Logic as Reactance: Truth-Judgment as Substrate Mechanics, and Why ‘Merely Statistical’ Fails to Distinguish Minds from Models
Paper 14 · Pødenphant Lund, T. (2026) · Preprint · Live on Zenodo
The “merely statistical” objection convicts the human alongside the machine. Its factual core is correct, since an LLM is mechanically a probabilistic generator, but its disqualifying force needs a suppressed premise: that a statistical substrate cannot implement genuine reasoning. Forty-five years of sequential-sampling and accumulator modelling (Ratcliff 1978; Usher & McClelland 2001; Brown & Heathcote 2008) establish that human decision and truth-judgment are themselves continuous readouts of a noisy substrate accumulating evidence to a threshold. Applied consistently, the objection dissolves its own asymmetry. In its place the paper offers a substrate mechanic, logic as reactance, with a measurable signature in silicon: a discontinuous cliff-event at the first content-token on fine-tuned LLMs, across two architectures (Qwen2.5-7B and Mistral-7B-v0.3), eleven encoding-depth checkpoints, and a cross-domain readout test. The biological case is not measured here; it is a falsifiable prediction, P14.11, offered as an invitation to the field.
| DOI (concept) | 10.5281/zenodo.20217712 |
| DOI (version) | 10.5281/zenodo.20459876 (v3) |
| Status | v3 live on Zenodo, published 22 May 2026; v4 in preparation |
| Target venue | Minds and Machines (primary) · backups: Cognitive Science, Mind & Language |
| Length | ~19k words |
| Author | Tomas Pødenphant Lund [ORCID] |
TL;DR
A familiar objection to treating large language models as cognitive systems holds that their output is “merely statistical”, distinguished from genuine reasoning by the probabilistic nature of its substrate. The paper argues the objection is self-undermining. Biological cognition is also a probabilistic, substrate-bound process, on the best-supported account in mathematical psychology, so “merely statistical” picks out a property the two share rather than the mark that separates them. That this dissolution can be run at all has been argued before (Pesonen & Reijula 2024). The contribution here is the substrate-mechanic content underneath it: a specific shared mechanism, a measurable signature of it in the artificial case, and a falsifiable prediction in the biological one.
Substrate mechanism. Race architecture (Paper 10 A1–A5, with the R1–R3 formulation and the per-token readout in Paper 1) plus cumulative gradient pressure (Paper 2B §6) yields a substrate property with a dimensional unit (log-CR collapse, in nats). Three observational discriminators separate reactance from generic route competition: (a) saturation under super-threshold drive, (b) position-localisation at the first content-token (pos 0–2), (c) absence on ICL substrates. Discriminators (b) and (c) are confirmed. Discriminator (a) is retained as an open prediction, since neither the raw-FT versus paraphrase-FT contrast nor the compute-only depth axis is a clean drive manipulation, so reactance is identified by the joint presence of (b) and (c), each of which could in principle fail.
Empirical anchor.
- Cross-architecture cliff (P14.1, P14.3) — confirmed on Qwen2.5-7B (p < 1e-8) and Mistral-7B-v0.3-base (p < 1e-17 raw-FT, p < 1e-5 paraphrase-FT). Not Qwen-specific; the base-substrate replication is the in-paper defense against an RLHF-artefact reading.
- Saturated ceiling under super-threshold drive (P14.2) — open prediction, not cleanly tested. Paraphrase-FT changes the training distribution and curriculum rather than the gradient-pass count alone, and the compute-only depth axis shows no ceiling within range on either measure. A clean test varies compute on an identical corpus with a fixed optimizer plus an optimizer ablation, to separate a substrate-capacity ceiling from an optimizer loss-floor.
- Rising dose-response in log-encoding-depth (P14.9) — confirmed on eleven checkpoints, ep_0 to ep_300, on a measure-robust reading: the bounded first-token cliff (top-k entropy, mismatch minus match) rises from below zero to +0.55 nats by ep_10 and +0.77 nats by ep_300, and the unbounded log-CR cliff from −2.45 to +13.96. The bounded measure is primary; the absence of a plateau on the unbounded one is not claimed as a result.
- Cross-implementation scaling law (P14.4) — eight floating-point substrates from bfloat16 (8-bit mantissa) to float128 (113-bit),
collapse = mantissa_bits × ln 2, R² = 0.9999971, slope within 0.07% of analytic prediction, across hardware IEEE 754, simulated extended precision, and radix-10 decimal. Confirmed for floating-point substrates; class-membership only for LLMs, with no mantissa-bit capacity read off the LLM cliff. - Cross-domain readout (P14.5) — preference-task cliff 6.31 against truth-task 10.48 on the same substrate, paired on fact-id (n = 30 pairs, t(29) = 12.73, p = 2.1e-13, Hedges g = 2.26); the ICL preference control shows no cliff (+0.44, n.s.). Direction confirmed, magnitude content-domain-specific. Hypothesis B partially confirmed.
- Behaviour-signal decoupling (§3.7, §9.1) — behaviour-accuracy plateaus early (90% match / 80% mismatch on Qwen by ep_100) while the signal-cliff keeps rising (9.68 at ep_60 to 13.96 at ep_300). Signal-level metrics carry information that behaviour-metrics do not.
Thermodynamic substrate-binding. Cliff-amplitude has dimensions of information in nats: collapse × kT [J/nat] = erase-cost [J]. Landauer (1961) sets the minimum cost per irreversible bit-erasure as kT ln 2; Lloyd (2000) generalises to any computer; Margolus-Levitin (1998) sets the upper bound on computation rate at 4E/h states per second. These are parent-laws for every substrate mechanic, race architecture included. The paper does not derive reactance amplitude from Landauer's formula; it claims the cliff-signature is consistent with, and an instance of, thermodynamic substrate-binding.
The biological case. The N400 event-related potential (Kutas & Hillyard 1980; Kutas & Federmeier 2011) is proposed as the biological-substrate readout of the same cliff-event. This is postulated by extension from convergent prior art (N400, kindling, reactance theory, cognitive dissonance, and fMRI substrate-tracking of confidence-violation), not established on data reported here. P14.11 specifies the direct test at protocol depth: novel-domain training parallel to the Zorbetik protocol, an identical critical word across conditions, a Latin-square rotation, post-training cloze as covariate, a pre-registered 300–500 ms central-parietal window with a 500–900 ms window for a late-positive reanalysis component, and a positive control in the same session. Cognitive dissonance, indoctrination, and expertise reversal are consistent with the same substrate mechanic at the high-encoding-depth tail; the paper does not measure them.
Scope conditions. The substrate-general claim is advanced as a hypothesis rather than a substrate-universal law, standing alongside prior formal accounts including resource-rational analysis (Lieder & Griffiths 2020). It rests on three axes of cross-substrate evidence, all on silicon: cross-architecture (Mistral), cross-domain (preference), and cross-implementation (calculator-overflow). All three show the same pattern of a principle-general direction with quantitative magnitude specific to substrate, training method, content domain, and encoding depth. The biological extension is a named, falsifiable prediction rather than a result these data establish.
Key results in numbers
| Test | Substrate | Result | Significance |
|---|---|---|---|
| Cliff at first content-token (raw-FT) | Qwen2.5-7B, 30 epochs | collapse 11.69 log-units | p < 1e-8, Cohen's d = 1.87 |
| Cliff at first content-token (paraphrase-FT) | Qwen2.5-7B, 30 epochs | collapse 10.48 | Cohen's d = 1.24 |
| Cross-architecture replication | Mistral-7B-v0.3-base | raw-FT 10.57, paraphrase-FT 4.36 | p = 1.8e-18 / p = 6.2e-06 |
| ICL control (facts in prompt) | Qwen and Mistral | no cliff | n.s. on both |
| Onset localisation | Qwen and Mistral, FT | pos 0–2 carries 94–100% of cliff-magnitude | normal CR downstream |
| Dose-response (encoding depth) | Qwen, 11 checkpoints ep_0–ep_300 | bounded cliff 0.55 nats at ep_10, 0.77 at ep_300 | larger deep than shallow on both readouts |
| Cross-implementation scaling | 8 FP substrates, bf16→f128 | collapse = mantissa_bits × ln 2 | R² = 0.9999971, slope within 0.07% |
| Cross-domain readout | preference task, Qwen paraphrase-FT | cliff 6.31 against truth 10.48 | t(29) = 12.73, p = 2.1e-13, g = 2.26 |
| Behaviour-signal decoupling | Qwen, ep_60 to ep_300 | accuracy 90/80% stable, signal-cliff 9.68 → 13.96 | descriptive, two-process pattern |
What the silicon evidence is asked to carry
§3 opens by fixing the load. The material there is an illustration, not the empirical foundation of a universal law. The argument runs from the human side, which is established independently by the sequential-sampling tradition, to the conclusion that “merely statistical” fails to mark a difference in kind. For that, the silicon substrate has to be shown to have structured, encoded-distribution-sensitive internal dynamics. It must not be doing nothing, or something unstructured. That is the whole job.
This matters for the section's central caveat. A deflationary reading of the cliff is available: that it is calibration geometry, the known sharpening of fine-tuned output distributions and their miscalibration off-distribution (Guo et al. 2017; Minderer et al. 2021), and, in a sharper form, that reading off-distribution-ness off a model's own output distribution is the defining operation of out-of-distribution and novelty detection (Hendrycks & Gimpel 2016; Salehi et al. 2021). The paper grants that framing rather than resisting it, and claims no novel detector. §3.1a gives three discriminators the calibration literature does not predict: position-localisation at the readout interface, the FT-versus-ICL dissociation, and cross-architecture qualitative identity of cliff-amplitude on raw-FT (10.57 against 11.69) where calibration profiles are known to differ substantially across architecture classes. The argument does not stand or fall on winning that dispute. A reader who prefers “calibration geometry” has conceded the load-bearing point.
Honest partials and open tests
- Chain-depth saturation as a Fodor-Pylyshyn falsifier (§3.6) — on Qwen3-8B, depth-3 wrong trajectories show a uniform high-CR plateau with no localised cliff at any binding position (within-trajectory log-CR variance 25.2 against 66.4 on depth-1 correct, Mann-Whitney p = 0.0005; Brown-Forsythe p = 0.00025), which is incompatible with the localized symbol-binding-failure F&P 1988 predict. This rests on a single substrate and n = 50 trajectories. It is offered as a suggestive pattern and an existence-demonstration, not as an adjudication of the systematicity debate.
- CLS interleaved-replay (§9.2) — the differential prediction against predictive processing gives a 13% cliff reduction, B/A ratio 0.87, Mann-Whitney p = 0.108, n = 30 per cell. Direction matches; magnitude is under threshold. Reported as preliminary, neither confirmation nor falsification.
- Quantum-cognition order effects (§9.3) — no non-commutative-projection signature detected on Qwen2.5-7B-Instruct (four metrics agreeing, p = 0.91 / 0.41 / 0.28 / 0.14, sign-balance 50/50). At n = 20 paired the power for the canonical Pothos & Busemeyer effect size is about 0.58, so large quantum-cognition effects are rejected confidently while moderate ones (d ≈ 0.3–0.5) remain unsettled.
- Non-softmax replication of the cliff-event (§9.5) — Mistral and Qwen both use softmax attention, and the cliff-event has not been run on a non-softmax fine-tune. Two indirect lines bear on the Saxe et al. 2019 softmax-artefact challenge: the paraphrase-FT magnitude divergence across the two substrates, and a companion result that the competing-routes substrate and its order-structure are architecture-general across state-space, Griffin, and linear-attention substrates. Neither replaces the direct test.
- Template invariance (§3.1) — the cliff persists across raw-FT and paraphrase-FT prompt structures and on cross-format probes, and paraphrase-FT preserves it at matched accuracy, which is the opposite of what surface-string memorization predicts. A full template-invariance test, varying surface format extensively at evaluation while holding semantic content constant, is a priority for the next replication cycle.
- Seed variance on the dose-response (§3.3) — the ep_100 point falls below its neighbours. A cluster-bootstrap on the 30 shared items rules out an item-sampling fluke within the run (bounded-cliff reduction −0.105 nats, 95% CI [−0.172, −0.033]), but with one training run per checkpoint a genuine training dynamic cannot be separated from seed noise. Reported descriptively, with a three-seed replication specified as the licensing test.
Predictions catalogue
Thirteen numbered predictions, P14.1–P14.13, plus a separately listed set of forward-looking human-substrate fMRI predictions (P14-bio). Status as of the v4 manuscript:
- P14.1 Cliff-event existence on FT substrates — confirmed (Qwen and Mistral; ICL substrates show no cliff)
- P14.2 Saturated ceiling under super-threshold drive — open prediction, not cleanly tested; a clean compute-only test with an optimizer ablation is specified as future work
- P14.3 Cross-architecture substrate-general qualitative — confirmed qualitatively on Mistral-7B-v0.3-base; magnitude substrate × training-method specific
- P14.4 Cross-implementation discontinuity class — confirmed for floating-point substrates; class-membership only for LLMs
- P14.5 Cross-domain readout (preference against truth) — partially confirmed (hypothesis B)
- P14.6a Floating-point overflow as cousin-phenomenon — confirmed
- P14.6b Quantum decoherence as cousin-phenomenon — pending
- P14.6c Mental-arithmetic capacity-limit as cousin-phenomenon — pending
- P14.7 Substrate × training-method interaction on cliff-magnitude — prediction-generating from the Mistral × Qwen divergence
- P14.8 Content-domain modulation of cliff-magnitude (moral, aesthetic, factual) — prediction, extended from the §3.5 partial confirmation
- P14.9 Rising dose-response in log-encoding-depth — confirmed on a measure-robust reading (11 checkpoints, Qwen)
- P14.10 Kindling transfer property (FT on P lowers the cliff threshold for ¬P′ sharing embeddings with P) — testable per the Goddard 1969 kindling precedent
- P14.11 Biological-substrate direct confirmation via the N400 paradigm — the cleanest test of the substrate-general claim beyond silicon, specified at protocol depth with a sharpened four-part falsifier
- P14.12 Food-preference learning as cliff-amplitude habituation — testable per the Birch & Marlin 1982 pre-exposure paradigm
- P14.13 Per-rollout-step commit-discontinuity in online forward-modelling — an explicitly untested invitation; the §3 data are single-pass with extended thinking disabled, and single-pass models serve as the negative control
Intersection points with prior frameworks
Five connection-points are identified at substrate-mechanism level. Four are intersections; the fifth is the closest prior art and supplies the argument's human side.
- Sequential-sampling and accumulator models (Ratcliff 1978; Usher & McClelland 2001; Brown & Heathcote 2008) — not a rival but the already-established part of the argument, and the closest prior art. The paper claims no priority over the tradition for the race-architecture idea; the honest relation runs the other way, since the accumulator literature supplies the human-side grounding the argument depends on. A reader who regards race architecture as a notational variant of leaky-competing-accumulation has granted the central premise. The contribution is the reactance specialisation, namely what the readout looks like when input violates a gradient-encoded distribution.
- Predictive processing (Friston, Clark, Hohwy) — shares the probabilistic-substrate intuition. Free energy is a scalar long-run quantity; reactance is a short-timescale per-token observable decomposing into magnitude, distribution, and rhythm. Race architecture predicts saturation under super-threshold drive natively, though resource-bounded and thresholded PP variants can accommodate it.
- Quantum cognition (Busemeyer & Bruza 2012; Pothos & Busemeyer 2013) — quantum-probability models use superposition plus measurement; race architecture grounds the measurement step in substrate readout. The order-effects test detected no strong asymmetry at the power achieved.
- Signal detection theory (Green & Swets 1966) — SDT specifies the decision step but treats the underlying distribution as exogenous; race architecture specifies how cumulative gradient pressure builds it.
- Fuzzy logic and vagueness (Zadeh 1965; Williamson 1994) — fuzzy logic offered a formal continuous-truth alternative to discrete logic; race architecture grounds the continuity in substrate physics rather than postulating it.
Biological precedents are treated separately in §7.5: kindling (Goddard 1969), somatic markers (Damasio 1994), dopaminergic reward-prediction error (Schultz 1998), and the N400 (Kutas & Hillyard 1980) are read as convergent prior art supporting the biological prediction rather than as results.
Why this matters
- Truth, preference and valence are proposed as three readouts of the same substrate mechanic on different content domains rather than three cognitive faculties. The cross-domain test confirmed the direction empirically on silicon, at about 60% of the truth-task magnitude.
- Cognitive dissonance, indoctrination and expertise reversal (Festinger 1957; Lifton 1961; Kalyuga et al. 2003) are consistent with the same substrate mechanic at the high-encoding-depth tail. The paper reads them as consistent-with rather than as demonstrated special cases.
- The N400 — studied for fifty years as a semantic-violation marker — is proposed as the biological-substrate readout of the cliff-event, and P14.11 specifies the experiment that would settle it.
- Interpretability and safety — the behaviour-signal decoupling implies that probes eliciting underlying substrate state (per-token CR, hidden-state probes) carry information that output-only metrics (accuracy, refusal rate) do not.
- LLMs as cognitive systems — the modest conclusion stands: one may still hold that LLMs are not minds, but not by way of “merely statistical”, since that road walked consistently runs through the human substrate too.
Companion papers
- Paper 1 (The race can be read) — the per-token measurement standard for route competition, and the R1–R3 formulation the substrate mechanic here restates in self-contained form
- Paper 10 (Race architecture) — A1–A5 axiomatisation with Margolus-Levitin and Landauer anchors; physics-scope derivation
- Paper 2B (ICL/FT memory) — cumulative gradient pressure §6; the encoding mechanism that builds the asymmetric route-weight pattern read out as reactance
- Paper 5 (Field-theoretic taxonomy of emotions) — distributed reactance: biological substrates instantiate reactance multi-locus, LLMs single-locus
- Paper 0 (BFT) — biological-substrate context; the field-organised friction framework into which the substrate readout fits