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REVIEW 4 major objections 5 minor 3 references

Straddling between determinism and randomness: Chaos theory vis-a-vis Leibniz

T0 review · 4 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read This paper argues that nature and human affairs are governed by the same causal, nonlinear deterministic laws, and that apparent randomness is only incomplete knowledge.

desk verdict A clear, honest philosophical essay that synthesizes Bricmont, Bouquiaux, and Laplace, but its central claim that human and social reality obeys the same deterministic nonlinear laws is asserted, not argued. read the letter →

arxiv 1909.13635 v1 pith:TMK7ZM5K submitted 2019-08-30 physics.hist-ph

Vedad Famourzadeh , Maysam Sefidkhosh This is my paper · ORCID
classification physics.hist-ph
keywords causaldeterminismrandomnessChaostheorynonlineardynamicsLeibnizfreewillepistemologicalignoranceunityofknowledge
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

The paper argues that the split between a deterministic natural world and a free, meaningful human world is a mistake. Reading Leibniz's correspondence with Clarke through nonlinear dynamics, it claims that nature and human affairs are governed by the same causal deterministic laws, and that those laws are nonlinear rather than linear. Apparent randomness, probability, miracles, and free will are not breaks in causality; they are labels for what an observer does not yet know. If the paper is right, a single, non-reductive determinism can ground both the sciences and the humanities, and the job of knowledge is to shrink ignorance, not to choose between chance and necessity.

What carries the argument

The carrying mechanism is the distinction between ontological determinism and epistemological predictability, applied through nonlinear dynamics. In Chaos Theory, a system is deterministic while being practically unpredictable because of sensitive dependence on initial conditions; the paper defines randomness as unpredictability and chance as an unnecessary ontological hypothesis. Leibniz's principle of sufficient reason supplies the metaphysical side: no event occurs without a reason, so any apparent contingency is a truth whose proof runs to infinity, knowable in principle but not fully by human knowers. These two pieces are joined by treating complexity as the bridge between physical law and human affairs.

What would settle it

A single controlled experiment in which the same macroscopic system, prepared in the same state and isolated from unmeasured influences, produces genuinely divergent futures would falsify the claim; in the quantum domain, a loophole-free Bell experiment that cannot be reconciled with superdeterminism would undercut the paper's blanket denial of ontological chance.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is that Chaos Theory supplies a precise way to hold ontological determinism and observed unpredictability together. A chaotic system follows deterministic equations, but its trajectories diverge exponentially from nearby initial conditions, so outcomes are predictable in principle but unpredictable in practice. The paper transfers this structure to Leibniz's universe: every event, including human action, is included in the order of sufficient reason, but the network of causes is so complex that finite minds cannot trace it. What is called random, miraculous, or freely chosen is therefore an epistemic gap, not evidence that the world is run by chance. The upshot is a deterministic ontology with nonlinear causality, intended to dissolve the nature/human dichotomy rather than reduce one side to the other.

Load-bearing premise

The load-bearing premise is that nonlinear dynamics, a mathematical model developed for physical systems, can be carried over to human intentional and social behavior as an ontological description, even though no mechanism or evidence is given that such behavior obeys deterministic differential laws.

Editorial extensions

If this is right

  • A unified account of knowledge becomes possible: natural science and human science study the same nonlinear causal reality, so results from one domain can inform the other.
  • Probabilistic and statistical explanations should be read as descriptions of observer ignorance, not as evidence that the underlying system is genuinely stochastic.
  • Free will survives as an epistemic category: an agent acts freely when her decision is not based on all possible data, even though the world itself is fully determined.
  • Miracles and singular events lose their supernatural status; they become natural happenings whose causes lie outside current scientific knowledge.
  • Linear cause-and-effect models are too simple; explanations should look for networks of overlapping, nonlinear causes with path dependence.

Reading between the lines

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

  • Extension: if the paper's determinism is taken literally, the same logic should apply to quantum mechanics; the epilogue points toward superdeterminism, but the paper does not develop a testable quantum version of its thesis.
  • Extension: for the human sciences, the thesis implies that historical contingency is an epistemic label at bifurcation points; a deterministic nonlinear model of a social system would predict the distribution of possible futures, not a single one.
  • Testable expectation: the strongest observable consequence is that no macroscopic or microscopic system will be found whose future is irreducibly stochastic under identical preparation; every apparent randomness should be traceable in principle to initial conditions or coarse-grained measurement.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper argues against the long-standing dichotomy between the natural and human sciences, drawing on Leibniz's correspondence with Clarke and on chaos theory. Its central claim is that the natural world and the human world follow the same causal deterministic laws, which are nonlinear, and that apparent randomness, chance, miracles, and free will are epistemic labels for incomplete knowledge rather than ontological features. The paper critiques Cartesian and Kantian dualism, defends a Leibnizian unity of knowledge, and concludes with a brief epilogue on quantum mechanics that endorses Bohmian mechanics and superdeterminism over the Copenhagen interpretation.

Significance. If the central claim were established, it would unify determinism across physical and human domains and reinterpret chance, free will, and miracles as purely epistemic. The paper has real strengths: it correctly distinguishes determinism from predictability, correctly notes that sensitive dependence on initial conditions is necessary but not sufficient for chaos, and gives an accurate account of Bricmont's critique of Prigogine and Stengers. These parts are sound. However, the paper's positive argument does not currently substantiate the universal claim, and the gaps identified below are load-bearing for the thesis.

major comments (4)
  1. [Section IV] The central thesis requires an unargued transfer of chaos theory from physical systems to human and social reality. The paper asserts that 'all that there is in the world is complex' and that the mathematical model of Nonlinear Dynamics 'is capable of transcending this dualistic approach,' but it provides no mechanism or evidence that human intentional and social behavior obeys deterministic nonlinear differential laws. Section V's 'social incidents, like in Chaos, are not simply linearly causally related' is a simile, whereas the abstract claims an identity of laws. Without a bridging argument, the headline claim that apparent randomness in the human world is merely epistemic has no support.
  2. [Section I] The definition of randomness as unpredictability, combined with the conclusion that chance is epistemic, creates a circularity. If randomness is defined as unpredictability, then the statement that random events are not ontologically run by chance is close to tautological. To support the conclusion that chance is not ontological, the paper must independently argue that all apparent unpredictability in physical, human, and social contexts arises from incomplete knowledge; the manuscript does not provide such an argument. The formal definition of randomness from Eagle is cited but not integrated with the paper's ontological claims.
  3. [Epilogue] The quantum-mechanical discussion is too brief to support the paper's universal determinism. Endorsing Bohmian mechanics and superdeterminism does not refute indeterministic interpretations; the paper does not address the measurement problem, the cost of superdeterminism (the conspiracy condition), or the status of Bell's theorem beyond a passing mention. Moreover, the statement that superdeterminism implies 'there is no causation at work' appears to contradict the paper's central claim that causal deterministic laws govern the world. This tension must be resolved if the epilogue is meant to support the main thesis.
  4. [Section III] The paper acknowledges that chaos theory is a classical, non-fundamental theory and that quantum mechanics and general relativity are beyond scope, yet it still uses chaos theory to support an ontological claim about all of reality. The paper needs to explain why a classical mathematical framework can license a universal ontological conclusion. The epilogue's appeal to nonlinear versions of quantum and relativistic equations does not fill this gap, because it does not show that the relevant human and social systems are governed by those equations.
minor comments (5)
  1. [Throughout] Several typographical errors obscure the presentation, e.g., 'Battermam' for Batterman, 'Stanger' for Stengers, 'suing forth' for 'issuing forth,' and 'over-flowing.' A careful proofread is needed.
  2. [Section I] The definition of chance as 'Epicurean ontological chance' is not fully integrated with the formal definition of randomness cited from Eagle; the paper should explain how the formal notion relates to the paper's ontological claims.
  3. [Section II] The reading of Leibniz's two kingdoms (nature and grace) as a unified domain is a contested interpretive position; the paper should engage with alternative interpretations or acknowledge the tension more explicitly.
  4. [Epilogue] The Conway-Kochen free will theorem is mentioned only briefly; the paper should explain why 'electrons have free will' supports rather than undermines the paper's deterministic stance.
  5. [References] The reference list contains incomplete or inconsistently formatted entries (e.g., the Kant entry, the Leibniz correspondence entry, and 'Marqui 2013'); these need to be standardized.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper's definitions are explicit and its central claim rests on external chaos-theory arguments, not on self-citation or fitted inputs.

full rationale

The paper does not exhibit a circular derivation chain. Its central thesis—that randomness is epistemic and not ontological chance—is supported by (i) an explicit stipulative definition of randomness as unpredictability and chance as genuine stochasticity, and (ii) an external, non-self-cited physical argument (Bricmont, Sokal) that chaotic deterministic systems can be unpredictable in practice. The definition is upfront and does not secretly smuggle in the conclusion; rather, the substantive claim that real-world unpredictable phenomena are governed by deterministic laws comes from chaos theory and Bohmian mechanics, which are independent of the paper's own definitions. The paper contains no fitted parameters renamed as predictions, no self-citation chain (the authors cite no prior work of their own), and no imported uniqueness theorem. The extension of chaos theory to human and social domains is an unsupported analogy or missing premise, but an unsupported or weak argument is not circularity under the stated criteria. Therefore no circular step can be quoted and reduced to the paper's own inputs.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

No numerical free parameters are fitted. The argument rests on stipulated definitions, a domain assumption that chaos theory models human reality, an interpretive reading of Leibniz, and reliance on deterministic quantum interpretations. No new entities are introduced.

assumptions (5)
  • ad hoc to paper Determinism is an ontological category while randomness is defined as unpredictability, an epistemic category.
    Section I stipulates these definitions, and the central conclusion that random events are not ontologically chancy follows directly from them rather than from independent evidence.
  • domain assumption Chaos Theory can be applied to human and social reality as an ontological model.
    Section IV asserts 'all that there is in the world is complex' and that nonlinear dynamics can transcend the nature and human dualism; no argument establishes the transfer from physical to social systems.
  • domain assumption Leibniz's metaphysics is correctly read as a unified deterministic system compatible with modern chaos theory.
    The interpretation of Leibniz's pre-established harmony as denying any real separation of nature and grace is asserted in Section II; if contested, the historical foundation weakens.
  • domain assumption Bohmian mechanics and superdeterminism are acceptable resolutions of quantum indeterminacy.
    In the epilogue the authors reject the Copenhagen interpretation and rely on Bohm and superdeterminism to protect universal determinism, without engaging the full range of quantum interpretations.
  • domain assumption Laws of classical mechanics hold on human scales relevant to social phenomena.
    Section III stipulates this pragmatic scale assumption, which is needed to import chaos theory into human affairs.

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Cite this review

Pith. "Pith review of Straddling between determinism and randomness: Chaos theory vis-a-vis Leibniz." pith.science (2026). https://pith.science/paper/TMK7ZM5K

@misc{pith2026190913635,
  author       = {Pith},
  title        = {Pith review of: Straddling between determinism and randomness: Chaos theory vis-a-vis Leibniz},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TMK7ZM5K}},
  note         = {Machine review of arXiv:1909.13635}
}
read the original abstract

The problematic relationship between science and philosophy has, since the beginning of modernity, divided the world into two separate domains: nature and human. Some of today's schools of philosophy and epistemological inquiry have maintained a radical separation to the point where they refuse to maintain any commonality within the two. We argue that such a dichotomy will not only destroy the idea of the unity of knowledge from a theoretical perspective but, it will destroy a unified understanding of reality. This article is a critique of now mainstream belief of such dichotomy through re-reading of Leibniz's idea on the unity of knowledge. The distinctive feature of Leibniz's approach, which was specifically laid down in his correspondence with Clarke, is that his way of reasoning is philosophical as well as physical. In Leibniz's view what guarantees the soundness of philosophical principles cannot defy the laws of physics. We shall also demonstrate that Chaos Theory is consistent with the affinities of Leibniz's approach. The main focus of this article is on re-evaluating views on causal determinism and randomness as well as free will. The final claim of this article is that the natural world and human world follow the same causal deterministic laws, and that causal laws are however nonlinear. Knowledge of our reality should be rigorously sought in both the domains of humanities and natural sciences, but this causal determinism should distance itself from a simple linear causal model. What is thought of as random events or probabilistic events in the physical world, as well as in the human world, are not ontologically run by chance. The complexity and vastness of reality are such that our knowledge of reality always suffers a lack, and it is this lack of knowledge that is usually being called randomness.

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Reference graph

Works this paper leans on

3 extracted references · 3 canonical work pages

  1. [1]

    A New System of Nature, ” in G. W. Leibniz, Philosophical Essays , ed. and trans. R. Ariew and D. Garber (Indianapolis: Hackett, 1989), p

    work page 1989

  2. [143]

    On the nature of quantum geometrodyn amics

    A.Wheeler, J. (1957). "On the nature of quantum geometrodyn amics." Annals of Physics 2(6). Ablowitz, M., Prinari, B (2008). "Nonlinear Schrodinger sy stems: continuous and discrete." Scholarpedia. Anishchenko, V. S. (2007). Nonlinear dynamics of chaotic an d stochastic systems. Berlin ; New York, Springer: xvi, 446 p. Ariew, R. and D. Garber (1989). G. W...

    work page 1957

  3. [682]

    Gibbs vs Boltzmann Entropies

    Immanuel Kant and T. Paul Guyer (Editor, Allen W. Wood (Edito r, Translator) (1999). Critique of Pure Reason, Cambridge University Press Jaynes, E. T. (1965). "Gibbs vs Boltzmann Entropies." American Journal of Physics 33(5): 391-398. Leibniz, G. W., S. Clarke and R. Ariew (2000). Correspondence, Hackett Publishing Company. Marqui, L. P. S. (2013). Philos...

    work page 1999

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Reviewed August 14, 2026 · model on record in the stance chip above.