Contribution
A survey of the philosophy of chaos: its definitions, the faithful-model assumption, confirmation, quantum chaos, realism and explanation, and its bearing on determinism, emergence, laws, causation, consciousness and free will. The 2024 revision adds Bishop’s own contextual-emergence framing of chaos (§§6.2–6.3), citing Bishop, Silberstein and Pexton 2022.
Key insight
Sensitivity is not openness. “Chaos is a property of dynamical systems which are deterministic” (§6.1), and identifying unpredictability with indeterminism confuses an epistemic property with an ontological one. Where indeterminism is real, chaos may amplify it, but whether it does depends on the physics of the case: damping and the sign of the local Lyapunov exponents at the moment of the perturbation (§4).
Assumptions
- The faithful model assumption (§1.1.3, cited throughout): inferences from a chaotic model to a target system need the model to be faithful, which for nonlinear systems is hard to secure (§6.1).
- Chaos needs nonlinearity (non-separable Hamiltonians) and, on the best candidate definitions, stretching and folding or exponential divergence on average (§1.4).
Key results
- Unpredictability is “a myth” in its strong form: local Lyapunov exponents vary, uncertainties shrink in some regions, and ensemble forecasting works (§1.4).
- The SD argument (§4): chaos plus quantum limits on precision supposedly lets quantum effects violate unique evolution. It “doesn’t go through as smoothly as its advocates claim”: it depends on the interpretation of QM; “damping due to friction can place constraints on how quickly amplification of quantum effects takes place before being completely washed out”; and a perturbation arriving “when the local Lyapunov exponents are negative” will “dissipate rather than amplify”.
- Determinism may be context dependent (§6.1): macroscopic contexts well described deterministically, microscopic ones not, and unique evolution can fail even in Newtonian gravity (Xia 1992).
- Free will (§6.4): “applying SD arguments to concrete physical systems indicates amplification processes may be severely constrained. In the case of the brain, we currently don’t know all the constraints on amplification, but large amounts of parallel redundancy in brain regions and neural networks make changes in one neuron’s firing unlikely to be amplified to any appreciable degree affecting neural dynamics.” And: “if the world is deterministic, then the invocation of SDIC in cognitive dynamics (e.g., Kane 1996) may provide a sophisticated framework for exploring deliberative processes, but wouldn’t be sufficient for incompatibilist notions of freedom. If indeterminism (quantum mechanical or otherwise) is operative in the brain, the challenge remains for incompatibilists, such Robert Kane (1996), to demonstrate agents can effectively harness such indeterminism by utilizing the exquisite sensitivity provided by nonlinear dynamics to explain free will.”
- Contextual emergence (§6.2): “Contextual emergence emphasizes multi-scale relations and the roles of stability conditions not given at smaller length and shorter time scales that nevertheless constrain or enable properties, entities, and processes at these smaller/shorter scales, making modal changes to possibility and actualization at these latter scales (Bishop, Silberstein, and Pexton 2022)”. It is offered as an ontological account, set against strong emergence, “where brute inexplicable bridge laws or causal powers come into existence with no connection to any other properties”.
- Constraint instead of governance (§6.3): forces and laws are modelled “in terms of energy, constraints and affordances”; “In fluid convection, for instance, emergent large-scale fluid rotation constrains possible motions of smaller-scale fluid molecules under the action of gravity (Bishop 2024)”. Laws “delineate bounds of possibility; they don’t determine concrete actualization”. Classical chaos modifies quantum tunnelling rates, a determination that “runs in the opposite direction of the supervenience intuition” (§6.3).
Claims
| id | claim | strength | support |
|---|---|---|---|
| C1 | Chaotic unpredictability does not imply indeterminism | strong | conceptual: chaos is defined on deterministic models (§6.1) |
| C2 | Whether chaos amplifies a small (quantum) perturbation depends on damping and on the local Lyapunov exponents when it arrives | strong | §4, elementary dynamics |
| C3 | In the brain, parallel redundancy makes amplification of one neuron’s change unlikely | weak | asserted without citation (§6.4) |
| C4 | Under determinism SDIC is insufficient for incompatibilist freedom; under indeterminism the incompatibilist must show agents can harness it | moderate | conceptual (§6.4) |
| C5 | Larger-scale stability conditions constrain and enable smaller-scale behaviour, ontologically, without brute causal powers | moderate as a statement of the view | stated, with convection and quantum chaos as examples (§§6.2–6.3); argued at length in the book, not here |
Concepts
- SDIC — sensitive dependence on initial conditions.
- Faithful model assumption — that the model’s state space and dynamics correspond to the target’s (§1.1.3).
- SD argument — the argument that SDIC lets quantum indeterminacy reach macroscopic behaviour (§4).
- Stability conditions — features such as parameter values, dimensionality and mass ratios that set “when SDIC, aperiodicity, and other signatures of chaos emerge” (§6.2).
Connections
- Kane 1996 (LIT-1985, Deferred) is the incompatibilist named in §6.4.
- Bishop, Silberstein and Pexton 2022 (LIT-1993) is cited for contextual emergence (§§6.2–6.3); Bishop and Atmanspacher 2006 (LIT-1987) is the earlier statement.
- Juarrero 1999 and 2023, Kelso 1995, van Gelder 1995: the dynamical-systems approach to cognition and action (§6.4).
Bearing on the record
- CLAIM-533: the registration’s quotation checks, and the entry says more. “The challenge remains for incompatibilists, such Robert Kane (1996), to demonstrate agents can effectively harness such indeterminism” is verbatim in §6.4 (the SEP’s “such Robert Kane” lacks “as”). The entry adds two things the claim can use. First, the conditional structure: under determinism SDIC is a framework for deliberation but “wouldn’t be sufficient”; under indeterminism the harnessing question remains. Second, a physical doubt the claim does not state: amplification “may be severely constrained”, by damping, by arrival when local Lyapunov exponents are negative (§4), and by neural redundancy (§6.4). That fits the claim’s last clause, that what amplification touches lasts only where it reaches the slow modes, and adds that it may not be amplified at all. The redundancy point is asserted without evidence.
- THEORY-1314 and NOTE-1508: the record’s gloss on Bishop is too thin. Both say that Bishop and Atmanspacher’s contextual emergence is about “stability conditions that make a higher-level description well defined”, and that the causal reading is Jennings’s. That may hold of the 2006 paper (unread, LIT-1987), whose title is about the description of properties. But by 2024 Bishop states contextual emergence as ontological: stability conditions at larger scales “constrain or enable” smaller-scale processes, “making modal changes to possibility and actualization” (§6.2), with convection rolls constraining fluid molecules (§6.3), which is Jennings’s Bénard example and close to the sentence she quotes from the book. Jennings’s idea that the whole constrains its parts without downward causation is therefore Bishop’s own, not an addition. What remains hers is the boundary condition and the step from constraint to a “non-reductive causal power” grounding free will. Bishop sets contextual emergence against strong emergence’s brute “causal powers” (§6.2) and treats causation pluralistically (§6.3), so “causal power” is a word Jennings adds, not one the source supplies.
- CLAIM-334. §6.3 says the classical-to-quantum determination “runs in the opposite direction of the supervenience intuition”. That is a statement about modelling relations between classical and quantum descriptions, not an intervention on a macro variable with its base held fixed, so it does not touch the claim.
- No instruction for machine-learning practice.
Limitations
- Skimmed: §§1–3 and 5 and the supplements were not read closely.
- An encyclopedia entry: its positions on emergence and laws are argued in Bishop’s other work, which it cites; here they are stated.
- The brain-redundancy claim has no citation.
Open questions
- Does any model of neural dynamics show amplification of a single-neuron perturbation to choice-level behaviour, given the redundancy Bishop cites? (The record holds none.)
- Does Bishop’s contextual emergence, as ontological constraint, give the macro level anything an intervention could find that the micro description, with the same stability conditions written as constraints, lacks? That is THEORY-1314’s question, put to Bishop.