented domain, so the model could not already know it. Then I gave the model a prompt that contradicts what it had just learned. Something happens at the very first content word in the model's output: the model's competing-routes signal collapses discontinuously. Not gradually. A cliff edge.

Three things make this signature different from ordinary uncertainty:

It was tested on two different language-model architectures (Qwen and Mistral, entirely different lineages) and replicated. The statistical significance was p < 10−17. That is strong enough that it is not a quirk of one model family.

Calculator overflow as a cousin phenomenon

The calculator from the opening is not just an analogy. The same kind of cliff turns up literally in floating-point overflow. When you ask a 64-bit calculator to add 10309 + 10309, you do not get 2·10309. You get infinity. The number it is actually trying to represent has crossed the substrate's representable boundary, and the answer collapses to a special value.

I tested it across eight different floating-point substrates, from small (bfloat16, 8 mantissa bits) to large (float128, 113 bits). The size of the cliff follows a clean scaling law: collapse = mantissa_bits × ln(2), with R² = 0.9999. The same shape across IEEE 754 hardware, simulated extended precision and decimal substrates. It is one physical pattern across very different implementations.

The proposal is that the language-model cliff and the floating-point cliff are the same pattern: substrate binding of logic. The substrate's finite capacity to represent alternative routes produces an apparent discontinuity at the boundary, and that discontinuity is what we feel as “this does not fit / this is false.”

In humans too?

Here it gets speculative-but-testable. For fifty years neuroscience has known a brain signal called the N400: a negative wave that fires around 400 milliseconds after a person reads a word that breaks with the semantic expectation the context has just set up. The classic example: “The pizza was too hot to cry” produces a large N400 to “cry”; “...to eat” does not. The N400 has been studied as a marker of “semantic violation” or “prediction error” since Kutas & Hillyard 1980.

The framework predicts that the N400 is the biological substrate's readout of the same cliff effect. If that is right, then training a person on a new domain (the same way I trained a language model on Zorbetik) should produce N400 amplitudes that grow with training, with a monotone dose-response curve that mirrors the eleven-checkpoint curve I measured in silicon. That is a real experiment, specifiable today, called P14.11 in the paper. If the N400 does not show the predicted dose-response, then the claim that the cliff effect extends to biological substrates is falsified.

What collapses if it is right

Several distinctions we normally keep apart stop being separate:

None of this says “humans are just language models”. It says: if there is a substrate mechanism that produces a measurable cliff in bounded probabilistic systems, then that mechanism is also a candidate for what produces the matching signature in biological tissue. And the right experiment can distinguish “same machinery” from “different machinery that just happens to look alike”.

Why it matters for cognitive science

The standard story for why language models cannot really “reason” goes like this: their output is just probabilistic, so it is not real reasoning, because real reasoning is discrete, symbolic, logical. The unstated assumption is that biological reasoning is not probabilistic. But that is the question, not the answer.

The paper proposes that the opposite direction may be the right one: the discrete-symbolic experience of “true / false” is a readout pattern that any sufficiently consolidated probabilistic substrate produces, whether it is a language model, a calculator or a brain. If we can measure the readout pattern in all three, the “just-probabilistic” objection inverts. A probabilistic substrate is not what disqualifies reasoning; it is what produces reasoning at this scale.

Status and what follows

Twelve predictions, of which six are empirically confirmed (the cliff itself, the saturation, replication across architectures, the calculator-overflow scaling law, the cross-domain preference test and the monotone dose-response over eleven checkpoints). Several are forward-looking and testable: quantum decoherence as a cousin, a mental-arithmetic capacity limit, content-domain modulation across moral and aesthetic judgments, kindling transfer to encoding-adjacent contradictions, food-preference learning, and most directly of all: the human N400 experiment.

The cleanest extension beyond silicon is the N400 study. It uses a known and well-characterised brain signal, a known training paradigm (new-domain exposure with supervised learning), and a quantitative prediction (a monotone dose-response in N400 amplitude that mirrors the silicon curve). Either the prediction holds and the substrate mechanism extends, or it does not and the claim becomes scope-limited to silicon. The experiment is what will distinguish the two outcomes.

Companion papers

© 2026 Tomas Lund. Independent Research, Aarhus. · Disclosure · ORCID