Diaputatio XXVI: De Universalibus Immanentibus et Necessitatione

On Immanent Universals and Necessitation

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.

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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

Objiectio 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.

Objiectio 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.

Objiectio 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.

Objiectio 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.

Objiectio 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.

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.

Disputatio XXV: De Regularitatibus Humeanis

On Humean Regularities

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.

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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

Objiectio 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.

Objiectio 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.

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

Objiectio 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.

Objiectio 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.

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.

Disputation XIV: De Legibus Primitivis

On Primitive Laws

Quaeritur utrum leges naturae possint esse facta prima et inexplicata intra ordinem finitum, an vero talis primitivismus sit contradictorius intentioni rationis, quae exigit ut ipsa necessitas habeat causam suam.

It is asked whether the laws of nature can be primitive and unexplained facts within the finite order, or whether such primitivism contradicts reason’s own demand that necessity itself must have a cause.

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Thesis

Law primitivism fails as an account of the laws of nature because it secures its necessity only by denying its own explanation. To treat the deepest, most intelligible features of reality as the least explicable is to invert the order of reason. If the finite claims to ground its own lawfulness, it asserts a self-sufficiency it cannot justify. Accordingly, the necessity of the finite’s own laws implies dependence upon an infinite truthmaker.

Locus Classicus

“By him all things were created, in heaven and on earth, visible and invisible… and in him all things hold together.”
— Colossians 1:16–17

Aquinas comments on this passage: “Ordo naturae participatio est legis aeternae” (ST I.91.2 ad 3). Augustine had earlier taught that “lex temporalis a lege aeterna derivatur” (De Libero Arbitrio I.6). The tradition thus affirms that the order and necessity observed within creation participate in the eternal act of divine reason. Against this background, primitivism, which asserts that the finite holds together of itself, appears as a metaphysical contradiction within Christian and classical realism alike.

EXPLICATIO

Law primitivism, as developed by Tim Maudlin in The Metaphysics Within Physics (Oxford University Press, 2007) and later refined in Philosophy of Physics: Laws, Explanation, and Symmetry (Princeton University Press, 2019), holds that the fundamental laws of nature are ontologically primitive; they are basic facts of the world that govern what is physically possible. As such, they are neither reducible to regularities among events nor analyzable in terms of universals or dispositions.

Central to Maudlin’s view is the notion of modal governance. According to this doctrine, laws are not descriptive generalizations but governing realities that determine the modal structure of the universe, that is, they determine the domain of what can and cannot occur. The laws of nature are “facts of governance,” possessing intrinsic modal authority; they make things behave lawfully, rather than merely record how they behave.

The philosophical motive behind this position is clear. Humean accounts reduce necessity to description; Maudlin restores it as an objective feature of reality. Unfortunately, by making the laws themselves fundamental, primitivism converts what should be explained into the ultimate explainer. The very intelligibility of the cosmos—its coherence, uniformity, and mathematical precision—becomes that about which reason is forbidden further to inquire. The result is a paradoxical ontology in which the finite behaves as if it were self-sufficient and necessary

Maudlin’s “governing facts” thus occupy an ambiguous status: they are finite in existence but infinite in function. They are everywhere present, universally binding, and unconditioned by what they govern. Primitivism thereby yields what may be called functional theism without God: the cosmos as self-grounded lawgiver. 

Philosophically, this position is unstable. If laws are grounded, they are not primitive; if ungrounded, their modal authority is arbitrary. To recognize necessity but deny its cause is to paralyze reason at the point of its deepest activity.

Obiectiones

Objiectio I. According to Maudlin, every chain of explanation must terminate somewhere. Laws are where it properly ends, for they make explanation possible. To ask for a ground of law is to misunderstand law’s ontological role as modal governor.

Objiectio II. Empirical realism holds that seeking a metaphysical ground for laws exceeds the limits of science and contributes nothing to explanation or prediction.

Objiectio III. Neccessitarian naturalism opines that necessity is simply a feature of the finite. If the world exhibits regularity, that regularity is ultimate. Therefore, to postulate an Infinite truthmaker is gratuitous metaphysics.

Objiectio IV. Antifoundationalists argue that every worldview ends in some ungrounded posit: the theist in God, the naturalist in law. To stop with God rather than law merely renames the brute.

Objiectio V. Theological minimalism asserts that Scripture itself portrays the world as ordered by fixed ordinances: “He set them in their courses.” Hence, the lawful structure of nature may rightly be regarded as primitive, though originally created.

Responsiones

Ad I. Explanation must terminate, but not in the arbitrary. A proper terminus is self-explanatory, not self-assertive. To stop at finite laws is to call contingent necessity ultimate. Modal governance, if real, cannot itself be without a governor; an ungrounded modal authority is a sovereignty without legitimacy.

Ad II. Science is methodologically modest but metaphysically neutral. Its refusal to ask “why these laws?” does not license the claim that no answer exists. Philosophy begins where empirical explanation ends.

Ad III. The finite cannot generate its own necessity. Coordination among laws, constants, and symmetries presupposes a unity transcending each. To make the contingent itself the source of the necessary is to conflate participation with origin.

Ad IV. The Infinite is not a renamed brute fact. A brute fact is contingent yet unexplained, while the infinite is necessary per se. Appeal to theiInfinite transforms unintelligibility into intelligibility, grounding rather than relocating the unexplained.

Ad V. The “courses” of creation imply stability of operation, not independence of being. Biblical lawfulness manifests divine fidelity, not divine withdrawal. Autonomy of process does not entail autonomy of existence.

Determinatio

From the foregoing it is determined that:

1. Law primitivism secures modal governance by fiat; it asserts necessity without explaining it. It halts reason precisely where reason most demands sufficiency.

2. The finite cannot serve as its own lawgiver. A world of contingent things and relations cannot contain the source of its universal necessity. “Necessary facts” arising contingently are self-contradictory.

3. The appeal to an infinite ground is therefore a philosophical, not merely theological, conclusion. The rational structure of the finite world points beyond itself to an unconditioned truthmaker, to an infinite act by which self-explanatory being confers order and modal unity upon the finite.

4. In this light, participatory ontology emerges as reason’s completion. If the infinite grounds the finite’s necessity, every law, structure, and regularity exists per participationem in that infinite act. Law is the trace of participation, and modal governance is the finite expression of the Infinite’s continuous act of holding-together.

5. The statement in ipso omnia constant thus names not a pious mystery but a metaphysical necessity. Theology and philosophy converge: what theology calls Word and Spirit, philosophy recognizes as the infinite cause through which all finite law receives its being and coherence.

Disputatio XXIII: De Fundamento Legum Naturae

On the Ground of the Laws of Nature

Quaeritur utrum mundus finitus per se possit rationem reddere regularitatum quae in ipso obtinent, an vero requirat veritatis factorem infinitum qui earum necessitatem et convenientiam inter proprietates constituat.

It is asked whether the finite world can of itself give an account of the regularities that obtain within it, or whether it requires an infinite truthmaker that constitutes both their necessity and their coordination among properties.

__________

Thesis

No finite reason can adequately explain the necessity of natural law without recourse to an unconditioned truthmaker. Every attempt to ground lawfulness within the finite order ends either in brute fact, in mere description, or in regress. The necessity and coordination of the finite therefore presuppose an infinite ground.

Locus Classicus

“He himself gives to all mortals life and breath and all things… for in him we live and move and have our being.”
— Acts 17:25, 28

Patristic commentators from Athanasius (Contra Gentes 41) to Augustine (De Trinitate I.6) read Paul’s words as denying that creatures possess in themselves either being or order. Aquinas echoed this interpretation (ST I.105.5): “Since the being of a creature depends upon the Creator’s influx, so too does its operation and order.” Thus the tradition rejects any claim that the finite law of things is self-grounding.

Explicatio

Since the rise of modern science, the regularities of nature have been taken as the paradigm of intelligibility. The deductive–nomological model of explanation sought to show how particular happenings follow from general laws, much as the medieval astronomer derived eclipses from celestial mechanics. Yet this model silently presupposes the existence and stability of those laws; it uses them without explaining why they obtain.

Microphysical explanation was meant to improve upon this by tracing macro-level regularities to the behavior of elementary particles. But it soon became clear that the very behavior of these particles -- obeying field equations, conservation laws, and symmetry constraints -- rests again upon ultimate regularities that are themselves unexplained.

Accordingly, the philosophical task is to ask what truthmaker accounts for the existence and necessity of these basic laws. Must we accept them as primitive features of the finite, or do they point beyond the finite to an infinite ground making possible their order and coordination?

The following trilemma arises:

1. Primitivism holds that laws are ultimate facts of the finite world, self-standing and unexplained.

2. Descriptivism claims that laws are linguistic or mathematical summaries of what happens, containing no real necessity.

3. Those allowing an Infinite Ground argue that laws possess genuine necessity only if their order is constituted by an unconditioned truthmaker that grounds their coordination.

The first halts inquiry; the second dissolves necessity; only the third preserves both intelligibility and modality.

Objectiones

Objectio I: The empiricist claims that science does not seek metaphysical grounds but predictive success. To demand a truthmaker beyond empirical law is to mistake the limits of scientific explanation for a deficiency in reality itself.

Objectio II.  Primitivists like Maudlin declare that laws are fundamental ontological features. To ask “why these laws?” is a category mistake. Explanation ends rightly where necessity begins.

Objectio III.  Humeans like David Lewis say that there are no governing laws over and above the mosaic of events. Laws merely describe the best systematization of what occurs. Necessity is a manner of speaking, not a metaphysical tie.

Objectio IV.  Immanent realists like David Armstrong argue that immanent universals and their relations of necessitation suffice. The finite already contains within itself the structures that make lawfulness intelligible. No appeal to an infinite ground is required.

Objectio V. Kant and transcendental philosophy generally hole that necessity belongs to the conditions of human cognition, not to things in themselves. To seek a truthmaker beyond the phenomenal order is to step outside the bounds of reason.

Responsiones

Ad 1. Predictive adequacy is not metaphysical sufficiency. Scientific method may stop at empirical laws, but reason does not. To confuse epistemic limits with ontological closure is to mistake what we cannot measure for what cannot be.

Ad 2. To call a law “primitive” is to give it the status of a brute fact, and this is an admission that it is unexplained. Primitivism therefore secures necessity only by halting explanation, treating the finite as self-grounding without warrant.

Ad 3. The best-system analysis reduces necessity to description. But description, however elegant, cannot make a law necessary. It says how the world behaves, not why it must. Humeanism thus exchanges being for grammar.

Ad 4. Relations among finite universals can explain why certain properties co-occur, but not why these universals and these relations exist. The “necessitation” relation itself either regresses or becomes primitive. The coordination of all such relations across the cosmos still calls for a higher unity.

Ad 5. Transcendental necessity explains how we must think the world, not how the world is. If the phenomenal order is intelligible only through the assumption of stable laws, then reason itself points beyond phenomena to that which makes stability possible.

Determinatio

The search for the ground of natural law thus faces a decisive choice.

If we remain within the finite, explanation ends either in brute fact (primitivism) or in empty description (Humeanism). If we turn inward to the structures of the finite (immanent realism), we face regress or unexplained selection. The explanatory trilemma of bruteness, vacuity, or transcendence is therefore unavoidable.

From this it follows that the finite cannot be complete unto itself. The very intelligibility of law points toward an unconditioned truthmaker—an Infinite ground that confers necessity and coordinates the manifold of the finite. The appeal to such an Infinite is not a theological excess but the only philosophically adequate completion of explanation.

From the foregoing it is determined that:

1. Every finite explanation of natural law fails by terminating in one of three defects:
     (a) brute necessity (primitivism),
     (b) vacuous description (Humean regularity), or
     (c) infinite regress (immanent relationalism).

2. The finite as finite is composite, coordinated, and contingent; it cannot be the source of its own necessity.

3. The unity of laws and their coherence across domains demand a ground that is simple, self-explanatory, and unconditioned — an Infinite truthmaker.

4. This conclusion is not a theological intrusion but a philosophical necessity. Reason itself, in seeking sufficient cause, transcends the finite and implicitly participates in the Infinite.

Therefore the order of nature is not self-grounding but participatory: its necessity and coordination are signs of dependence upon an Infinite act in which the finite both is and is held together.