On Explanatory Closure, Intelligibility, and the Limits of Algorithmic Rationality.

I. Explanatory Success and a Residual Question

Recent work in metaphysics, philosophy of science, and the theory of explanation has emphasized the structural parallels between causal, logical, and metaphysical explanation. In each domain, explanation appears to involve a tripartite structure: an explanans (that which explains), an explanandum (that which must be explained), and a principled relation that connects them. Causes explain effects by standing in law-governed relations; axioms explain theorems by inferential rules; fundamental facts explain derivative facts by relations of metaphysical dependence.

This structural alignment is not accidental, but reflects a broader aspiration toward explanatory closure: the ideal that, once the relevant principles are specified, what follows is fixed. Explanation, on this picture, consists in situating a phenomenon within a framework whose internal relations determine its place. The better the framework, the less residue remains.

There is much to recommend this ideal. It captures the power of formalization, the success of scientific modeling, and the clarity afforded by explicit inferential structures. It also motivates the widespread hope that explanation can, in principle, be rendered algorithmic: given sufficient information about initial conditions and governing principles, outcomes should be derivable.

And yet, explanatory practice itself resists this aspiration in subtle but persistent ways. Even in domains where formal rigor is maximal, explanation does not terminate merely in derivation. Judgments of relevance, adequacy, scope, and success continue to operate, often tacitly, at precisely those points where explanation appears most complete.

The question to be pursued in what follows is therefore not whether explanation works—it manifestly does—but whether explanatory success exhausts the conditions under which explanation is recognized as success. What remains operative, even where explanation appears closed?

II. Dependence Relations and the Temptation of Functionalism

The appeal of tripartite explanatory models lies in their promise of determinacy. Once the intermediary relation is fixed—causal law, inference rule, metaphysical dependence—the explanandum appears as a function of the explanans. To explain is to map inputs to outputs under stable rules.

This functional picture has been especially influential in recent metaphysics. If derivative facts depend on more fundamental facts in accordance with metaphysical principles, then explanation seems to consist in exhibiting a function from the fundamental to the derivative. Once the base facts and principles are in place, the result follows.

However compelling this picture may be, it quietly imports a further assumption: that the adequacy of the explanatory mapping is itself secured by the same principles that generate it. In other words, it assumes that once the function is specified, there is nothing left to assess.

But this assumption is false to explanatory practice.

Even in logic, where inferential rules are explicit, the correctness of a derivation does not by itself settle whether the axioms are appropriate, whether the system captures the intended domain, or whether the conclusion answers the question posed. Similarly, in metaphysics, identifying a dependence relation does not determine whether it is explanatory rather than merely formal, illuminating rather than trivial, or relevant rather than artificial.

The functional picture thus explains too much too quickly. It conflates derivability with explanatory satisfaction. The former can be fixed by rule; the latter cannot.

This gap is not accidental. It reflects a structural feature of explanation itself.

III. Explanatory Adequacy and the Irreducibility of Judgment

Consider the role of judgment in explanatory contexts that are otherwise maximally formal. In logic, the selection of axioms, the interpretation of symbols, and the identification of an intended model are not dictated by the formal system itself. In science, empirical adequacy underdetermines theory choice; multiple frameworks may fit the data equally well while differing in unification, simplicity, or fruitfulness. In metaphysics, competing accounts of grounding may be extensionally equivalent while differing profoundly in explanatory character.

In each case, explanation requires decisions that are not compelled by the formal machinery. These decisions are not arbitrary, nor are they merely psychological. They are normative: they concern what counts as explaining rather than merely deriving.

Crucially, these judgments are not external add-ons to explanation. They are conditions under which explanatory relations can function as explanations at all. A mapping from explanans to explanandum becomes explanatory only insofar as it is situated within a space of assessment in which relevance, adequacy, and success can be meaningfully evaluated.

Attempts to eliminate this space by further formalization merely reproduce it at a higher level. Meta-rules governing relevance or adequacy would themselves require criteria for correct application. The regress does not terminate in a final algorithm. What persists is the necessity of judgment.

This necessity should not be misunderstood. It does not signal a failure of rationality, nor an intrusion of subjectivity. Rather, it reveals that rational explanation presupposes a non-algorithmic space within which determinate relations can be taken as intelligible, appropriate, or successful.

Explanation, in short, presupposes intelligibility. And intelligibility is not itself a function of the explanatory relations it makes possible.

IV. Theory Choice, Model Adequacy, and the Limits of Formal Closure

The persistence of judgment becomes especially visible in contexts of theory choice and model adequacy, where formal success does not settle explanatory priority. In such cases, multiple frameworks may satisfy all explicitly stated constraints while nevertheless differing in their capacity to illuminate, unify, or orient inquiry. The choice among them is not determined by additional derivations, but by evaluative considerations that are internal to rational practice yet irreducible to rule.

This phenomenon is familiar across domains. In logic, distinct formal systems may validate the same set of theorems while differing in expressive resources or inferential economy. In the philosophy of science, empirically equivalent theories may diverge in their explanatory virtues—simplicity, coherence, depth, or integration with neighboring domains. In metaphysics, competing accounts of dependence or fundamentality may agree extensionally while offering incompatible explanatory narratives.

What is striking in these cases is not disagreement as such, but the form disagreement takes. The dispute is not over whether a rule has been followed correctly, nor over whether a derivation is valid. It concerns whether a framework makes sense of the phenomena in the right way—whether it captures what is explanatorily salient rather than merely formally sufficient.

No finite list of criteria resolves such disputes without remainder. Attempts to formalize explanatory virtues inevitably encounter the same problem they seek to solve: the application of the criteria themselves requires judgment. To ask whether a model is sufficiently unified, sufficiently simple, or sufficiently illuminating is already to presuppose a background sense of what counts as unity, simplicity, or illumination here rather than there.

This does not imply that theory choice is subjective, conventional, or arbitrary. On the contrary, the judgments involved are responsive to real features of the domain under investigation. But responsiveness is not compulsion. The domain constrains judgment without dictating it. Explanatory rationality thus occupies a space between determination and indifference—a space in which reasons can be given, criticized, refined, and sometimes revised, without being reduced to algorithmic selection.

The significance of this point is often underestimated because it emerges most clearly at moments of philosophical maturity rather than at the level of elementary practice. When a framework is first introduced, its power lies in what it enables. Only later, once its success is established, does the question arise of how that success is to be assessed, limited, or compared with alternatives. At that stage, explanation turns reflexive: it must account not only for its objects, but for its own adequacy as explanation.

What becomes apparent in such moments is that explanatory closure is never purely internal to a system. Even the most formally complete framework remains dependent on a space of evaluation in which its claims can be judged relevant, sufficient, or illuminating. This space is not itself a further theory competing with others. It is the condition under which theories can compete meaningfully at all.

The persistence of this evaluative dimension should not be regarded as a temporary limitation awaiting technical resolution. It is a structural feature of rational inquiry. Explanation advances not by eliminating judgment, but by presupposing it—quietly, continuously, and indispensably.

V. Articulation, Revision, and a Limit Case for Algorithmic Explanation

The limits identified above become especially clear when we consider not the objects of explanation, but the activity of explanation itself: the practices of articulation, revision, and defense through which theoretical frameworks are proposed and sustained. These practices are not peripheral to rational inquiry. They are constitutive of it. Yet they sit uneasily within accounts that aspire to explanatory closure through algorithmic or law-governed relations alone.

Consider a familiar kind of case from the history of twentieth-century psychology and philosophy of science: a theorist committed to a thoroughly naturalistic and algorithmic account of human behavior undertakes the task of writing a systematic defense of that very account. The activity involves drafting, revising, responding to objections, anticipating misunderstandings, and adjusting formulations in light of perceived inadequacies. The goal is not merely to produce text, but to get the account right—to articulate it in a way that clarifies its scope, resolves tensions, and persuades a critical audience.

From the standpoint of the theory being defended, the behavior involved in this activity may be describable in causal or functional terms. One may cite conditioning histories, environmental stimuli, neural processes, or computational mechanisms. Such descriptions may be true as far as they go. But they do not yet explain what is explanatorily central in the context at hand: namely, why this articulation rather than another is judged preferable, why a given revision counts as an improvement rather than a mere change, or why the theorist takes certain objections to matter while setting others aside.

These judgments are not epiphenomenal to the enterprise. They are what make the activity intelligible as theorizing rather than as mere behavior. To revise a manuscript because a formulation is inadequate is to operate with a norm of adequacy that is not supplied by the causal description of the revision itself. To aim at persuasion is to treat reasons as bearing on belief, not merely as inputs producing outputs.

Importantly, the difficulty here is not that the theory fails to predict or describe the behavior in question. It may do so successfully. The difficulty is that prediction and description do not exhaust explanation in this context. What remains unexplained is how the theorist’s activity can be understood as responsive to reasons—as governed by considerations of correctness, clarity, and relevance—rather than as merely following a causal trajectory.

One might attempt to extend the theory to include meta-level explanations of these practices. But such extensions merely relocate the problem. Any account that treats theoretical articulation as the output of a function—however complex—must still presuppose criteria by which one articulation is taken to be better than another. Those criteria cannot themselves be generated by the function without circularity. They must already be in place for the function to count as explanatory rather than as merely generative.

Consider a function d that specifies the dependency relations by virtue of which a metaphysical system M is explained on the basis of more fundamental objects, properties, relations, or states of affairs F. On this view, F together with d metaphysically explains M.

The question that immediately arises concerns the status of d itself. Is d something that admits of explanation, or is it not? If d is explained, then there must be some more basic function p in virtue of which d obtains. But once this path is taken, it is difficult to see how an infinite regress is avoided, since the same question must then be raised concerning p.

Suppose, alternatively, that d is not in need of explanation—that it is primitive, incorrigible, or somehow self-evident. This move, however, is problematic. Why should a metaphysical dependency function enjoy a privileged status denied to laws of nature or other explanatory principles? One might argue that certain transformation rules in logic possess a form of self-evidence or decidability, but this cannot plausibly be extended to metaphysical dependency relations. If it could, metaphysics would collapse into a formal logical system, contrary to its actual practice.

The difficulty, then, is not that metaphysical explanation fails, but that modeling it as a function obscures the normative and non-algorithmic judgments that are required to identify, assess, and deploy dependency relations in the first place.

This point does not target any particular theory as incoherent or self-refuting. The issue is structural, not polemical. Explanatory frameworks that aspire to algorithmic completeness necessarily presuppose a space in which articulation, revision, and defense are assessed as norm-governed activities. That space is not eliminated by successful explanation; it is activated by it.

The case thus serves as a limit test. Where explanation turns reflexive—where it must account for its own articulation and adequacy—the aspiration to closure gives way to dependence on evaluative judgment. The theorist’s practice reveals what the theory itself cannot supply: the conditions under which its claims can be meaningfully proposed, criticized, and improved.

VI. Explanatory Ambition and a Structural Constraint

The preceding analysis does not challenge the legitimacy of algorithmic, causal, or formally articulated explanation. Nor does it deny the success of contemporary explanatory frameworks in their respective domains. What it challenges is a specific aspiration: the hope that explanation can be rendered fully self-sufficient—that once the relevant relations are specified, nothing further is required for explanatory adequacy.

What emerges instead is a structural constraint on explanatory ambition. Explanatory relations, however rigorous, do not determine their own adequacy as explanations. They presuppose a space in which relevance, success, and improvement can be meaningfully assessed. This space is not external to rational inquiry, nor does it compete with formal explanation. It is internal to the very practice of offering, revising, and defending explanations as such.

This conclusion should not be misunderstood as reintroducing subjectivism, voluntarism, or irrationalism. The judgments involved are constrained by the domain under investigation and answerable to reasons. But they are not compelled by rules alone. Explanation constrains judgment without exhausting it. The possibility of error, disagreement, and revision is not a defect of rational inquiry but a condition of its vitality.

Nor does this conclusion invite a regress to foundational doubt. The space of judgment at issue is not a prior theory awaiting justification. It is operative wherever explanation functions successfully. To recognize its indispensability is not to abandon explanatory rigor, but to acknowledge what rigor already presupposes.

The temptation to explanatory closure is understandable. It reflects the genuine power of formal systems and the desire to secure rationality against arbitrariness. But when closure is taken to be complete, it obscures the very practices through which explanations gain their standing. What is lost is not explanation itself, but intelligibility—understood as the condition under which explanation can count as illuminating rather than merely generative.

The upshot, then, is modest but firm. Explanation does not collapse into derivation, because rational inquiry cannot dispense with judgment. This is not a contingent limitation to be overcome by future theory, but a permanent feature of explanatory practice. Any account that neglects it risks mistaking formal success for explanatory sufficiency.

The Ontological Priority of Law and Gospel: Why Reality is Not about Being Human

Intelligibility and the Ontological Priority of Law and Gospel

Modern theology habitually begins with the self. Law and Gospel are therefore read first as modes of human experience, as the ways in which God confronts consciousness. The Law accuses, the Gospel consoles. Within this horizon they function as psychological or existential dispositions, structures of address within the drama of conscience. There is truth here, but it is only a derivative truth.

What if this familiar orientation were reversed? What if Law and Gospel were not first about how human beings experience God, but about how reality itself is rendered intelligible before God? What if they name not anthropological postures, but ontological structures? What if they belong not merely to theology’s linguistic grammar, but to the grammar of being itself?

This is the wager of the reflection that follows.

The inquiry does not begin with salvation, piety, or the psychology of faith. It begins with intelligibility itself, with the question of what must be the case for finite being to be knowable at all. If intelligibility is real and not merely projected by human cognition, then it must exhibit distinct and irreducible modes. Finite being is intelligible either as grounded in itself or as grounded in another. There is no tertium quid.

This fundamental differentiation yields the primal metaphysical distinction between necessity and contingency. What is necessary is intelligible in virtue of itself. What is contingent is intelligible only by reference to another. Yet necessity and contingency cannot stand as isolated poles. Contingency must be intelligible as received rather than arbitrary, as given rather than brute. At this juncture possibility emerges, not as a merely logical modality, but as ontological openness, the teleological space within which being can be bestowed, received, and sustained.

Intelligibility therefore exhibits a twofold structure. There is intelligibility in se, in which being is measured by what it must be in virtue of itself, and intelligibility ab alio, in which being is constituted by what it receives from another. These are not optional perspectives. They are the only two ways in which finite being can stand as intelligible at all.

At this level, what theology will later name Law and Gospel are already operative as the two basic structures of intelligibility. Law names the mode of necessity, that which is self-measured and self-grounded. Gospel names the mode of donation, that which lives from another and by gift. These are not affective states, moral descriptions, or linguistic conventions. They are ontological modalities of intelligibility itself.

To collapse one into the other is not a minor theological error. To moralize the Gospel is to convert gift into requirement. To reduce the Law to description is to evacuate necessity of its binding force. In either case, the architecture of intelligibility is destroyed.

Only on this basis can Luther’s distinction be properly understood. The polarity of Law and Gospel is not a pastoral invention, nor a merely rhetorical contrast within preaching. It is a faithful theological articulation of a metaphysical differentiation already inscribed into being itself. The Word of Law and the Word of Gospel do not merely address human consciousness in different ways. They disclose different modes of being and therefore different structures of understanding. Human beings do not generate this polarity. They find themselves always already located within it.

The priority of Law and Gospel is therefore neither chronological nor epistemic. It is ontological. They name the two fundamental ways in which finite being stands before God, either under the intelligibility of self grounded necessity, which is Law, or under the intelligibility of gifted contingency, which is Gospel.

Theology does not invent this distinction. It confesses it. For when reality is pressed for intelligibility, it yields nothing else.

Law and Gospel Are Older Than We Are

The claim is simple to state and difficult to absorb. Law and Gospel are ontological before they are experiential. They do not arise from moral reflection, religious sentiment, or linguistic convention. They are not products of human awareness. They are conditions that make awareness itself possible. They name two real and irreducible ways in which intelligibility is given.

Law names the order of intelligibility grounded in itself. It designates the mode in which what is stands under necessity, coherence, and closure. In the Law, reality is intelligible as that which must be so. This is not moralism but metaphysics. It names the structure of being that is self measured, self contained, and internally determined. In this mode, being is intelligible because it conforms to its own necessity.

Gospel, by contrast, names the order of intelligibility grounded in another. It designates the mode in which what is stands as gift, as reception, as donation. In the Gospel, reality is intelligible not as what must be, but as what is given. This too is not sentiment but ontology. It names the structure by which being receives itself from beyond itself. In this mode, what is depends upon generosity rather than necessity, upon grace rather than self-sufficiency.

Law and Gospel are therefore not two competing interpretations of a neutral world. They are not alternative descriptions imposed upon the same reality. They are the two real modes in which reality itself can stand as intelligible. One names necessity. The other names gift. One is self-grounding. The other is received.

Human beings do not invent these structures. We discover and inhabit them. We find ourselves always already located within their tension, already addressed by their grammar. To exist at all is to dwell within the polarity of Law and Gospel, to live between the closure of necessity and the openness of donation.

To say that Law and Gospel are older than we are is to recognize that they belong to the constitution of creation itself. They are woven into the fabric of reality, into the rhythm of being’s self coherence and being’s givenness. They are not doctrines imposed upon the world from without. They are the world’s own ways of standing before God, the measure of what must be and the gift of what is.

Why Speak of Intelligibility at All?

A fair question arises at this point. In speaking of Law and Gospel, why turn to intelligibility at all? Why not remain with Scripture, proclamation, or experience? Why introduce a term that sounds abstract, philosophical, perhaps remote from the concrete life of faith?

The answer is unavoidable. Theology already presupposes intelligibility. The only question is whether this presupposition will be acknowledged or left unexamined. To speak of God, to confess Christ, to distinguish Law and Gospel, to proclaim grace, to discern truth from falsehood, already assumes that reality can be understood. Theology does not create intelligibility. It depends upon it. The task is therefore not to stipulate that the world is intelligible, but to ask what must be true of reality for theology to be possible at all.

Modern thought has trained us to assume that intelligibility is something we supply. Meaning is said to arise from the subject, from cognition, language, or social practice. When meaning becomes difficult to ground, it is psychologized, reduced to experience. Or it is linguisticized, reduced to use. Or it is proceduralized, reduced to rule following. Despite their differences, these strategies share a single conviction: intelligibility is derivative of human activity.

What if this conviction were mistaken? What if intelligibility were not the product of thought, but its precondition? What if intelligibility were ontologically prior to perception, judgment, language, and will? On this account, human understanding does not generate meaning but participates in it. We do not first think and then discover a meaningful world. We awaken within a world that already gives itself as capable of being understood.

For this reason, intelligibility must be addressed as such. If it is not, it will be quietly replaced by something else, by consciousness, discourse, power, or will. When this substitution occurs, theology is forced to speak of God within a framework that God did not give.

Once intelligibility is acknowledged as real and prior, several consequences follow.

First, Law and Gospel can no longer be treated as human reactions to divine address. They are not psychological responses but ontological orders. Law names intelligibility closed upon itself and grounded in necessity. Gospel names intelligibility opened as gift and grounded in another. They are not rhetorical tools of preaching but conditions that make preaching truthful.

Second, grace can be conceived without arbitrariness. Grace is not a rupture in an otherwise self-sufficient system. It is the manifestation of how reality itself is constituted, as reception rather than possession, as givenness rather than achievement. What metaphysics names possibility, theology encounters as the work of the Spirit.

Third, truth itself must be rethought. Truth is not merely the correspondence of language to fact. It is participation in the Logos through whom being and meaning coinhere. To inquire into intelligibility is to ask after the deepest grammar of truth.

In this light, the question of intelligibility is not a speculative luxury. It is a theological responsibility. It is the refusal to allow theology to borrow its foundations from accounts of reality that cannot sustain them. The move is bold because it reverses the settled habits of modern thought. Instead of asking how human beings make sense of God, it asks about the conditions under which anything can make sense at all.

When intelligibility is once again recognized as a real feature of creation, the Lutheran distinction between Law and Gospel is freed from the confines of psychology and proclamation. It appears instead as something far more basic: a differentiation woven into the very fabric of reality itself.

Why the Modern Turn Went Wrong

Much of modern thought has operated with a single, rarely questioned assumption: if intelligibility exists, it must be grounded in the subject. Kant’s so-called "Copernican Revolution" marks the decisive articulation of this conviction. When it became untenable to anchor meaning directly in the empirical self, Kant reconstituted the self as transcendental, assigning it the task of supplying the conditions under which anything could appear as meaningful at all. The move was extraordinary in its rigor and fertility. It yielded lasting insights into cognition, judgment, freedom, and normativity. Yet it carried a cost that has only gradually become visible.

Necessity was relocated into the structures of experience itself. What must be so was no longer a feature of reality but a function of the mind’s synthesizing activity. Contingency was displaced into the realm of practical reason. Teleology was retained only in attenuated form, as purposiveness without purpose. Nature no longer possessed an end of its own. Intelligibility ceased to be something reality had and became instead a heuristic imposed upon it. Meaning survived, but only as method.

The outcome of this shift was not atheism but anthropocentrism. Reality increasingly appeared as a mirror reflecting our own operations back to us. Theology, often without realizing it, absorbed this posture. Law and Gospel were reinterpreted as expressions of conscience, existential moods, or linguistic practices. The deeper question was quietly abandoned: What must reality itself be like for Law and Gospel to be true? Once that question falls away, theology becomes commentary on experience rather than confession of what is.

Luther stands on the far side of this modern reversal. For him, the human being is not an origin but a site. The spirit is not sovereign but inhabited. His unsettling image remains decisive: the human being is like a beast that is ridden, either by God or by the devil. This is not a piece of religious psychology. It is an ontological claim about how intelligibility is borne.

To live curvatus in se ipsum is not merely to feel guilt or anxiety. It is to exist under a false grounding, to live as though intelligibility could be secured by the self. The Law exposes this condition and kills precisely because it names what is. It strips away the illusion that being can justify itself from within.

To live by the Gospel is not to adopt a new affective posture or a more hopeful interpretation of existence. It is to be re-grounded in reality itself, to exist as gift rather than possession. The Gospel does not negate the Law. It relocates intelligibility. What was falsely assumed to be self-grounded is revealed to live from another.

At this point the governing metaphysical problem comes fully into view. How can necessity and contingency both be real without collapsing into determinism on the one hand or arbitrariness on the other? The answer is possibility, understood not as unrealized potential but as the ontological openness of intelligibility itself. Possibility names the space in which contingency can be received rather than forced, and necessity can give without coercion.

What metaphysics names possibility, theology encounters as grace. Grace arises necessarily from God, who is love, yet it is received contingently by creatures. This contingency is not a defect. It is the very form divine love takes in time. The Holy Spirit is not an addition to this structure but its living enactment, the divine act by which eternal necessity becomes temporal gift. Grace is not God’s response to us. It is the continual donation of reality itself anew.

This same structure extends into the nature of truth. Theology cannot rest content with defining truth as correspondence between propositions and an already settled world. That account presupposes what it cannot explain. Christian theology confesses something deeper. The Logos gives being and meaning together. Reality is intelligible because it is spoken.

Truth, therefore, is not merely descriptive. It is participatory. We do not stand outside the world and measure it. We are drawn into the act by which reality becomes intelligible at all. Law, Gospel, grace, and truth are not late theological overlays. They belong to the primal order of creation, to the rhythm by which being is both coherent and given.

None of this requires the rejection of modern philosophy, nor does it indulge nostalgia for a pre modern certainty. Kant’s detour was illuminating. Existentialism disclosed genuine anxiety. The linguistic turn taught us to attend to the density of speech. But the time has come to recover what these movements forgot. Reality does not depend on being human. Humanity depends on reality.

Law and Gospel do not arise from within us. They name the way the world itself stands before God. Only because this is so can preaching still kill and make alive, grace still arrive as surprise, and truth still exceed the mirror of our own reflection.

This is not an argument for demolition but an invitation. It is an invitation to leave the playground of self-enclosed thought and return to the open field of reality itself. At this point one may cautiously recover Luther’s language of the Left and Right Hands of God, provided it is properly understood. Law and Gospel are not two competing principles, nor are they reconciled by a higher synthesis. They arise from a single ground of intelligibility, the teleological space in which reality stands before God. As the Left and Right Hands are united in the one God without confusion of their work, so Law and Gospel are united in their ground without collapse of their modes. The unity is ontological, not dialectical. The distinction remains irreducible. The Law still kills. The Gospel still makes alive. And precisely because their unity does not neutralize their opposition, preaching can still strike reality itself rather than merely reflect our own thought back to us.

Disputatio XXVII De Essentiis Dispositionalibus

On Dispositional Essences

Quaeritur

Quaeritur utrum necessitas legum naturae possit sufficienter explicari per essentias dispositionales ipsarum rerum, an vero talis explicatio tandem recidat in naturalem essentialismum sine fundamento ontologico, qui rursus ad participationem infiniti redigitur.

It is asked whether the necessity of natural laws can be adequately explained by the dispositional essences of things themselves, or whether such an explanation ultimately collapses into an unfounded natural essentialism that once again requires participation in the Infinite.

Thesis

Dispositional essentialism seeks to ground the laws of nature in the intrinsic powers of entities. Accordingly, each thing, by virtue of what it is, behaves as it does. Laws are thus expressions of essence, not external constraints. Yet finite essence itself requires grounding for its actuality and coordination. Therefore, the appeal to dispositional essences displaces but does not resolve the need for an infinite ground of law.

Locus Classicus

“In him we live and move and have our being.” — Acts 17:28

The early Fathers, having read Paul in light of Hellenic metaphysics, interpreted this as a declaration that all powers and movements within creation presuppose divine causality. For example, Basil of Caesarea (Hexaemeron I.5) taught that “every natural power is the gift of divine energy,” and Aquinas affirmed that “omnis operatio naturae est actus Dei in natura” (ST I.105.5). Thus, even when power is intrinsic to a creature, its being and operation participate in the act of the Creator.

Explicatio

Dispositional essentialism emerged in late twentieth-century metaphysics as a reaction against both Humean regularity and Armstrong’s relational realism. This view aims to secure necessity without appeal to external laws or transcendent governance. Philosophers such as Brian Ellis, C. B. Martin, and Stephen Mumford argued that laws do not govern things from without but that the flow from within from the very essences or natures of entities. Accordingly, an electron repels another not because a law commands it, but because repulsion belongs to its nature. The behavior is thus essential and not contingent.

In this view, every natural property is dispositional; it is defined by its powers and tendencies. To possess a charge, mass, or spin just is to manifest appropriate dispositions under suitable conditions. Laws of nature are thus derivative descriptions of the necessary behaviors of these dispositional essences. Therefore, there are no separate laws or external principles, but only powers whose exercise constitutes the order of nature.

This approach elegantly restores necessity to the finite without invoking extrinsic governance. But the question remains: Whence the unity of this system of powers? If every essence carries its own necessity, what guarantees the coherence of those necessities across the totality of the world? Why do distinct powers not conflict or dissolve into chaos? While the finite essence, to be actual, must exist and operate within a coherent totality of being, that totality cannot itself be one of the powers. Rather, it must be the condition of their coexistence and harmony.

Hence, while dispositional essentialism succeeds in moving the locus of necessity inward—from external law to internal essence—it fails to remove the need for ontological participation. While essence, in so far as it is essence, is an intelligible structure of being, powers, however intrinsic, can only be participatory modes of a deeper enabling act.

Obiectiones

Ob I. According to Ellis in 2001, the essence of each natural kind explains its behavior. Thus, no further metaphysical foundation is required, and to demand more is to mistake explanation for regression.

Ob II. Martin argued in 2008 that dispositions constitute causal grounds for their manifestations. Since power is primitive and self-explanatory, the world’s order is the network of powers acting according to their natures.

Ob III. Mumford in 2004 argued that laws are supervenient on dispositional essences, and hence add nothing ontologically to them. Thus, the finite order is self-sufficient so long as it consists of stable powers and their mutual tendencies.

Ob IV. Naturalistic Metaphysics claims that to appeal to an Infinite act is unnecessary duplication. If dispositions suffice for explanation, positing divine participation is a metaphysical surplus.

Ob V. Sometimes the theological tradition assumed that grounding the powers of things directly in the infinite may risk erasing natural causality. But the integrity of secondary causes requires that creatures possess genuine powers of their own.

Responsiones

Ad I. While essence may explain behavior, it does not explain existence. To say “the electron repels because it is its nature to repel” still leaves unasked why such a nature exists at all. Essence is formal cause and being is act. The latter cannot be derived from the former without reference to a self-sufficient act of existence.

Ad II. Power cannot be self-explanatory, for power is always power to act.The actuality of its exercise depends on a larger order within which it operates. Without a unifying act of being, powers remain mere potentialities without coherence.

Ad III. Supervenience explains correspondence but not causation. That laws supervene on essences tells us that essence and law covary, not why such correlation obtains. The dependence relation itself requires grounding.

Ad IV. Appealing to the infinite is not an additional move but a natural completion in the order of explanation.The Infinite is not another entity among the powers but the act in which all finite essences receive their actuality and unity. Without such an act, the multiplicity of powers lacks ontological coherence.

Ad V. Participation does not abolish finite agency but founds it. Creatures possess true powers because the infinite communicates actuality to them. Their independence as secondary causes is secured by the divine act that continuously sustains them in being.

Nota

Dispositional essentialism rightly perceives that the necessity of nature arises from within things themselves. It holds that each being acts according to what it is, and thus, its tendencies are not imposed from without but flow from its essence. The very intelligibility of this insight, however, betrays its limit, for the intrinsic power of a thing explains its manner of acting, not its capacity to act at all. Accordingly, the essence that disposes toward activity still requires an act that gives it existence and coherence.

Hence, the metaphysical question beneath dispositional essentialism is not why things act as they do, but why there are things capable of acting at all. To say that the stone falls because it has mass, or that the charge repels because it is charged, presupposes the ontological act by which stone and charge subsist. Clearly, while the essence disposes, only the act sustains.

The theological transformation of this view is participation. On this view, every finite power is a communicated potency; it receives from the Infinite Act not only its existence but its coordination with all others. The unity of law in the world, that is, the harmony among dispositions, is thus the reflection of the divine unity that gathers all powers into a single order of being. Nature’s lawfulness is the shadow of grace: finite essences cooperate because they share in one act of creation.

Dispositional essentialism, therefore, contains a veiled confession:
to affirm inner necessity is already to acknowledge the immanence of the divine act within creation. The Spirit is the bond that makes powers conspire toward intelligibility, and the Logos is the act through which each essence becomes dispositional at all. Necessity, properly understood, is participation in the divine constancy by which all things are held in being.

Determinatio

From the foregoing it is determined that:

1. Dispositional essentialism internalizes necessity but does not abolish dependence. Thus, finite essences are intelligible structures whose actuality presupposes a unifying act of being.

2. The unity of natural order cannot arise from a plurality of isolated powers. Coordination among dispositions requires an ontological ground transcending them.

3. Essence without act is impotent. The existence and operation of every power presuppose an act that is not itself one power among others. They thus presuppose an infinite act of being.

4. The participation of finite essences in the Infinite corresponds to the metaphysical structure of creation. As Augustine said, “Omne bonum quod habet creatura, habet participando” (De Diversis Quaestionibus 83.46). Powers are real and finite, and their actuality is participatory.

5. Hence, dispositional essentialism, though the most promising finite account, nonetheless points beyond itself. Its truth lies not in rejecting participation but in clarifying the mode of it: each finite power is a share in the creative act that sustains and orders all powers.

Therefore, the necessity of natural law is neither imposed from without nor self-generated from within. It arises from the participation of dispositional essences in the infinite act of being, in the Word through whom all powers subsist and in the Spirit who continuously actualizes their operation.

Transitus ad Disputationem XXVIII

The unity of nature cannot be secured from within the multiplicity of powers. The next disputation therefore asks whether finite systems, even when internally coherent, can ever be complete in themselves. 

We proceed to Disputatio XXVIII: De Systemate Incompleto et Veritatis Factore Infinito, in which the Gödelian structure of dependence reveals that every finite necessity presupposes an infinite act of truth.

Disputatio XXVI: De Universalibus Immanentibus et Necessitatione

On Immanent Universals and Necessitation

Quaeritur

Quaeritur utrum necessitas legum naturae sufficienter explicari possit per relationes reales inter universalia immanentia, an vero talis explicatio aut in regressum, aut in factum brutum, aut in participationem infiniti deveniat.

It is asked whether the necessity of natural law can be adequately explained by real relations among immanent universals, or whether such an explanation must ultimately collapse into regress, brute fact, or participation in the Infinite.

Thesis

Immanent realism explains regularity by positing universals instantiated within things and connected by real relations of necessitation. Yet the nexus that binds one universal to another either becomes an infinite regress, a brute primitive, or an implicit participation in an infinite unity. Thus, while immanent universals preserve realism, they cannot close the circle of explanation within the finite.

Locus Classicus

“He is before all things, and in him all things hold together.”
— Colossians 1:17

Patristic and scholastic theology interpreted this not as poetic hyperbole but as a metaphysical statement. Athanasius (Contra Gentes 41) held that creatures “stand fast by participation in the Word.” Aquinas, commenting on the same verse, wrote: “In ipso omnia constant, quia ipse est ratio essendi et ordinis in rebus.”(Super Colossenses I.17.) The order and interrelation of created forms thus depend upon the Logos as their unifying act.The attempt to ground such order solely in finite relations among universals severs form from source and leaves unity unexplained.

Explicatio

D. M. Armstrong, seeking a realist alternative to both Humean descriptivism and Platonic transcendence, developed a theory of immanent universals in What Is a Law of Nature? (Cambridge University Press, 1983) and A World of States of Affairs (1997). For Armstrong, universals are not abstract entities existing apart from things but real features instantiated in rebus. A natural law is then a relation of necessitation between such universals:

N(F, G) means that every instance of F is necessarily also an instance of G.

For example, the law “All electrons repel each other” corresponds to a relation N (being an electron, repelling other electrons). This N-relation is itself a real universal connecting others, not a mere linguistic rule.

Armstrong’s system preserves a realist ontology, for lawfulness exists in the world, not in our descriptions. It also avoids Platonism by keeping universals immanent.Yet the decisive problem lies in the status of the necessitation relation itself.

If N is simply another universal, it must stand in further relations explaining how it binds F and G—relations such as N′(N, F, G)—and so on ad infinitum. If N is primitive, we are left with unexplained necessity. If N is grounded in the overall structure of being, that structure functions as a transcendent unity, in effect, a metaphysical participation in the Infinite.

Thus Armstrong’s account, while internally rigorous, cannot ultimately provide a self-sufficient finite explanation. It gives us the mechanics of law but not its metaphysical coherence. The problem is not empirical but ontological: what makes the system of immanent relations one and necessary rather than a contingent web of co-instantiated properties?

Obiectiones

Ob I. In 1983 David Armstrong argued that immanent universals provide the ontological structure science presupposes. The relation of necessitation N is real and sufficient. No further grounding is needed.

Ob II. Moderate realism claims that by positing universals in rebus rather than ante res, we respect the finitude of creation and avoid both Humean nominalism and Platonic abstraction.

Ob III. Scientific pragmatism holds that the theory of immanent universals aligns well with scientific practice, which operates by discovering relations among properties, not by appealing to transcendent causes.

Ob IV. Empiricists argue that an infinite ground multiplies entities beyond necessity. The unity of laws is a consequence of the shared structure of matter and fields, not of any higher participation.

Ob V. The theologicus cautus ("cautious theologian") opines that to require an infinite explanation of finite order threatens to erase the integrity of secondary causes and the natural autonomy of creation.

Responsiones

Ad I. To say that N(F, G) is real explains that the relation exists, not why it obtains. Unless N itself is grounded, the account halts in primitive necessity. A brute tie between universals is no advance over the brute law it replaces.

Ad II. Immanent universals are indeed within things, yet their coordination across all things remains unexplained.The in rebus does not by itself yield the per se unity of the real. Participation in a higher act of being is required for coherence among universals.

Ad III. Scientific adequacy differs from metaphysical sufficiency.
Empirical inquiry describes how properties are correlated; metaphysics asks why such correlation is necessary. Armstrong’s ontology presupposes the unity it should explain.

Ad IV. The claim that matter and fields explain law simply restates the problem at a lower level. For the structure of matter and fields is itself law-like and requires grounding. Invoking the material order as ultimate converts contingent structure into absolute necessity without reason.

Ad V. Participation in the Infinite does not annul finite autonomy but establishes it. Only what is grounded in the Infinite can act coherently according to its own nature. The Spirit’s causal presence secures the creature’s integrity by making its lawfulness possible.

Nota 

The idea of universal immanence captures a profound half-truth.
On the one hand, it rightly discerns that the divine is not absent from the world but intimately present within it, sustaining the being of all that is. On the other hand, when detached from the transcendence that grounds it, immanence collapses into necessity without freedom, into an all-encompassing process in which God and world dissolve into one another.

Theology must therefore distinguish immanentia participationis from immanentia identitatis. In the first, the divine act is interior to all things as their sustaining cause; in the second, the divine and the creature are confused as modes of one process. But true immanence is participatory, not monistic. God is within all things precisely because all things are within God.

Necessity, when viewed in this light, is not mechanical but the mark of divine fidelity. The stability of natural law expresses the constancy of the creative Word, whose will does not waver. The same act by which God gives being gives order, and thus the regularity of the world is grace made habitual. Accordingly, immanence and necessity are not rival to transcendence and freedom; they are its temporal manifestation.

The absolute dependence of creatures upon the divine act entails that while God is more interior to them than they are to themselves, yet God remains infinitely beyond them. The world’s necessity is therefore double. It is necessary in itself because the divine act holds it in being, and yet contingent before God, who freely gives it.

Universal immanence, properly understood, is the metaphysical form of providence:the Creator’s continuous presence as the reason for the world’s coherence. This providence is the “necessity of grace,” the steady rhythm of divine constancy through which all that is remains possible.

Determinatio

From the foregoing it is determined that:

1. Armstrong’s immanent realism preserves ontology but not ultimacy. The N-relation that ties universals together is either another universal (regress), an unexplained primitive (brute fact), or a reflection of a deeper unity (participation).

2. Finite relations cannot ground universal coherence. The multiplicity of universals demands a unifying act that is not itself one among them. Without such an act, law remains accidental coordination.

3. The appeal to the Infinite is not extrinsic but intrinsic. The very notion of “necessitation” implies participation in an unconditioned ground of necessity. The Infinite is the metaphysical horizon within which immanent universals receive their order.

4. The participation of universals in the Infinite corresponds to the theological doctrine of the Logos. As the eternal form of all forms, the Logos is the ratio essendi and ratio ordinis of finite properties. Law, in this light, is the reflection of divine intelligibility within creation.

5. Hence, immanent realism, while the most sophisticated of finite explanations, points beyond itself. Its internal coherence is the sign of participation, not self-sufficiency. In the Infinite Word, the many relations of the finite find their unity; in the Spirit, they find their continuous actuality.

Therefore, the necessity of natural law cannot rest in the N-relations of universals alone but requires the participation of all finite forms in the Infinite act of being — in ipso omnia constant.

Transitus ad Disputationem XXVII

If universal immanence reveals that the divine act is interior to all things as the ground of their necessity,then theology must next inquire how that immanent act manifests within the distinct natures of creatures themselves. After all, divine constancy, to be real, must articulate itself in finite structures of power and tendency. The same Word who upholds all being also orders its operations; the regularity of nature is the expression of this inner form.

Hence we turn to Disputatio XXVII: De Essentiis Dispositionalibus,
in which we ask whether the necessity of natural law arises from the intrinsic powers of things, or whether even these dispositions, in all their apparent autonomy, depend upon participation in the infinite act that both constitutes and coordinates them.

Disputatio XXV: De Regularitatibus Humeanis

On Humean Regularities

Quaeritur

Quaeritur utrum leges naturae sint tantum descriptiones constantium eventuum in mundo, an vere exprimant necessarias rationes essendi quae exigunt causam extra ipsam seriem eventuum.

It is asked whether the laws of nature are merely descriptions of the constant conjunctions of events in the world, or whether they express necessary relations of being that require a cause beyond the series of events themselves.

Thesis

The Humean account of natural law as mere regularity confuses description with necessity and drains law from having real ontological force. If laws are nothing but patterns within phenomena, then the world lacks any genuine principle of order. Accordingly, to recover necessity, the finite must once again refer beyond itself to an infinite ground in which the possibility of law is constituted.

Locus Classicus

“He makes his sun rise on the evil and on the good, and sends rain on the just and on the unjust.”
— Matthew 5:45

The constancy of divine action in nature, understood here as fidelitas Dei, was read by Augustine (Enarrationes in Psalmos 147.18) and Aquinas (ST I.103.8) as evidence that natural regularities are not self-existent but proceed from a sustaining cause. Luther, in his lectures on Genesis, described the continuance of natural order as the “mask of God” (Larva Dei), behind which divine agency preserves creation. Thus, constancy itself is a sign of dependence, not autonomy.

Explicatio

The Humean conception of law arose in the Treatise of Human Nature (1739–40) and the Enquiry Concerning Human Understanding (1748), where David Hume denied that we ever perceive necessary connection between events. From this epistemic premise, he concluded that laws of nature are nothing more than uniform patterns of experience: a "constant conjunction" of similar events leading the mind to expect one after the other. On this view, necessity is not in things but in thought; it is a “habit of imagination.”

In the twentieth century, David Lewis sought to preserve Hume’s metaphysics while providing a systematic account of laws. In A Subjectivist’s Guide to Objective Chance (1980) and Philosophical Papers, vol. II (1986), Lewis articulated the Best-System Analysis (BSA) in which laws are the generalizations that occur given the axioms of the simplest and strongest deductive system that best summarizes all particular facts: the “Humean mosaic” of local matters of fact. A law, then, is whatever appears in the optimal balance between simplicity and strength in describing the total history of the world.

The appeal of this position is its ontological economy: no mysterious necessities, only patterns; no governing principles, only description.
Yet its cost is high: it leaves the world without internal order or modal depth. The regularity of events may be observed, but the reason for that regularity is left unspoken. On Humeanism, the universe is a sequence without syntax, a film of contiguous frames in which connection is projected by the mind. In such a world, the word law is metaphor; nothing obliges events to recur, and the distinction between possible and impossible collapses into mere fact and non-fact.

Theologically, this view is untenable. It denies both creation’s intelligibility and divine fidelity. To call law a mental convenience is to deny that the world speaks truthfully of its Maker. Reason, however, testifies otherwise, for the constancy of nature presupposes an underlying act of being that makes regularity possible.

Obiectiones

Ob I. Already in 1748 David Hume had argued that all necessity arises from habit. We never perceive any power or connection in nature. Therefore, what we call a law is only an observed uniformity in experience.

Ob II. In 1980 David Lewis claimed that to treat laws as abstract necessities adds ontological baggage. The world is a mosaic of local facts. The “Best System” captures their pattern without positing mysterious connections.

Ob III. Empiricists say that science requires only prediction, not metaphysical grounding. Whether laws “exist” beyond description is irrelevant to the success of physics.

Ob IV. According to nominalism, the notion of an infinite truthmaker is incoherent. Necessity is linguistic convenience; to speak of grounding is to confuse semantics with ontology.

Ob V. Liberal theology avers that reading divine causality into natural regularity is to return to pre-critical metaphysics. Lawfulness may express God’s reliability metaphorically, but it requires no metaphysical participation.

Responsiones

Ad I. Observation alone yields correlation, not connection. If necessity were merely mental habit, then any sequence could become law through repetition, which contradicts both experience and reason. Our recognition of constant conjunction presupposes that reality itself is structured for recurrence.

Ad II. The Best-System Analysis transforms the ontological into the epistemic. It tells us what generalizations we find simplest, not why the world is ordered so as to be summarized. The balance of simplicity and strength explains convenience, not causation.

Ad III. Science as practice may ignore metaphysical foundations, but the intelligibility of science presupposes them. If the universe were pure contingency, induction itself would be unjustified. The success of empirical prediction depends upon a real order antecedent to observation.

Ad IV. To reduce necessity to language is self-refuting, for the reduction itself claims necessity. Semantic regularity cannot explain ontological stability. Laws must be more than linguistic; they must participate in a structure of being.

Ad V. The metaphysical reading of divine causality is not regression but completion. Scripture’s description of the world’s constancy as divine faithfulness grounds natural order in personal being. To deny participation is to make the creation silent about its Creator.

Nota 

This disputation confronts the decisive modern rupture in the understanding of law and causality. Whereas the preceding disputations discerned in natural order the reflection of divine reason and the imprint of legibus primitivis, modern empiricism, epitomized by Hume, denies that any necessity or intrinsic connection binds events together. According to this view, so-called “laws of nature” are but habits of observation—regular successions that the mind projects as necessity out of custom. The world thus loses its inner ratio; causality becomes expectation, and order a fiction of the perceiving subject.

In this disputation we examine the implications of this Humean reduction. Can theology accept a cosmos governed only by constant conjunction without undermining the very possibility of providence, creation, and divine intelligibility? If natural law is but descriptive regularity, how can the world be a medium of revelation or a site of divine action? The question touches not only metaphysics but also epistemology, for in the collapse of necessity the mind itself loses participation in the rational structure of being.

Therefore Disputatio XXV tests the theological coherence of the modern naturalist paradigm. It contrasts the participatory order of lex aeterna and legibus primitivis with the secularized uniformity of Humean regularity, seeking to determine whether a purely empirical account of law can sustain the intelligibility of creation or whether it inevitably dissolves the Logos into the contingencies of perception. In this way, it prepares the path toward the retrieval of a richer metaphysical realism in Disputatione XXVI: De Immanentia Universali et Necessitate.

Determinatio

From the foregoing it is determined that:

1. The Humean and Lewisian accounts evacuate natural law of real necessity. By reducing law to description, they destroy the very distinction between order and coincidence.

2. Regularity theory fails the coordination test. It cannot explain why distinct patterns harmonize across domains,why electromagnetism and gravitation, time and entropy, compose one coherent cosmos.

3. Reason’s demand for sufficient cause (PSR) re-emerges. If law is mere pattern, PSR is violated, and intelligibility perishes.The mind’s refusal to accept brute regularity is itself evidence of participation in an Infinite intelligibility.

4. The finite order requires a ground that is both necessary and self-explanatory. Such a ground cannot lie within the Humean mosaic; it must transcend it while remaining immanent as its condition.

5. Hence, the constancy of nature is participatory: the world’s regularities exist not ex se but per participationem in the Infinite act of being. What the theologian calls divine providence, the philosopher names the unconditioned truthmaker of order.

Therefore, the Humean view of law as regularity fails both scientifically and metaphysically. While it can describe, it cannot explain; while it can record, it cannot ground. Thus, the world is not a mosaic of inert facts but a living participation in the Logos, in whom all order holds together.

Transitus ad Disputationem XXVI

In the preceding disputation it was shown that the Humean conception of law as mere regularity severs the bond between mind and world, dissolving necessity into habit and rendering the cosmos unintelligible from within. The world thus appears as a theater of sequences without reasons—an ordered surface lacking interior logos. Against this view, theology must ask whether there remains a deeper mode of necessity, one not imposed from without nor abstracted by thought, but immanent in things themselves as their participation in divine reason.

This question turns our attention from the empirical pattern to the metaphysical structure that makes such pattern possible. If order is real, it must inhere in being as such; universals must be operative within the concrete, not floating above it. How, then, are these universalia immanentia to be conceived? Are they divine ideas within things, the ontological forms of their participation in the Logos, or the very conditions of their acting and being acted upon?

Therefore we advance to Disputationem XXVI: De Universalibus Immanentibus et Necessitatione, in which we shall inquire how necessity arises from within the order of being itself, how universals dwell in the particular as formative presence, and how through this immanent structure the world remains transparent to the intelligibility of God.