The Triptychs of Publius

Oliver Whetstone · November 2026

Abstract

This paper develops a general architectonic of science from the principle that nothing determinate is exempt from the conditions of its determination. Every determinate subject possesses conditions necessary for its identity or realization. Where a subject is composite, these conditions include the organization of its constituents. Where it possesses a function, successful operation depends upon the compatibility of its activities with the conditions of that function. Where an agent pursues an end, successful action depends upon means compatible with its realization.

These results establish a general theory of constitutive coherence applicable to natural and constructed systems. The theory brings an Aristotelian concern with form, organization, and ends into relation with modern empirical investigation of mechanisms and interactions.

Its principal contribution is methodological. Constitutive analysis supplies a common framework for identifying explanatory omissions, determining when constituent-level models are insufficient, and constructing competing empirical hypotheses. A formal theorem establishes the conditions under which a model cannot distinguish systemic outcomes because it omits relevant constitutive relations.

The theory does not replace the particular sciences or determine their empirical findings in advance. It establishes a general framework for investigating the conditions of determinate existence, organized functioning, and successful action.

Keywords: constitutive coherence; determinacy; systems theory; composition; scientific explanation; reductionism; functional calibration; Aristotle; practical reason; mēden agan

I. Introduction

The Delphic maxim mēden agan—“Nothing too much”—is ordinarily understood as practical advice against excess. Yet the maxim raises a more fundamental question: why should excess, deficiency, or improper measure matter at all?

The present argument begins with the conditions of determinate being.

To be something is to be something determinate. To be determinate is to possess conditions distinguishing what a thing is from what it is not. Whatever negates a condition necessary for a thing’s identity or realization cannot preserve that identity or realization in the relevant respect.

Nothing determinate is exempt from the conditions of its determination.

Taken alone, this principle does not constitute a new empirical theory. The originality of the present paper lies in the architectonic derived from it.[1]

Determination establishes constitutive conditions. Composition establishes organized dependence. Function establishes the conditions of successful operation. Conditional instrumentality establishes the dependence of means upon ends. Together, these results provide a general framework for investigating systems and evaluating scientific explanations.

The theory’s scope must be distinguished from the scope of its particular consequences. The foundational principle applies to every determinate subject. The organizational theorems apply to determinate composites. The functional theorems apply wherever a function is specified. The practical theorems apply wherever means are employed toward ends.

These distinctions preserve the universality of the foundation without assuming that every subject is composite, material, or purposive.

The resulting theory is both systematic and empirical in orientation. It identifies general explanatory requirements while leaving the discovery of particular conditions to the sciences.

Its historical antecedent is Aristotelian natural philosophy, which investigates beings through their matter, form, sources of change, and ends. Its modern counterpart is the empirical investigation of constituent mechanisms and their interactions. Constitutive coherence brings these approaches into a common framework: the organization and requirements of a system help determine what must be explained, while the investigation of mechanisms establishes how the relevant phenomena occur.[2]

The paper proceeds from the universal principle to composition, function, practical action, and scientific methodology. It concludes by showing how the framework can guide research across natural and constructed systems.

II. The Universal Law of Constitutive Coherence

1. Determination

To be determinate is to be something rather than something else.

A triangle has conditions constituting its geometrical identity. A chemical compound has conditions constituting its composition and structure. A function has conditions under which it is realized. A legal relation obtains under certain conditions rather than others.

These examples share a logical structure: each subject possesses conditions distinguishing its realization from its non-realization.

This establishes the foundational theorem.

Theorem 1. Universal Constitutive Coherence

1. Every determinate subject has conditions necessary for its identity or realization.
2. Negating a necessary constitutive condition is incompatible with preserving that identity or realization in the relevant respect.
3. Therefore, every determinate subject is constrained by the conditions of its determination.

Conclusion: Nothing determinate is exempt from the conditions of its determination.

The theorem applies to entities, structures, relations, activities, functions, and ends. It does not presuppose composition, finite resources, biological organization, or human purposes.[3]

2. Constitutive restriction

Let D denote a determinate subject and C_D the set of configurations compatible with its realization.

Then:

D(q) ⇒ q ∈ C_D.

A configuration incompatible with a necessary condition of D cannot realize D in the relevant respect.

Where at least one relevant possible configuration violates such a condition, the compatible domain is a proper subset of the relevant configuration space.

This establishes constitutive restriction.

It does not establish that every compatible domain is numerically bounded above and below, that every variable has a unique optimum, or that every response curve is non-monotonic.

Those conclusions require additional premises.

The universal law establishes the necessity of constitutive conditions. The particular sciences determine their content.

3. Standards of realization

Four standards must be distinguished.

Identity concerns the conditions under which a subject remains the subject it is.

Persistence concerns its continuation through time.

Viability concerns its capacity to continue existing or operating under specified conditions.

Function concerns the successful realization of a specified activity or capacity.

These standards may overlap without being identical.

A damaged bridge may remain a bridge while becoming unsafe. An organism may remain alive while losing a physiological function. An institution may continue to exist while failing to accomplish its purposes.

Every inquiry must therefore specify the relevant standard of realization.

The same subject may have different constitutive conditions under different standards.

III. Composition and Organization

4. Composite systems

A composite is a whole constituted by distinguishable parts standing in determinate relations.

An organism is not merely a collection of cells. A building is not merely a collection of materials. An institution is not merely a collection of individuals.

In each case, the organization matters.

The existence of the constituents alone is insufficient to establish the existence of the organized whole.

Theorem 2. Constitutive Dependence of Composites

1. A determinate composite depends upon certain constituents and relations.
2. Eliminating a necessary constituent or relation, without an identity-preserving substitute, negates a condition of the composite.
3. Therefore, the composite cannot remain constituted in the relevant respect under that negation.

Conclusion: Every determinate composite is governed by the conditions of its organization.

The theorem applies to natural and constructed systems alike.

The relevant relations may be chemical, physiological, mechanical, informational, institutional, or otherwise. Their differences do not alter the necessity of satisfying them.[4]

5. Constitutive bounds

Composition yields a more specific result concerning deficiency and excess.

Suppose a genuinely plural whole requires at least two distinct constituents, each occupying a positive share under an additive measure.

A necessary constituent cannot occupy none of the whole. Nor can it occupy the entire whole while excluding every other necessary constituent.

Thus, for the proportional share p of such a constituent:

0 < p < 1.

This is the theorem of proportional constitutive bounds.

Where multiple necessary functions require positive allocations from a finite resource, stronger absolute bounds may follow.

An allocation must satisfy its own necessary requirements without excluding resources necessary for the others.

These results establish limits without establishing a numerical midpoint or unique optimum.[5]

6. Recursive constitution

Composite systems frequently contain subordinate composites.

Organisms contain organs, tissues, and cells. Machines contain subsystems. Institutions contain offices and departments.

Each subordinate subject is itself determinate and possesses constitutive conditions.

The relations among these subjects are likewise determinate.

Theorem 3. Recursive Constitutive Coherence

The constitutive principle applies to every determinate constituent of a system and to every determinate relation among its constituents.

Consequently, constitutive coherence applies at every level at which a determinate subject can be identified.

The recursion is methodological rather than an assertion of infinite divisibility. Inquiry proceeds as far as real distinctions and available evidence warrant.[6]

IV. Function and the Constitutive Priority of the Whole

7. Local and systemic functioning

A constituent may operate successfully in isolation while impairing the system of which it forms a part.

A mechanical component may operate at maximum output while overloading another component. A physiological process may become more active while disrupting organismal regulation. A department may increase its productivity while undermining institutional performance.

The explanation is straightforward: successful functioning of the whole depends upon the compatibility of constituent activities.

Theorem 4. Constitutive Priority of the Whole

1. A constituent’s contribution to an organized whole depends upon the requirements of that whole.
2. Those requirements include relations among its constituents.
3. Local activity may vary independently of the successful realization of those relations.
4. Therefore, local functional success does not by itself establish systemic functional success.

Conclusion: The functional measure of a constituent qua constituent is determined partly by the constitutive requirements of the whole.

This is the constitutive priority of the whole.

It does not imply that wholes exist independently of their constituents. Nor does it deny that constituent mechanisms can explain systemic phenomena.

It establishes that a constituent’s systemic contribution cannot always be inferred from its isolated properties.[7]

8. Formal, final, and efficient explanation

The constitutive priority of the whole clarifies the relation between Aristotelian and mechanistic explanation.

Two questions must be distinguished.

First: What counts as the successful functioning of this constituent within the whole?

Second: By what mechanisms does the constituent produce its effects?

The first concerns the organization of the system and, where applicable, its end. The second concerns the processes through which the relevant activity occurs.

In Aristotelian terms, these questions engage formal and final causality on the one hand and efficient causality on the other.[8]

A heart’s contribution to an organism is understood partly through the physiological functions it serves. The mechanisms of contraction, electrical conduction, and circulation explain how that contribution is produced.

Neither explanation replaces the other.

The requirements of the whole help determine the standard of successful contribution. Constituent mechanisms explain how that contribution is produced.

The resulting framework joins systemic and mechanistic explanation without reducing one to the other.

This is not an argument against reduction. It is an argument for explanatory adequacy: a reduced model must preserve or adequately represent the relations material to the phenomenon being explained.[9]

9. Functional coherence

The converse of local-to-systemic failure is equally important: local impairment need not entail systemic failure.

A system may preserve a function through compensation, redundancy, repair, or substitution.

Accordingly, neither local success nor local failure establishes the condition of the whole without further information about its organization.

Functional coherence is the compatibility of constituent activities with the successful functioning of the organized whole.

It does not require every component to operate at maximum intensity.

It requires their activities to satisfy the conditions of the system.

V. The Constitutive Theory of Functional Calibration

10. Conditions of successful function

A determinate function depends upon conditions necessary for its realization.

Where a positive input is necessary, complete deprivation prevents the function from being realized.

Where an input exceeds finite capacities or displaces other necessary requirements, its excess may likewise prevent successful operation.

This yields a conditional theorem.

Theorem 5. Constitutive Functional Calibration

1. A determinate function depends upon conditions necessary for its realization.
2. Where a positive input is necessary, its absence negates a condition of the function.
3. Where unrestricted increase of that input violates finite capacities or competing requirements, such increase negates conditions of the function.
4. Therefore, where both conditions obtain, successful functioning is constrained by deficiency and excess.

Conclusion: Functional systems subject to necessary positive inputs and finite or competing capacities possess constitutively restricted domains of successful operation.

The theorem establishes neither a unique optimum nor a universal inverted-U response.

It establishes the necessity of conditions appropriate to successful functioning.

11. Proper measure

The conditions of successful realization concern more than quantity.

An intervention may be appropriate in amount but inappropriate in timing. An action may employ the correct instrument but direct it toward the wrong object. A component may possess the correct capacity but interact incompatibly with another necessary component.

Proper measure therefore extends across quantity, timing, duration, order, relation, location, and manner.

Excess and deficiency are familiar quantitative forms of a more general phenomenon: departure from the conditions of realization.

The Delphic maxim mēden agan is thus not reducible to the recommendation that one always choose an intermediate amount.

It expresses the requirement that determinate activity remain compatible with the conditions of its successful realization.[10]

VI. Conditional Instrumentality and Practical Action

12. Means and ends

A means is instrumental relative to an end.

Its value as a means depends upon its contribution to that end. Accordingly, the successful use of means depends upon the conditions necessary for realizing the objective.

Theorem 6. Conditional Instrumentality

1. A means is instrumental relative to a determinate end.
2. Realizing that end requires satisfying its necessary conditions.
3. A means that negates a necessary condition of the end cannot realize that end in the relevant respect.
4. Therefore, successful instrumentality is constrained by the constitutive conditions of the end.

Conclusion: No end can be successfully realized through means that negate the conditions necessary for its realization.

The theorem applies to any conditional instrumentality: medicine, engineering, education, strategy, economics, law, and personal action.

It establishes the conditions of effective action, not the moral worth of the end pursued.

13. Contingent powers

Finite agents exercise their capacities under circumstances they do not wholly control.

Resources may be unavailable. Conditions may change. Other activities may impose competing requirements. Opportunities may arise and disappear.

Consequently, the effectiveness of a means depends upon the circumstances in which it is employed.

A capacity that succeeds under one configuration need not succeed under another.

Practical judgment therefore concerns not merely the possession of means but their appropriate application in relation to an end, a subject, and an occasion.

This is the significance of kairos: action at the fitting time and under fitting circumstances.

VII. The Architectonic of Science

14. Theoretical science

Every theoretical science investigates determinate subjects and their conditions.

Physics investigates physical phenomena. Chemistry investigates substances and reactions. Biology investigates living systems. Economics investigates economic relations and institutions. Legal theory investigates legal validity, authority, and rules.

The subjects and methods differ, but each inquiry asks what its object is and under what conditions the relevant phenomena obtain.

What is this subject, and what conditions govern its identity, persistence, or realization?

The constitutive principle does not supply the answers. It explains why these questions are necessary.

15. Practical science

Practical sciences investigate the realization of ends through means.

Medicine seeks to preserve or restore health. Engineering seeks to construct functioning systems. Education seeks to develop capacities. Strategy seeks to achieve objectives through available resources.

Which means can realize the intended end under the conditions that obtain?

Practical science therefore presupposes theoretical knowledge while introducing the further problem of action.

16. Wisdom

Practical life involves multiple ends.

These ends may share resources, depend upon one another, or conflict. The successful pursuit of one end does not guarantee the successful organization of the whole.

Wisdom concerns the justified ordering of ends and activities within a life or other practical whole.

The architectonic therefore has three levels:

1. Theoretical science: What are the conditions of determinate subjects?
2. Practical science: Which means realize determinate ends under those conditions?
3. Wisdom: How should multiple ends be ordered within a finite whole?

Each level presupposes the preceding one and adds a further object of inquiry.

The architectonic is also recursive. Every determinate subdivision of a science remains subject to constitutive coherence, as do the relations among those subdivisions.

The resulting framework is both universal and differentiated: one principle governs the inquiry, while each science supplies its particular content.[11]

VIII. The Limits of Reductionist Explanation

17. Reduction and explanatory adequacy

Reductionist methods are indispensable to science.

A complex system may be investigated by isolating its components, identifying mechanisms, and studying their interactions.

Such methods become inadequate when the resulting explanation neglects conditions necessary for the phenomenon it claims to explain.

The relevant distinction is therefore not between reduction and holism, but between adequate and inadequate representation of constitutive organization.

This position is compatible with mechanistic explanation, which already recognizes the importance of organized entities and activities.[12]

18. Constituent-level model insufficiency

The constitutive priority of the whole yields a precise methodological result.

Theorem 7. Constituent-Level Model Insufficiency

1. A systemic outcome depends upon constituent behavior and certain relations among constituents.
2. A model represents the constituent behavior but omits one or more of those relations.
3. The omitted relations can vary while the model’s represented variables remain fixed.
4. Such variation changes the systemic outcome.
5. Therefore, the model assigns the same prediction to configurations that produce different outcomes.

Conclusion: A model is insufficient to distinguish systemic outcomes whenever omitted constitutive relations materially affect those outcomes while remaining unrepresented and unconstrained by the model.

The theorem identifies a specific limit of constituent-level explanation.

It does not imply that all reduced models are inadequate. A model may incorporate the relevant relations, represent their effects through effective parameters, or legitimately hold them constant within its domain.

The theorem establishes the conditions under which an isolated model cannot preserve its predictions when applied to an organized whole.[13]

19. Five predictable explanatory failures

Five recurrent failures follow.

First, neglect of constitutive relations. A model describes constituents while omitting relations necessary for the phenomenon.

Second, local-to-systemic inference. A model assumes that improvement in a constituent entails improvement in the whole.

Third, unrestricted extrapolation. A relationship established under specified conditions is extended beyond the domain in which those conditions remain satisfied.

Fourth, neglect of regulation and compensation. A model isolates a disturbance while omitting feedback, repair, substitution, or adaptation that materially alters the outcome.

Fifth, confusion of means and ends. A model treats the maximization of an instrumental variable as equivalent to the realization of the objective it serves.

These failures share a common structure: a partial relationship is treated as sufficient for an outcome whose realization depends upon additional conditions.

An explanation is inadequate insofar as it omits constitutive conditions necessary for the phenomenon and material to the explanatory claim.

This does not require every scientific model to represent every detail.

It requires that omitted conditions be irrelevant, adequately represented, or legitimately held constant.

IX. Constitutive Coherence as a Method of Scientific Discovery

20. Identifying omitted conditions

The central methodological contribution of constitutive coherence is a systematic way to identify conditions that an explanatory model may have omitted.

The inquiry begins with the phenomenon to be explained.

The investigator identifies the system and specifies the relevant standard of realization: identity, persistence, viability, or function.

Next, the investigator identifies the constituents and relations necessary for the phenomenon, insofar as they can be established.

The explanatory model is then examined to determine which of these conditions are represented, which are held constant, and which are omitted.

An omitted condition becomes a candidate for further investigation when its variation could alter the outcome without a corresponding change in the variables represented by the model.

The method thus proceeds from the requirements of the whole to the identification of explanatory omissions.

It reverses the order of an exclusively constituent-first inquiry without rejecting constituent-level explanation.

The system’s constitutive requirements guide the search for mechanisms and interactions that may otherwise have been overlooked.[14]

21. Constructing competing hypotheses

The same method generates empirical hypotheses.

Suppose an existing model predicts an outcome Y from represented variables X:

H₀: Y = f(X).

Constitutive analysis identifies a further relation R that may affect the outcome.

The investigator formulates a competing hypothesis:

H₁: Y = g(X, R).

The hypotheses may then be compared by examining configurations in which X remains fixed while R varies, where such variation is experimentally or observationally possible.

If the outcome changes in a way the original model cannot predict, the expanded model may identify an explanatory dependence omitted by the original.

The procedure does not assume that every proposed relation matters.

Nor does it assume that a model becomes more accurate merely by including more variables.

The proposed relation must improve explanation or prediction under appropriate validation.[15]

22. The method of constitutive inquiry

The resulting procedure is general:

1. Identify the determinate subject and phenomenon.
2. Specify the relevant standard of realization.
3. Identify candidate constitutive conditions.
4. Where the subject is composite, identify its constituents and relations.
5. Determine which conditions the existing model represents.
6. Identify omitted conditions capable of changing the outcome.
7. Construct competing hypotheses that differ in their treatment of those conditions.
8. Test the hypotheses under conditions capable of distinguishing them.
9. Retain, revise, or reject the proposed dependence in light of the evidence.

This procedure turns constitutive coherence into a research program.

The universal law supplies the organizing principle. The particular sciences supply the mechanisms, measurements, and evidence.

X. Applications to the Particular Sciences

23. Biology

Living organisms are organized systems that maintain many of their own constitutive conditions.

Metabolism, repair, regulation, and adaptation contribute to this maintenance. These processes are themselves determinate functions dependent upon appropriate conditions.

Biological organization is recursive: molecular processes contribute to cellular functions, cells to tissues, tissues to organs, and organs to organismal viability.

Yet local biological activity is not equivalent to organismal benefit.

A cellular response may protect one process while imposing costs on another. A physiological mechanism may preserve systemic function through compensation despite local impairment.

Constitutive coherence therefore directs biological inquiry toward the relations among molecular, cellular, physiological, and organismal conditions.

24. Medicine

Medicine concerns the preservation, restoration, or improvement of biological functions.

Medical interventions act upon organized systems whose responses depend upon exposure, physiological state, regulatory mechanisms, and competing functional requirements.

The theory of functional calibration provides a general framework for investigating these responses.

Where a biological function requires a positive input, deprivation may impair it. Where excessive input disrupts necessary relations or exceeds regulatory capacities, excess may likewise impair it.

Where repair and adaptation materially alter the response to exposure, the resulting dose-response relationship may exhibit thresholds, plateaus, discontinuities, or non-monotonicity.

These possibilities do not establish that every stressor has a beneficial low-dose range.

The universal principle establishes constitutive dependence. The presence and location of thresholds, beneficial ranges, and adaptive responses remain empirical questions.

This distinction is especially important in evaluating linear no-threshold models.

A relationship observed at the molecular level cannot automatically be treated as a complete description of cellular, tissue, or organismal outcomes. Nor can a relationship established within one exposure range automatically be extended beyond its conditions of validity.

The linear no-threshold model used in radiation risk assessment may be justified for specified endpoints and exposure ranges. Constitutive coherence does not independently establish its falsity. It requires that extrapolation be evaluated against the relevant mechanisms, endpoints, and evidence.[16]

The resulting program of Delphic Medicine is the systematic investigation of the constitutive conditions under which biological functions are maintained, improved, impaired, or destroyed.

25. Protein biophysics

A protein’s activity depends upon its structure, conformational dynamics, chemical environment, and molecular interactions.

The same protein may behave differently when isolated, incorporated into a complex, or situated within a living cell.

The constitutive framework therefore directs attention to the conditions under which molecular activity contributes to cellular and organismal function.

It distinguishes structural integrity, local biochemical activity, and contribution to a larger functional system.

These are related but distinct explanatory standards.

The method suggests a research procedure: identify a molecular function, determine its necessary structural and environmental conditions, examine how those conditions change upon incorporation into a larger system, and test whether models based upon isolated behavior remain adequate.

26. Engineering

Engineered systems depend upon the compatibility of components with the requirements of the assembled whole.

A component may perform successfully within its own operating range while imposing loads, demands, or disturbances incompatible with other necessary components.

Consequently, maximizing component performance need not maximize systemic performance.

Constitutive coherence provides a framework for identifying operating conditions, resource constraints, interactions, and modes of failure.

Its practical value lies in directing attention to the conditions under which individually functioning components constitute a successfully functioning system.

27. Economics

Economic systems contain interacting agents, institutions, resources, and incentives.

A relationship established for an isolated agent or process may change when embedded in a larger organization.

Likewise, maximizing one economic indicator need not establish successful functioning under a broader set of objectives.

The constitutive method therefore requires investigators to identify the relevant standards, institutional conditions, and interactions before transferring local conclusions to systemic outcomes.

The relevant relationships remain matters for economic theory and empirical investigation.

28. Law and institutions

Legal institutions depend upon rules, procedures, offices, and relations of authority.

Their formal validity, operational effectiveness, and normative legitimacy are distinct standards.

An institution may satisfy its formal conditions while failing to accomplish its practical purposes. A reform may improve one institutional function while weakening another.

Constitutive coherence supplies a framework for examining institutional identity, continuity, and operation.

It does not independently establish which laws or institutions are just. That question requires additional normative premises.

29. Strategy

Strategy concerns the realization of objectives through finite means under changing circumstances.

The value of an instrument depends upon its contribution to the objective and its compatibility with other necessary conditions.

Overextension, mistiming, incompatible objectives, and resource misallocation may defeat a strategy even where individual actions succeed.

Strategic success therefore requires the coordination of subordinate activities in relation to the whole.

XI. Conclusion

The universal principle of constitutive coherence is simple: nothing determinate is exempt from the conditions of its determination.

The contribution of the present theory lies in the architectonic derived from that principle.

Determination establishes constitutive conditions. Composition establishes organized dependence. Function establishes the conditions of successful operation. Conditional instrumentality establishes the dependence of means upon ends.

These results apply across theoretical and practical inquiry.

They also provide a general method for scientific explanation. By identifying the conditions necessary for a system’s realization, investigators can determine which relations an existing model may have omitted, construct competing hypotheses, and test whether those omissions materially affect the outcome.

The theory thus joins an Aristotelian concern with form, organization, and ends to the empirical investigation of mechanisms characteristic of modern science.

It does not replace specialized scientific methods. It supplies an architectonic within which their explanations can be organized, compared, and tested for constitutive adequacy.

The resulting claim is universal in foundation and conditional in application.

Every determinate subject is governed by the conditions of its determination. Every determinate composite is governed by the conditions of its organization. Every determinate function depends upon conditions of successful realization. Every practical end constrains the means by which it can be achieved.

The particular sciences determine what these conditions are.

The general theory establishes why they matter and how their investigation can be made systematic.

The argument may be summarized in four propositions:

Universal principle: Nothing determinate is exempt from the conditions of its determination.

Systemic consequence: No organized whole can be adequately understood independently of the conditions of its organization.

Functional consequence: No determinate function can be realized through the negation of its necessary conditions.

Practical consequence: No end can be successfully realized through means that negate the conditions necessary for its realization.

Together, these propositions establish constitutive coherence as a general principle of determinate being, organized systems, scientific explanation, and practical action.

The Delphic maxim mēden agan thus expresses more than a preference for moderation. It points toward the conditions of successful realization: every determinate thing, function, and end must be understood through the conditions that make its realization possible.

Notes

1. Originality and scope. The claim of originality concerns the derived architectonic, not the proposition that necessary conditions are necessary. The contribution is the systematic connection of determinate identity, organized composition, functional dependence, conditional instrumentality, and explanatory adequacy. The foundational law applies to determinate subjects generally; the systems-theoretic consequences require composition, and the functional consequences require a specified function. See Whetstone (2026a, 2026b).
2. Aristotelian natural philosophy and modern science. Aristotle’s fourfold explanatory scheme appears in Physics II.3, 194b16–195a26, and Metaphysics V.2. Physics II.7, 198a21–b9, treats different explanatory questions as complementary. The comparison with modern systems science is a philosophical reconstruction, not a claim that Aristotle possessed contemporary empirical systems theory. Compare Simon (1962), Bechtel and Richardson (1993), and Mitchell (2009).
3. The status of the universal principle. Constitutive coherence is a metaphysical constraint, not an empirical equation specifying the behavior of every system. Its substantive applications require additional premises concerning composition, capacities, relations, or functions. It therefore generates conditional consequences and research questions rather than a single quantitative law applicable to all systems.
4. Mechanisms and organization. Machamer, Darden, and Craver (2000) characterize mechanisms through organized entities and activities. Bechtel and Richardson (1993) investigate decomposition and localization as scientific strategies. The present theory does not claim to discover the importance of organization; it seeks to derive its explanatory relevance within a broader constitutive framework.
5. Proportional bounds. The result 0 < p < 1 presupposes an additive measure and at least two necessary constituents with positive shares. It does not apply indiscriminately to every property or relation. Stronger absolute bounds require additional premises, such as finite resources and positive minimum allocations. See Whetstone (2026a).
6. Recursive organization. Simon (1962) develops an influential account of hierarchy and near-decomposability. Recursive constitutive coherence does not require near-decomposability. It applies wherever determinate constituents and relations can be identified, including systems whose interactions resist simple decomposition.
7. The priority of the whole. The priority claimed is explanatory and relative to a constituent’s systemic role, not an assertion that the whole exists independently of its parts. Constituent mechanisms may explain how systemic contributions are produced. Compare Craver (2007) and Mitchell (2009).
8. Formal, final, and efficient causes. Aristotle distinguishes the form of a thing, its source of change, and that for the sake of which it acts or exists, where final explanation is applicable. Constitutive organization is not simply identical with final causality. The present account connects these explanatory roles without reducing them to one another. See Physics II.3 and II.7.
9. Compatibility with mechanistic explanation. The present theory should not be understood as a rejection of reduction or mechanistic analysis. Its claim is that explanations must adequately represent the conditions material to their objects. Compare Machamer, Darden, and Craver (2000), Craver (2007), and Bechtel and Richardson (1993).
10. The Delphic maxim and Aristotle’s mean. Aristotle distinguishes the arithmetic mean from the mean relative to us in Nicomachean Ethics II.6, 1106a26–1106b7, and emphasizes the importance of occasion, object, purpose, and manner at 1106b18–24. The present theory extends the concern with appropriate measure beyond ethical action without attributing universal inverted-U response curves to Aristotle.
11. The architectonic. Aristotle discusses the ordering of subordinate arts and ends in Nicomachean Ethics I.2, 1094a26–b7. The present argument generalizes architectonic organization to theoretical science, practical science, and wisdom. Compare Marr (1982) on distinct explanatory levels and Mitchell (2009) on integrative pluralism.
12. Reduction and organization. Existing mechanistic philosophy already recognizes the explanatory significance of organization. The present theory’s proposed contribution is the derivation of a common framework for identifying constitutive requirements and assessing explanations across disciplines. See Machamer, Darden, and Craver (2000); Bechtel and Richardson (1993); Craver (2007).
13. Model insufficiency. Theorem 7 is a conditional result concerning the inability of a model to distinguish outcomes dependent upon omitted variables. Its logical structure is related to established issues of model specification, abstraction, and explanatory completeness. Its role here is to connect these issues to a general constitutive method. No claim is made that the logical form of the result is independently unprecedented.
14. Constitutive guidance and empirical discovery. Constitutive analysis may identify candidate explanatory requirements without establishing that a particular empirical relation is necessary. Such claims must be investigated and may be rejected or revised. This distinction preserves the role of empirical science. Compare Bechtel and Richardson (1993) and Craver (2007).
15. Competing hypotheses. The contrast between H0 and H1 is schematic. An expanded model may fit existing observations better without improving prediction. Appropriate evaluation requires experimental design, validation, and consideration of alternative explanations. The contribution lies in the principled generation of candidate relations, not the assumption that adding variables necessarily improves a model.
16. Linear no-threshold models. The National Research Council’s BEIR VII Phase 2 (2006) supports the linear no-threshold model for estimating low-dose radiation-related cancer risk. The present paper does not dispute that conclusion by deduction. It identifies conditions under which extrapolation across levels, endpoints, or exposure ranges requires additional justification.
17. Teleology and systems. Not every organized system possesses an intrinsic purpose. Constitutive coherence applies to composites independently of teleology. Final-causal explanation becomes appropriate where a function or end has been identified and justified. This distinction is especially important when moving among organisms, artifacts, and institutions.
18. Constitutive limits and empirical response curves. The universal law establishes constitutive restriction. Two-sided quantitative bounds require additional premises, including necessary positive inputs, finite capacities, or competing requirements. Neither the universal principle nor these premises establishes universal hormesis, a unique optimum, or a particular response curve. See Whetstone (2026a).

References

Aristotle. Metaphysics. Especially V.2 and VII–IX.

Aristotle. Nicomachean Ethics. Especially I.2, II.6, and VI.

Aristotle. Physics. Especially II.3 and II.7.

Bechtel, William, and Robert C. Richardson. 1993. Discovering Complexity: Decomposition and Localization as Strategies in Scientific Research. Princeton, NJ: Princeton University Press.

Craver, Carl F. 2007. Explaining the Brain: Mechanisms and the Mosaic Unity of Neuroscience. Oxford: Oxford University Press. https://doi.org/10.1093/acprof:oso/9780199299317.001.0001.

Kauffman, Stuart A. 1993. The Origins of Order: Self-Organization and Selection in Evolution. New York: Oxford University Press.

Machamer, Peter, Lindley Darden, and Carl F. Craver. 2000. “Thinking about Mechanisms.” Philosophy of Science 67 (1): 1–25. https://doi.org/10.1086/392759.

Marr, David. 1982. Vision: A Computational Investigation into the Human Representation and Processing of Visual Information. San Francisco: W. H. Freeman.

Mitchell, Sandra D. 2009. Unsimple Truths: Science, Complexity, and Policy. Chicago: University of Chicago Press. https://doi.org/10.7208/chicago/9780226532653.001.0001.

National Research Council. 2006. Health Risks from Exposure to Low Levels of Ionizing Radiation: BEIR VII Phase 2. Washington, DC: National Academies Press. https://doi.org/10.17226/11340.

Simon, Herbert A. 1962. “The Architecture of Complexity.” Proceedings of the American Philosophical Society 106 (6): 467–482.

Whetstone, Oliver. 2026a. Nothing Too Much: Determination, Constitutive Limits, and the Foundations of Proper Measure. Unpublished manuscript.

Whetstone, Oliver. 2026b. Nothing Too Much: An Architectonic of Determinate Being, Action, and Human Life. Unpublished manuscript.