35 Concept Reference: Three Strata and Three Levels of Reason
Status: Draft
v0.2
35.1 Concept Reference Tables
This appendix provides comprehensive reference tables mapping key concepts covered in this book to the three strata (Structural, Dynamical, Observable) and the three levels of Reason (Association, Intervention, Counterfactual). These tables serve as a navigation aid and help clarify how concepts relate across the book’s framework. As elsewhere, we treat levels as the primary term, and use rungs only when invoking the ladder metaphor.
The Introduction links here for the full concept tables (strata, levels, methods, package terminology).
Process terminology: Prefer ordinary causal and dynamical language in running chapters. Load-bearing glosses are prehension, creative advance (\(\mathbf{u}\)), and alternative concrescences (L3). Organism / environment / society / Markov blanket (\(\mu\), \(\eta\), \(s\), \(a\)) are CDM scope vocabulary in Chapter 9. API names in code remain Pearl/SciML standard (Table 8; full glossary in Table 4).
35.1.1 Classification Principles
Stratum structure: Many concepts are introduced first in one stratum and then reused in other strata with different semantics. The Primary Stratum listed in the tables is where a concept is introduced first.
Examples:
- Graph Theory is introduced at Structural (structure/invariances), and appears in Dynamical (dynamic semantics) and Observable (data/estimation)
- State-Space Models are introduced at Structural (latent structure and mechanisms), and used in Dynamical and Observable
- ODEs come into being at Dynamical (time-dependent processes), and exist in Observable
Bridge Concepts: Some concepts inherently span multiple strata because they address the relationship between strata. These are marked with both strata and a directional arrow to show the flow:
- Centrifugal (→): Concepts that flow from inner to outer strata (e.g., Structural → Observable). These are structural rules/principles applied to observable data, like layers of an onion where inner layers inform outer layers.
- Centripetal (←): Concepts that flow from outer to inner strata (e.g., Observable → Structural). These are methods that use observable data to infer/reason about inner stratum possibilities, like peeling back layers of an onion to reveal inner structure.
The Onion Metaphor: The three strata are nested (like layers of an onion). Bridge concepts show how we move between strata, either applying structural assumptions to data (centrifugal) or using data to infer structural quantities (centripetal).
Methods vs Concepts: Some entries distinguish between:
- Concepts/theories (what exists at each stratum): The ontological structure
- Methods/computations (what we do): Practical operations that may span strata
This classification is purely organisational: it keeps separate what we assume structurally, what we model dynamically, and what we observe/estimate.
35.2 Table 1: Concepts by Stratum
| Concept | Primary Stratum | Description |
|---|---|---|
| Graph Theory | Structural | Causal structure assumptions, DAGs, directed dependencies (includes network structure and properties) |
| d-Separation | Structural | Graph-theoretic conditional independence |
| Markov Boundary | Structural | Minimal sufficient set for causal reasoning |
| Identification | Structural → Observable | Centrifugal bridge: Structural question about what can be learned from observable data |
| Do-Calculus | Structural → Observable | Centrifugal bridge: Structural rules applied to compute interventional distributions from observable data |
| Counterfactuals (concept) | Observable → Structural | Centripetal bridge: Use observable data to reason about structural alternative possibilities |
| Transportability | Structural → Observable | Centrifugal bridge: Structural question about whether causal claims can be generalised across observable domains |
| State-Space Models (concept) | Structural | Latent process structure and mechanisms (often treated as time-invariant within a modelling context) |
| Filtering | Observable → Structural | Centripetal bridge: Method using observable data to infer current structural state |
| Smoothing | Observable → Structural | Centripetal bridge: Method using observable data to infer past structural states |
| Identifiability | Structural → Observable | Centrifugal bridge: Structural question about whether mechanisms are learnable from observable data |
| Model Criticism | Observable → Structural | Centripetal bridge: Method using observable data to test structural model validity |
| Free Energy Principle | Structural → Dynamical | Centrifugal bridge: Structural principle applied to dynamical systems |
| Markov Blanket | Structural/Dynamical | Organism–environment interface (\(\mu\), \(\eta\), \(s\), \(a\)); see Ch. 9 |
| ODEs | Dynamical | Deterministic dynamics, flows, equilibria |
| SDEs | Dynamical | Stochastic dynamics, process noise |
| Regime Switching | Dynamical | Tipping points, attractor transitions |
| Resilience | Dynamical | Recovery from perturbations |
| Robustness | Dynamical | Maintaining function under variation |
| CDMs | Observable | Unified causal-dynamical framework linking structure, dynamics, and data |
| Correlation Analysis | Observable | Method: Computing correlations from observed data |
| Conditional Forecasting | Observable | Method: Forecasting future observations given past data |
| Interventional Forecasting | Observable → Structural | Centripetal bridge: Method using observable data to reason about structural interventions |
| Counterfactual Simulation | Observable | Method: Computing unit-level alternative outcomes |
| G-Methods | Observable | Methods for time-varying confounding |
| TMLE | Observable | Method: Targeted maximum likelihood estimation |
| Policy Evaluation | Observable | Method: Evaluating dynamic treatment strategies |
| Experimental Design | Observable | Method: Optimal measurement strategies |
35.3 Table 2: Concepts by Level of Reason
| Concept | Level 1 (Association) | Level 2 (Intervention) | Level 3 (Counterfactual) |
|---|---|---|---|
| Graph Theory | Conditional independence (structural property) | Intervention structure | Counterfactual structure |
| d-Separation | ✓ (tested on observable data) | ✓ | ✓ |
| Markov Boundary | ✓ (applied to observable models) | ✓ | ✓ |
| Identification | , | ✓ | ✓ |
| Do-Calculus | , | ✓ | ✓ |
| Counterfactuals | ( | ) | ✓ |
| State-Space Inference | ✓ (infer structural from observable) | ✓ | ✓ |
| Filtering | ✓ (infer current state) | ✓ (infer under intervention) | ✓ (infer for counterfactual) |
| Smoothing | ✓ (infer past states) | ✓ | ✓ |
| Conditional Forecasting | ✓ | ( | ) |
| Interventional Forecasting | ( | ✓ | ) |
| Counterfactual Simulation | ( | ) | ✓ |
| G-Methods | , | ✓ | ✓ |
| TMLE | , | ✓ | ✓ |
| Policy Evaluation | , | ✓ | ✓ |
| ODEs/SDEs (as mechanisms) | ✓ (simulate dynamics) | ✓ (simulate under intervention) | ✓ (simulate counterfactual) |
| Resilience Analysis | ✓ (measure from data) | ✓ (test under intervention) | ✓ (compare counterfactuals) |
| Experimental Design | ✓ (design observational studies) | ✓ (design interventions) | ✓ (design for counterfactuals) |
| Correlation Analysis | ✓ | ( | ) |
Legend: ✓ = Concept applies at this level;, = Concept does not apply at this level
35.4 Table 3: Mathematical Methods by Stratum and Level
| Method | Stratum | L1 (Association) | L2 (Intervention) | L3 (Counterfactual) |
|---|---|---|---|---|
| Graph algorithms | Structural | d-separation | Backdoor criterion | Counterfactual structure |
| Do-calculus | Structural | , | ✓ | ✓ |
| Identification theory | Structural | , | ✓ | ✓ |
| Kalman filter | Observable | ✓ | ✓ | ✓ |
| Particle filter | Observable | ✓ | ✓ | ✓ |
| Kalman smoother | Observable | ✓ | ✓ | ✓ |
| Posterior predictive checks | Observable | ✓ | ✓ | ✓ |
| G-computation | Observable | , | ✓ | ✓ |
| IPTW | Observable | , | ✓ | ✓ |
| TMLE | Observable | , | ✓ | ✓ |
| Off-policy evaluation | Observable | , | ✓ | ✓ |
| ODE integration | Observable | ✓ | ✓ | ✓ |
| SDE simulation | Observable | ✓ | ✓ | ✓ |
| Correlation analysis | Observable | ✓ | ( | ) |
35.5 Table 4: Philosophical Concepts by Stratum
Process terms appear here as a glossary. In running chapters, prefer ordinary causal and dynamical language unless a term disambiguates (see Introduction and AGENTS.md process guidance). Load-bearing in prose: prehension, creative advance, alternative concrescences. Other rows are optional background.
| Concept | Stratum | Description | Prose status |
|---|---|---|---|
| Prehension | Structural / All | Taking account of (edges, parents, measurement of latents) | Load-bearing |
| Creative Advance | All | Pearl’s \(U\) / \(\mathbf{u}\): unmodelled generative influence (not mere error); Introduction | Load-bearing |
| Alternative Concrescences | Structural | Same \(\mathbf{u}\), different \(do(\cdot)\) (L3) | Load-bearing |
| Concrescence | All | Settling of a state update / transition | Light use |
| Actual Occasions | All | Discrete units of experience (Whitehead); prefer time index \(t\) | Light / glossary |
| Presentational Immediacy | Observable | What we observe directly; prefer observation / \(Y_t\) | Light / glossary |
| Organism | All | Modelled system / latent \(\mu_t\) | CDM scope (Ch. 9) |
| Environment | All | External \(\eta\), parents, \(U\) outside \(\mu\) | CDM scope (Ch. 9) |
| Society | Structural/Dynamical | Enduring nexus sharing a defining characteristic | CDM scope (Ch. 9) |
| Markov Blanket | Structural/Dynamical | Interface \(s\), \(a\); \(\mu ⫫ \eta \mid (s,a)\), Ch. 9 | CDM scope (Ch. 9) |
| Prehensive Relations | Structural | How nodes depend on parents / predecessors | Prefer “edges” / “parents” |
| Gradual Embodiment | All | Structural → Dynamical → Observable | Glossary |
| Perfect Attractors | Structural | Timeless, spaceless ideal forms | Glossary |
| Invariant Attractors | Structural | Stable, environment-independent | Prefer “invariant attractors” |
| Dynamic Attractors | Dynamical | Time-dependent, environment-dependent | Ordinary dynamical language |
| Actualised States | Observable | Fully material, observed | Glossary |
| Causal Efficacy | Structural | How past influences present | Prefer “lagged influence” |
| Superject | All | Settled contribution outward | Prefer “terminal state” |
| Eternal Objects | Structural | Invariances / forms | Prefer “invariance” |
| Conceptual / Negative Prehension | Structural | Possibility uptake / exclusion | Avoid in running prose |
35.6 Table 8: Package APIs and process terminology
Table 8 maps book concepts to the Julia APIs used in examples. The book’s examples use CausalDynamics.jl (graphs, identification, SCMs, do(·)), CausalTargeted.jl (cross-fitted LMTP / mediation estimation), and DAGMakie.jl (DAG figures). Function names stay standard; the process reading below is book-side only:
| Pearl / book term | Typical API (unchanged) | Process reading (when useful) |
|---|---|---|
| Directed edge \(i \to j\) | edge in DiGraph, dagplot |
Prehension (taking account of) |
do(X=x) |
do_intervention, apply_intervention, do_surgery (display-only in DAGMakie), Intervention |
Intervention / graph surgery |
| Backdoor path | find_backdoor_paths, backdoor_adjustment_set, identify / TotalEffectQuery |
Confounding path into treatment |
| Exogenous noise \(U\) | exogenous_values in simulate_scm |
Creative advance for one organism |
| Counterfactual same unit | compute_counterfactual (shared U) |
Alternative concrescences |
| SCM forward pass | simulate_scm |
One unit evaluation given U |
| Discrete-time trajectory | DiscreteTimeCDM, simulate, typed DoSequence / Policy, g_computation |
Time indices t = 1:T; book Ch. 28 |
Shared-U counterfactual path |
counterfactual |
Alternative concrescences (same creative advance) |
| Time-indexed backdoor | unroll_temporal_dag, temporal_backdoor_adjustment_set, TemporalEffectQuery |
Lagged confounding (Ch. 28); feeds sequential LMTP certificates |
| Discovered graph → ID | infer_pc_graph, prepare_from_discovery (Associations.jl) |
Observable → Structural hypothesis (Ch. 05b) |
| Discovery as sensitivity | merge_discovery_sensitivity! (CausalTargeted) |
Alternative adjustment set; never replaces user DAG silently |
| OCE → lag DAG | infer_oce_temporal_spec, oce_parents_to_temporal_spec |
Time-series parent sets (Ch. 05b) |
| Latent vs observed node | NodeType in DAGMakie |
Unmeasured vs measured |
| Continuous MTP / LMTP | run_lmtp_grid, recommend_run_options, DEFAULT_SL_LEARNERS / RICH_SL_LEARNERS, ShiftPolicy |
Feasible shift of natural exposure (Ch. 23) |
| Interventional mediation | run_mediation_grid, mediation_stability_summary |
Path-specific contrasts under MTP (Ch. 20–23) |
| Positivity / support atlas | positivity_report |
Overlap diagnostics before interpreting TE curves |
| Omitted-confounder sensitivity | sensitivity_report, tipping_point_bias |
Partial-\(R^2\) / tipping-point diagnostics (Ch. 17, 29) |
| Multi-time sequential MTP | SequentialPolicy, run_sequential_lmtp |
Recursive LMTP-style regression (Ch. 23) |
35.6.1 Book–package map
| Book chapter | Biological narrative | Package surface |
|---|---|---|
| Causal discovery (Ch. 05b) | Observational cohort + immune–parasite lags | Associations.jl infer_pc_graph / infer_oce_temporal_spec → prepare_from_discovery; sensitivity via CausalTargeted |
| Ch. 28 confounded CDM | Host immunity under confounded treatment | DiscreteTimeCDM, typed do_sequence / policy, g_computation, simulate, counterfactual; TemporalDAGSpec / TemporalEffectQuery for ID |
| Ch. 28b case studies | GRN, transmission, MIRS transport | Full CDM pipeline + discovery bridge; small-\(n\) MTP stack for conservation-scale cohorts |
| Ch. 20 TMLE | ATE of treatment on worm burden | TMLE.jl + confounded_cohort_dgp; Continuous MTP / mediation → CausalTargeted (run_mediation_grid) |
| Ch. 23 policy evaluation | Continuous exposure shifts | recommend_run_options → lean run_lmtp_grid; opt-in RICH_SL_LEARNERS + positivity |
| Ch. 29 reporting | Reviewer-proof causal claims | Certificates, positivity, MC stability, Cinelli–Hazlett-style sensitivity |
| Structural ID (Ch. 3–7) | Toy pedagogical graphs | identify, d_separated, backdoor_adjustment_set, dagplot_adjustment, GraphSCM, do_intervention |
| Ch. 28 UDE / SciML bridge | , | CausalDynamics ContinuousCDMSpec / solve_cdm (OrdinaryDiffEq ext); UDE training in app env (package recipe) |
| Ch. 30 software patterns | , | CausalDynamics + CausalTargeted + DAGMakie layout; small-\(n\) checklist; optional MLJ / SciML extensions |
35.7 Table 5: Methods for Each Level of Reason
35.7.1 Level 1: Association (Seeing)
| Method | Stratum | Purpose |
|---|---|---|
| Conditional forecasting | Observable | Predict future given past observations |
| Filtering | Observable | Infer current structural state from observations |
| Smoothing | Observable | Infer past structural states from all observations |
| Correlation analysis | Observable | Find associations in observed data |
| d-separation | Structural | Graph-theoretic conditional independence |
| Model criticism | Observable | Validate structural model fit using observable data |
35.7.2 Level 2: Intervention (Doing)
| Method | Stratum | Purpose |
|---|---|---|
| Do-calculus | Structural | Rules for computing interventional distributions |
| Interventional forecasting | Observable | Forecast under interventions |
| G-methods | Observable | Handle time-varying confounding |
| TMLE | Observable | Robust causal effect estimation |
| LMTP / continuous MTP | Observable | Feasible shifts of continuous exposures (Díaz et al. 2023) |
| Interventional mediation | Observable | Path-specific effects under MTP (Díaz and Hejazi 2020; Liu et al. 2024) |
| Policy evaluation | Observable | Evaluate treatment strategies |
| Structural interventions | Structural | Concept of modifying mechanisms |
35.7.3 Level 3: Counterfactual (Imagining)
| Method | Stratum | Purpose |
|---|---|---|
| Counterfactual simulation | Observable | Unit-level alternative outcomes |
| Shared exogenous noise | Structural | Creative advance \(\mathbf{u}\); identifies one organism |
| Alternative concrescences | Structural | Concept of possibilities |
| Bounds | Observable | Partial identification |
| Sensitivity analysis | Observable | Test counterfactual assumptions |
35.8 Table 6: Cross-Stratum Concepts
Some concepts span multiple strata, showing how the framework unifies:
| Concept | Strata | Description |
|---|---|---|
| Edges (Prehensive Relations) | All | Fundamental unit connecting all strata |
| Attractors | All | Perfect → Invariant → Dynamic → Actualised |
| State Variables | Structural, Dynamical, Observable | \(X_t\) exists across these strata |
| Observations | Observable | \(Y_t\) manifests from inner strata |
| Interventions | Structural, Observable | \(do(\cdot)\) applies across strata |
| Exogenous Noise | All | Creative advance in all strata |
| Graph Structure | Structural, Dynamical | \(G\) constrains all strata |
| CDMs | All | Unified framework across all strata |
35.9 Table 7: Practical Workflows by Stratum and Level
35.9.1 Structural Stratum
| Workflow | Level | Steps |
|---|---|---|
| Causal Discovery | L1 | 1. Test conditional independences 2. Apply d-separation 3. Infer graph structure |
| Identification | L2 | 1. Specify estimand 2. Check identifiability 3. Apply do-calculus |
| Counterfactual Reasoning | L3 | 1. Fix creative advance \(\mathbf{u}\) (one organism) 2. Compute alternative concrescences 3. Compare outcomes |
35.9.2 Structural Stratum (continued)
| Workflow | Level | Steps |
|---|---|---|
| State Inference | L1 | 1. Filter 2. Smooth 3. Validate with PPCs |
| Interventional Inference | L2 | 1. Infer state under intervention 2. Propagate through mechanism 3. Compare to baseline |
| Counterfactual Inference | L3 | 1. Infer unit-specific noise 2. Simulate alternative mechanism 3. Compare trajectories |
35.9.3 Dynamical Stratum
| Workflow | Level | Steps |
|---|---|---|
| Dynamics Simulation | L1 | 1. Specify ODE/SDE 2. Integrate forward 3. Analyse trajectories |
| Intervention Simulation | L2 | 1. Modify mechanism 2. Integrate under intervention 3. Compare attractors |
| Counterfactual Dynamics | L3 | 1. Fix exogenous noise 2. Simulate alternative dynamics 3. Compare system evolution |
35.9.4 Observable Stratum
| Workflow | Level | Steps |
|---|---|---|
| Forecasting | L1 | 1. Fit CDM 2. Condition on history 3. Predict future |
| Policy Evaluation | L2 | 1. Identify adjustment 2. Choose MTP / policy 3. Estimate with positivity + sensitivity diagnostics |
| Counterfactual Analysis | L3 | 1. Infer unit-specific noise 2. Simulate counterfactual 3. Compare to observed |
35.10 How to Use These Tables
- Finding concepts by stratum: Use Table 1 to see which concepts belong to which stratum(s)
- Finding concepts by level: Use Table 2 to see which concepts apply at each level of Reason
- Finding methods: Use Table 3 for mathematical methods, Table 5 for methods by level
- Understanding philosophy: Use Table 4 for Whiteheadian/process philosophy concepts
- API map: Use Table 8 to map book/process terms to the Julia APIs used in examples (standard names; process reading is book-side)
- Cross-stratum connections: Use Table 6 to see how concepts span multiple strata
- Practical workflows: Use Table 7 to see step-by-step procedures
These tables complement the book’s structure by providing a cross-cutting view of how concepts relate to the three-strata ontology and three levels of Reason.