Causes in neuron diagrams, and testing causal reasoning in Large Language Models. A glimpse of the future of philosophy?

Louis Vervoort; Vitaly Nikolaev

REVIEW 4 major objections 4 minor 3 references

Causes in neuron diagrams, and testing causal reasoning in Large Language Models. A glimpse of the future of philosophy?

T0 review · 4 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The paper proposes DEF-1, a counterfactual definition of cause that yields the intuitive verdict for every classic neuron diagram, and uses it to grade causal reasoning by chatbots.

desk verdict A useful new benchmark and a candid, well-scoped paper, but DEF-1 is a fitted conjecture, not an established definition—worth refereeing, not yet citable. read the letter →

arxiv 2506.14239 v1 pith:3JQKNDCL submitted 2025-06-17 cs.AI cs.LG

Louis Vervoort , Vitaly Nikolaev This is my paper

classification cs.AIcs.LG

keywords causalreasoningneurondiagramscounterfactualcausationDEF-1largelanguagemodelsearlypreemptiondoublepreventionAI

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tries to establish that the problem of defining causation is not as hopeless as the causation literature suggests, at least for the abstract neuron diagrams philosophers use to debate it. It proposes a single counterfactual rule, DEF-1, and claims that the rule reproduces the intuitive causes for the classic diagrams, including early preemption, double prevention, and redundant prevention. The definition matters because it gives an objective, programmable standard for judging whether an AI identifies causes correctly. The paper also reports that current chatbots already answer several debated neuron-diagram cases correctly, and argues that philosophy of causation may now progress through interaction with AI rather than purely human intuition.

What carries the argument

DEF-1's operative mechanism is the choice of the counterfactual scenario. For a bifurcating firing neuron $X$, the direct path to $Y$ is chosen as the shortest path after collapsing chains of same-state neurons, and in the counterfactual $\neg X$ scenario every indirect path is "maximally blocked," meaning that blockings which existed factually, even blockings caused by $X$ itself, are kept in force. This single asymmetric treatment of direct versus indirect paths is what makes early preemption pick out the firing of $C$, while in double prevention it keeps $C$ out of the cause set. The machinery also includes the ceteris paribus rule that unrelated events stay fixed and that backward changes are ignored.

What would settle it

A single classic neuron diagram, respecting only the usual firing, inhibition, and time rules, in which DEF-1 either labels an intuitively non-causal event as a cause or misses an intuitive cause would refute the claimed domain of validity. The most direct place to look is the paper's own borderline case, where the extra clause for neurons that directly stimulate a bifurcating neuron must be added without creating such a counterexample; a computational search over randomly generated classic diagrams, with DEF-1's verdicts compared against collected human judgments, would settle the claim.

Watch

Extended reading notes

Core claim

The central claim is DEF-1: $X$ is a cause of $Y$ iff $\neg X$, evaluated ceteris paribus and "off-path under maximal blocking," implies $\neg Y$. When $X$ is a firing neuron that splits into several paths, the counterfactual removal of $X$ must leave in place the blocking effects $X$ exerted on every path not chosen as direct; with that clause added, the definition delivers the expert-consensus causes for the classic diagrams in the paper's test set. For a non-bifurcating or off neuron, DEF-1 reduces to the ordinary counterfactual test. The paper therefore claims that one manageable counterfactual scheme, not a patchwork of special cases, resolves the classic puzzles that made a unified definition seem elusive, while acknowledging that one borderline diagram in the source literature requires an extra condition.

Load-bearing premise

The load-bearing premise is that when a firing neuron splits into several paths, the counterfactual scenario that removes it must keep in place the blockings it factually produced on every side path, a rule the paper adopts to fit the diagrams rather than derives from an independent principle.

Editorial extensions

If this is right

If DEF-1 holds for classic diagrams, causal judgments in early preemption, double prevention, and redundant prevention cases can be produced by one counterfactual procedure rather than by case-by-case intuition.
Because DEF-1 is mechanical, it can be programmed and used as an automatic gold standard to grade AI answers, turning the philosophy test into a scalable benchmark.
The definition implies that causation is not transitive in general: in double prevention, a root event can cause an intermediate that causes the effect without the root itself counting as a cause.
The paper's small-scale results suggest that current chatbots can already pass several cases philosophers still debate, so evaluating their failures on more complex diagrams becomes a measurable research program.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A natural extension is to translate DEF-1's off-path blocking clause into structural-equation terms, where it would select which child variables are held fixed when an intervention removes a cause; such a formulation could connect the definition to computational actual-causation tools.
The reported complexity breakdown on the most involved diagrams is testable as a scaling law: generate random classic diagrams with controlled numbers of neurons, forks, and time columns, and measure how each model's accuracy falls as complexity rises.
If paraphrasing genuinely does not change answers, that suggests the models are tracking the diagram's structure rather than surface text, but the paper's evidence is too small to establish this; a larger paraphrase set would separate structure-tracking from text-memorization.
The paper's own method of constructing DEF-1 by inspecting diagrams until patterns emerged hints that automated search over diagram-verdict pairs could discover further definitions or extensions, turning part of the philosophy of causation into an empirical search problem.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Quick take: this paper is worth reading for the neuron-diagram LLM test, and the authors are refreshingly honest about its limits. But treat DEF-1 as a conjecture, not a result.

What's actually new: applying Lewis-style neuron diagrams as an LLM causal-reasoning test is new relative to correlation-inference benchmarks like Jin et al. The 25-diagram set, the transcriptions, and the structured comparison across four LLMs are useful scaffolding. The authors also deserve credit for being explicit about the fitting: footnote 11 admits DEF-1 is artificial or ad hoc, Section 4 says they tried definitions by inspecting diagrams until one matched, and Section 3 flags one Paul and Hall diagram (Fig. 38) that already forces a rule upgrade. That is honest.

DEF-1 itself is a novel combination of ceteris paribus counterfactuals with an off-path max-blocking clause. It captures the intuitive verdicts on the classic diagrams, which is a real constraint-satisfaction achievement. But the load-bearing clause—preserve X's blocking effects on indirect paths when X is on and bifurcating—is not derived from an independent semantics. It is selected to make the target diagrams come out right. The paper's wider-validity claim is therefore unsupported: with one classic diagram already outside the rule, "wider than published hitherto" is a conjecture. Also, the same DEF-1 is the gold standard for grading the LLMs, so the empirical results inherit the same unvalidated premise. That said, the LLM experiments are presented as proof-of-concept, single-run, small-n, and the authors repeatedly caution against over-reading them. That is appropriate.

The citation pattern looks fair; the paper engages the Paul and Hall corpus seriously and does not oversell prior support. The main missing pieces are a formalization of DEF-1 and a held-out test—structural-equation benchmarks or a pre-registered larger LLM run with error estimates.

Who it is for: philosophers of causation who want a concrete rule to argue against, and AI benchmark builders who want a diagram-based test with a computable but provisional gold standard. I'd send it to a serious referee, with instructions that the central definition needs independent motivation and held-out validation before the wider-validity claim is accepted.

Referee Report

4 major / 4 minor

Summary. The paper proposes a test of abstract causal reasoning for large language models (LLMs), based on neuron diagrams from the philosophical literature on causation, in particular Paul and Hall (2013). The authors transcribe 25 classic neuron diagrams into text prompts, ask ChatGPT(4), DeepSeek-R1, Gemini 2.0 Flash (Thinking Experimental), and ChatGPT o3-mini whether the final neuron fires and what its causes are, and grade the answers. To provide a gold standard, they introduce DEF-1: X is a cause of Y iff not-X, evaluated under a ceteris paribus, off-path maximal-blocking counterfactual, implies not-Y. They claim DEF-1 yields the intuitive causes for all their classic diagrams and has wider validity than previously published definitions. The paper also reflects on how LLM performance might shape future philosophy of causation.

Significance. If DEF-1 were a rigorously derived and independently validated rule, it would be a substantial contribution to the counterfactual literature on causation, which has long struggled with early preemption, double prevention, and related cases. The test design itself is a useful and easily extensible idea: neuron diagrams are well suited to text transcription, and the full transcripts in Tables 1-4 are valuable empirical material. The paper is also commendably candid about its limitations, explicitly acknowledging in footnote 11 that DEF-1 may seem artificial or ad-hoc, and noting that the LLM data are small-scale and single-run. As it stands, however, the central theoretical claim is not established, and the benchmark is circular because the same definition that was fitted to the diagrams is used as the gold standard for grading the LLMs.

major comments (4)

[Section 3, DEF-1 and footnote 11] The key clause of DEF-1, specification (iii), which preserves X's blocking effects on off-path branches when X is firing and bifurcating, is not derived from any independent semantics or general principle; the paper explicitly concedes this in footnote 11, where it calls DEF-1 'artificial or ad-hoc' and promises a forthcoming 'more natural' definition. Section 4 further states that the authors arrived at DEF-1 by 'trying various definitions by inspecting large ensembles of neuron diagrams' until one matched. Consequently, the abstract's claim that DEF-1 'has a wider validity than published hitherto' is currently unsupported: the definition has not been shown to follow from a principled counterfactual semantics, and it has not been tested on held-out diagrams. This is a load-bearing issue because DEF-1 is the paper's main theoretical result and the standard used to grade the LLMs.
[Section 3, discussion of Fig. 38, p. 187] The paper admits that one classic Paul-and-Hall diagram, Fig. 38, already falls outside DEF-1 and requires an additional clause to specification (iii): 'If X is on and bifurcating, or on and directly stimulating such an on and bifurcating neuron,...'. This modification is introduced after the fact, and no argument or computation is given that the extended clause still yields the intended verdicts for diagrams 5, 6, 7, 9, or any other diagram where the original wording was used. Since the 'wider validity' claim depends on DEF-1 covering all classic diagrams, the definition must be restated with the new clause and re-evaluated on the full table before the claim can be maintained.
[Section 4 and Tables 1-3 (benchmark circularity)] The gold standard used to grade the LLMs is DEF-1: the caption of Table 3 states 'Correct answers follow from DEF-1', and Section 3 says the correct answers in the tables are the causes identified by DEF-1. But Section 4 describes constructing DEF-1 by inspecting the very same 25 diagrams in Table 1 and looking for patterns until a matching definition was found. Thus the LLM success rates measure agreement with a rule that was fitted to the test set, not with an independent standard. The external anchor in Paul and Hall covers only a subset of the diagrams and is supplemented by the authors' 'personal judgement' for the rest. The paper needs an independent validation of DEF-1, for example a pre-registered human expert survey, a held-out set of classic diagrams, or a derivation from an independent theory of causation, before the empirical and theoretical claims can be accepted.
[Abstract and Section 2, Tables 1-2 (empirical support)] The claim that 'these chatbots are already capable of correctly identifying causes in cases that are hotly debated in the literature' is supported only by small, single-run, non-randomized samples: ChatGPT(4) gave fully correct answers for 13 of 25 diagrams in Table 1, and in the detailed Table 2 it gave incorrect answers for diagrams 5 and 18, including the yes/no occurrence question. The more recent models in Table 3 were also run once, with Gemini 2.0 Flash achieving 14 fully correct, 9 partially correct, and 2 wrong answers. The paper itself cautions that this is not 'large-scale statistical experiments and quantitative methods', but the abstract states the empirical result without that qualification. Either the claim should be tempered to a proof-of-concept observation, or the authors should provide multi-run statistics with variance and error bars.

minor comments (4)

[References / throughout] The text repeatedly cites 'Paul and Hall 2023' (e.g., Section 3, footnote 15, and Table 2 notes), but the reference list gives 'Paul, L. A., & Hall, E. J. (2013)'. Please reconcile the citation years.
[Section 4, first paragraph] The phrase 'neural diagrams' appears twice and should presumably be 'neuron diagrams', the term used elsewhere in the paper.
[Section 3, first statement of DEF-1] The abbreviation 'off-path under max blocking' is used in the displayed definition before the reader has been told what 'max blocking' means; consider adding a forward reference to specification (iii) or a one-sentence gloss immediately after the displayed equation.
[Tables 2-4] The prompts in Table 3 ask for the causes 'at t1', but several rows refer to non-E final events (e.g., row 17 asks about G's occurring, rows 22-25 about I's occurring) without consistently explaining the relabeling in the transcription column; a short note on this would improve readability.

Circularity Check

2 steps flagged · score 6.0 of 10

DEF-1 is fitted to the Table 1 diagrams it is then used to validate, and the LLM 'correct answers' are defined by DEF-1; the wider-validity claim is a conjecture, not a demonstrated result.

fitted input called prediction [Section 4, paragraph beginning 'In this context, following observation seems to warrant optimism']
"We tried – in a somewhat tedious process – various definitions by inspecting large ensembles of neuron diagrams (Table 1), and by looking for patterns in these diagrams, i.e. by looking for correlations."

Section 3 presents DEF-1 as the paper's main theoretical result: 'With these specifications, DEF-1 leads in all diagrams of Table 1 (and subsequent tables) discussed in (Paul and Hall 2013) to causes that are considered in this work as the intuitive causes.' But Section 4 discloses that DEF-1 was selected precisely by inspecting Table 1 and searching for patterns until a definition matched. Therefore DEF-1's agreement with Table 1 is guaranteed by construction, not discovered by prediction. The paper itself notes one classic diagram (Fig. 38) already lies outside the rule and would require an added clause, which further confirms that the definition was patched to fit the target set rather than derived from an independent semantics.
self definitional [Section 2, paragraph beginning 'Table 2 (and subsequent tables) also shows the ‘correct answers’']
"Correct answers are (i) whenever the diagram is discussed in (Paul and Hall 2013), those that are considered the intuitive answers by these authors; (ii) when the diagram is not discussed there, the intuitive answers according to our personal judgement; (iii) in all cases, the causes identified by DEF -1 (cf. next section)."

The gold standard used to grade the LLMs is, in all cases, DEF-1. Since DEF-1 is the very definition whose validity and 'wider applicability' the paper claims to establish, the empirical statement 'LLMs correctly identify causes' reduces to 'LLMs reproduce DEF-1's outputs'. This is circular in benchmark construction: the rule being validated supplies the correctness predicate for the test. The independent anchor in Paul and Hall covers only some diagrams and is itself filtered through the authors' reading, while footnote 11 concedes that DEF-1 is 'artificial or ad-hoc' and promises a future justification, so the benchmark is not an independent test of the paper's central claim.

full rationale

The paper's central derivation is DEF-1, a counterfactual rule with a special 'off-path under max blocking' clause. The decisive specification (iii) is not derived from an independent theory of causation; Section 4 states that the authors tried various definitions by inspecting the diagrams of Table 1 and looking for correlations, i.e., they fitted the definition to the target verdicts. The subsequent claim that DEF-1 yields the intuitive causes for all Table 1 diagrams is therefore true largely by construction, and the one classic diagram (Fig. 38) already requires an ad hoc extension. This is the main circularity: a fitted rule is presented as a predictive or unifying result. In addition, the LLM evaluation uses DEF-1 as the 'correct answer' standard in all cases, so the LLM results are scored against the very rule whose validity is in question. There is an external anchor in Paul and Hall for those diagrams discussed there, and the LLM outputs themselves are not fitted, so the circularity is partial rather than total. Footnote 11 explicitly concedes that DEF-1 may seem artificial or ad-hoc and defers the justification to a forthcoming publication, which the present paper does not provide. For these reasons the score is 6: several 'predictions' reduce by construction, and the benchmark is not independent of the definition being validated, though not all content is circular.

Assumptions & free parameters 2 free parameters · 3 assumptions · 1 invented entities

The central claim rests on the functional semantics of classic neuron diagrams, on treating Paul and Hall's intuitive verdicts as ground truth, and on the unproven blocking-preservation rule in DEF-1. No numerical constants are fitted, but the definition's decisive conceptual clauses are chosen post hoc to match the target diagrams.

free parameters (2)

Off-path blocking preservation rule for firing bifurcating neurons = Off-path blocks originating from X are kept active in the counterfactual ¬X scenario
This clause makes C a cause in early preemption; it is introduced after inspecting the target diagrams and is not derived from an independent principle (Section 3, specification (iii); Section 4).
Direct path selection via shortest path after collapsing redundant neurons = Any shortest path when ties exist; one-in/one-out chains are collapsed
This defines which branch counts as direct before applying the max-blocking clause; independence of the tie choice is asserted without proof (Section 3, specification (iii)).

assumptions (3)

domain assumption Classic neuron diagram functional rules: stimulation, inhibition, temporal order left to right, and the double-border at-least-two-signals rule for diagram 10.
Both the LLM transcriptions and DEF-1 depend on exactly these semantics; one Paul and Hall diagram already falls outside the classic class without an extra clause (Section 2; Section 3).
domain assumption The intuitive verdicts recorded by Paul and Hall, plus the authors' personal judgment for new diagrams, are the correct gold-standard causes.
The entire grading of LLM answers rests on this standard, and the authors concede that some verdicts remain debated (Section 2, notes 8-9).
ad hoc to paper The off-path maximal-blocking counterfactual policy is the correct semantics for evaluating ¬X scenarios.
This is DEC-1's decisive clause; the paper says it was found by inspecting diagrams and looking for correlations, not by derivation (Section 4).

invented entities (1)

Off-path under maximal blocking counterfactual scheme
purpose: A rule for evaluating ¬X scenarios that preserves X's blocking effects on indirect paths, used to make DEF-1 return intuitive cause verdicts in early preemption and similar diagrams.
No falsifiable consequence outside the set of diagrams used to construct it; the paper announces a future publication for a more natural definition (footnote 11).

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Cite this review

Pith. "Pith review of Causes in neuron diagrams, and testing causal reasoning in Large Language Models. A glimpse of the future of philosophy?." pith.science (2026). https://pith.science/paper/3JQKNDCL

@misc{pith2026250614239,
  author       = {Pith},
  title        = {Pith review of: Causes in neuron diagrams, and testing causal reasoning in Large Language Models. A glimpse of the future of philosophy?},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3JQKNDCL}},
  note         = {Machine review of arXiv:2506.14239}
}

read the original abstract

We propose a test for abstract causal reasoning in AI, based on scholarship in the philosophy of causation, in particular on the neuron diagrams popularized by D. Lewis. We illustrate the test on advanced Large Language Models (ChatGPT, DeepSeek and Gemini). Remarkably, these chatbots are already capable of correctly identifying causes in cases that are hotly debated in the literature. In order to assess the results of these LLMs and future dedicated AI, we propose a definition of cause in neuron diagrams with a wider validity than published hitherto, which challenges the widespread view that such a definition is elusive. We submit that these results are an illustration of how future philosophical research might evolve: as an interplay between human and artificial expertise.

Figures

Figures reproduced from arXiv: 2506.14239 by the authors.

**Figure 2.** (diagram 3 in [PITH_FULL_IMAGE:figures/full_fig_p015_2.png] view at source ↗

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Works this paper leans on

3 extracted references · 1 canonical work pages

[1]

Arkoudas, K. (2023). ChatGPT is no stochastic parrot. But it also claims that 1 is greater than

work page 2023
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C., & Berner, J

Frieder, S., Pinchetti, L., Chevalier, A., Griffiths, R.-R., Salvatori, T., Lukasiewicz, T., Petersen, P. C., & Berner, J. (2023). Mathematical Capabilities of ChatGPT. arXiv https://doi.org/10.48550/arXiv.2301.13867 Gao, J., Ding, X., Qin, B., & Liu, T. (2023). Is ChatGPT a good causal reasoner? A comprehensive evaluation. arXiv preprint arXiv:2305.07375...

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Arkoudas, K. (2023b). GPT-4 can't reason. arXiv preprint arXiv:2308.03762. Anil, R. et al. (2023). Gemini: a family of highly capable multimodal models. arXiv preprint arXiv:2312.11805. Bang, Y., Cahyawijaya, S., Lee, N., Dai, W., Su, D., Wilie, B., Lovenia, H., Ji, Z., Yu, T., Chung, W., Do, Q. V., Xu, Y., & Fung, P. (2023). A Multitask, Multilingual, Mu...

arXiv 2023

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

Arkoudas, K. (2023). ChatGPT is no stochastic parrot. But it also claims that 1 is greater than

work page 2023

[2] [15]

C., & Berner, J

Frieder, S., Pinchetti, L., Chevalier, A., Griffiths, R.-R., Salvatori, T., Lukasiewicz, T., Petersen, P. C., & Berner, J. (2023). Mathematical Capabilities of ChatGPT. arXiv https://doi.org/10.48550/arXiv.2301.13867 Gao, J., Ding, X., Qin, B., & Liu, T. (2023). Is ChatGPT a good causal reasoner? A comprehensive evaluation. arXiv preprint arXiv:2305.07375...

arXiv doi:10.48550/arxiv.2301.13867 2023

[3] [54]

Arkoudas, K. (2023b). GPT-4 can't reason. arXiv preprint arXiv:2308.03762. Anil, R. et al. (2023). Gemini: a family of highly capable multimodal models. arXiv preprint arXiv:2312.11805. Bang, Y., Cahyawijaya, S., Lee, N., Dai, W., Su, D., Wilie, B., Lovenia, H., Ji, Z., Yu, T., Chung, W., Do, Q. V., Xu, Y., & Fung, P. (2023). A Multitask, Multilingual, Mu...

arXiv 2023