Hobbes-Edwards-Prior Principle (HEPP)

• HEPP is the thesis that if the causal principle were false, no adequate explanation would account for why entities begin at specific times, locations, numbers, or kinds.
• It formalizes a counterfactual link using modal logic to show that denying universal causation leads to an absence of good explanations for the observed order in beginnings.
• HEPP plays a dialectical role by challenging Neo-Russellian views and asserting that non-causal, law-based explanations can account for the non-arbitrariness of existence.

Searching arXiv for the cited HEPP paper and a closely related background paper on Neo-Russellianism. The Hobbes-Edwards-Prior Principle (HEPP) is the thesis that if the Causal Principle were false, there would be no good explanation for why entities do not begin at arbitrary times, in arbitrary spatial locations, in arbitrary number, or of arbitrary kind. In Linford’s formulation, the Causal Principle is not treated as merely accidental or as logically necessary, but as a matter of metaphysical or physical necessity: anything that begins to exist has a cause. HEPP is then formalized as a counterfactual, or possibly a counterpossible, linking the falsity of that principle to the absence of a good explanation of the observed non-arbitrariness of beginnings. The contemporary significance of HEPP lies in its dialectical role within causal and cosmological arguments, and in Linford’s claim that it has no dialectical force against Neo-Russellian views on which causation is absent from fundamental physics (Linford, 15 Jul 2025).

1. Canonical formulation and logical structure

Linford’s canonical formulation states:

The Hobbes-Edwards-Prior Principle (HEPP): If the Causal Principle is false, then there would be no good explanation for why entities do not begin at arbitrary times, in arbitrary spatial locations, in arbitrary number, or of arbitrary kind.

To regiment the thesis, he introduces three schematic components. First, $C$ denotes the Causal Principle:

$$C: \text{“As a matter of metaphysical or physical necessity, anything that begins to exist has a cause.”}$$

Second, $F$ denotes the relevant observed order:

$$F: \text{“entities do not begin at arbitrary times, in arbitrary locations, in arbitrary number, or of arbitrary kind.”}$$

Third, $E(\cdot)$ is a monadic predicate for good explanation:

$$E(p): \text{“there is a good explanation of } p\text{”.}$$

HEPP is then expressed as:

$$\text{HEPP} \equiv (\neg C \Box\!\rightarrow \neg E(F)).$$

The modal force is crucial. HEPP is false just in case the closest worlds in which $\neg C$ holds are worlds in which $\neg E(F)$ is false, that is, worlds in which there is a good explanation of $F$. Linford’s argument is designed to apply whether the antecedent $$C: \text{“As a matter of metaphysical or physical necessity, anything that begins to exist has a cause.”}$$0 is regarded as genuinely possible or as counterpossible.

This formalization clarifies the inferential role HEPP is supposed to play. Its defenders combine it with the premise that there is a good explanation of the non-arbitrariness of beginnings:

$$C: \text{“As a matter of metaphysical or physical necessity, anything that begins to exist has a cause.”}$$1

From $$C: \text{“As a matter of metaphysical or physical necessity, anything that begins to exist has a cause.”}$$2 together with $$C: \text{“As a matter of metaphysical or physical necessity, anything that begins to exist has a cause.”}$$3, they infer that $$C: \text{“As a matter of metaphysical or physical necessity, anything that begins to exist has a cause.”}$$4 must be rejected, and hence that $$C: \text{“As a matter of metaphysical or physical necessity, anything that begins to exist has a cause.”}$$5 holds. Structurally, HEPP is meant to show that denying universal causation for beginnings yields explanatory disaster. The principle therefore functions not merely as an intuition pump about disorder, but as a bridge from explanatory order to a strong causal premise.

2. Historical sources in Hobbes, Edwards, and Prior

Linford presents HEPP as a unifying label for a line of thought reconstructed from Thomas Hobbes, Jonathan Edwards, and Arthur Prior. It is not a slogan they themselves used; rather, it is synthesized from a common argumentative pattern (Linford, 15 Jul 2025).

For Hobbes, the central thought is that, absent a cause, there would be equal reason for a thing to begin at one time rather than another. He argues that if there is no cause of the thing, one has as much reason to think it should begin at one time as at another, and thus equal reason to think it should begin at all times, which he regards as impossible. He draws analogous conclusions about direction of motion and cessation of motion: if movement began without a cause, there would be equal reason to move in any direction, and if motion could cease without a cause, it would cease in every particle of time alike. In Linford’s reconstruction, Hobbes’s impossibility claim rests on a strong combinatorial intuition: if multiple ways are equally eligible and nothing selects among them, all are realized in a single world.

Edwards generalizes the concern beyond times and directions to kinds and numbers of entities. His claim is that, without $$C: \text{“As a matter of metaphysical or physical necessity, anything that begins to exist has a cause.”}$$6, stones, stars, beasts, angels, souls, sensations, ideas, volitions, or anything else of all the infinite number of possibles could begin to exist. The structure of the argument is that an entity’s nature cannot explain why it exists rather than some alternative, because before existing its nature is not there to select it, and after existing it is too late to explain its own beginning. Whatever selects something for existence must therefore exist prior to it. If something begins uncaused, there is nothing prior to do that selecting. Edwards accordingly concludes that “contingence is blind and does not pick and choose for a particular sort of events.” Although he defines cause very broadly as the nature of a ground or reason why some things are rather than others, Linford notes that Edwards’s notion remains asymmetric, antecedent, necessitating, and tied to constant conjunction, and therefore is not simply the Neo-Russellian relation of non-causal determination.

Prior accepts the core HEPP-style thought but weakens Hobbes’s impossibility claim to incredibility. Without $$C: \text{“As a matter of metaphysical or physical necessity, anything that begins to exist has a cause.”}$$7, he says, it would be incredible that beginnings should all turn out to be objects of the same sort. Prior also introduces a major qualification. It is, in his view, metaphysically obfuscating to treat modes such as headaches as things that begin to exist and require causes. What constrains possible uncaused happenings is instead the nature and capacities of already existing substances. An electron may have the capacity to jump to orbits $$C: \text{“As a matter of metaphysical or physical necessity, anything that begins to exist has a cause.”}$$8 or $$C: \text{“As a matter of metaphysical or physical necessity, anything that begins to exist has a cause.”}$$9, but not $F$0; persons may have powers that oysters lack; and turning into a dragon may be something no existing object has the power to do. This yields a form of limited indeterminism: some things may happen uncaused, but the range of such happenings is constrained by the capacities of existing substances.

3. Arbitrariness, non-arbitrariness, and the dialectical role of HEPP

The notion of arbitrariness operative in HEPP is highly specific. An arbitrary time is a time at which something begins without anything making it the case that it begins then rather than earlier or later. An arbitrary spatial location is one for which there is no explanation of why the entity appears here rather than there. An arbitrary number is the absence of any explanation for why this many entities appear rather than more or fewer. An arbitrary kind is the absence of any explanation for why the spontaneously appearing entity is of one kind rather than another, or why wildly heterogeneous entities do not appear indiscriminately (Linford, 15 Jul 2025).

HEPP advocates maintain that non-arbitrariness in these respects requires a cause in a robust sense. If there is no cause, then all times, locations, numbers, and kinds are on a par, with nothing to prefer one over another. The alleged consequence is either that arbitrary beginnings should occur, or at minimum that there would be no good explanation for why they do not occur.

In cosmological and causal arguments, HEPP functions as a reductio against denying $F$1. One assumes that sometimes things begin to exist without causes. One then argues that nothing would select which things begin, where, when, how many, or of which kinds. From that, one infers either arbitrary beginnings everywhere or at least the absence of any good explanation for the ordered pattern actually observed. Since the world displays highly non-arbitrary beginnings, denial of $F$2 is said to be untenable. On this use, HEPP is not itself a cosmological conclusion; it is a support premise meant to motivate a strong causal principle, which can then be deployed in arguments for a First Cause or related metaphysical conclusions.

4. Neo-Russellianism and the denial of fundamental causation

Linford frames the contemporary dispute through Neo-Russellianism, which he defines by two commitments: causation is not physically fundamental, and there are real but non-fundamental causal relations that help guide effective strategies. Neo-Russellianism is therefore distinct from Russell’s eliminativism. It does not deny higher-level causal discourse in the special sciences or ordinary practice; it denies only that causation belongs to the ontology of fundamental physics (Linford, 15 Jul 2025).

Four routes to Neo-Russellianism are identified. On the first route, temporal symmetry in microphysics undermines causation because past and future nomologically determine each other symmetrically, whereas causation is paradigmatically asymmetric. On the second route, non-local or holistic microphysical determination conflicts with the locality of paradigm causal relations such as throwing a rock or lighting a match. The laws relate entire regions, whole Cauchy surfaces, or full past light cones rather than localized cause-effect pairs. On the third route, fundamental indeterminism is taken to indicate that certain events occur without micro-causes, not merely with indeterministic causes. On the fourth route, inspired by Kuhn and Redhead, all fundamental motion is treated as natural motion rather than as the product of efficient causes; inertial motion in general relativity is then a matter of following geodesics due to the metric, not a case of efficient causal production.

What these routes share is a distinction between causation and explanation. Neo-Russellians do not deny explanation at the fundamental level. They deny causal explanation there. In its place they appeal to laws, symmetries, constraints, global determination relations, and statistical structure. This is the framework within which Linford argues that HEPP loses its force. If explanation at the fundamental level need not be causal, then the inference from the falsity of $F$3 to the absence of any good explanation is immediately put under pressure.

5. Linford’s argument against HEPP

Linford’s central thesis is that objections based on HEPP do not move Neo-Russellians because Neo-Russellians already have reason to reject $F$4, and because they can explain $F$5 without invoking $F$6 (Linford, 15 Jul 2025).

The first step is directed at the Causal Principle itself. Given any of the four routes to Neo-Russellianism, either $F$7 is false or it is vacuously true at the micro-level because nothing begins to exist in the relevant sense. Linford rejects what he calls the Trivialism Reply, according to which time-symmetric microphysics blocks genuine beginnings. Even on time-symmetric microphysics, there can be macrophysical arrows of time defined by entropy, as in Boltzmann-style cosmology. Macroscopic entities such as Boltzmann brains can then begin to exist at entropy minima without macrophysical causes. This is meant to show that there are nomologically possible worlds in which $F$8 fails even at the macro-level.

The second step targets the counterfactual structure of HEPP. If $F$9 is actually true, then a Neo-Russellian can simply hold that the actual world lacks fundamental causation and yet still contains good explanations of non-arbitrary beginnings. In that case, $$F: \text{“entities do not begin at arbitrary times, in arbitrary locations, in arbitrary number, or of arbitrary kind.”}$$0 is actual, which directly falsifies HEPP. If $$F: \text{“entities do not begin at arbitrary times, in arbitrary locations, in arbitrary number, or of arbitrary kind.”}$$1 is instead vacuously true in the actual world, Linford asks about the closest worlds in which $$F: \text{“entities do not begin at arbitrary times, in arbitrary locations, in arbitrary number, or of arbitrary kind.”}$$2 non-vacuously holds. He argues that those worlds still contain robust non-causal explanations of $$F: \text{“entities do not begin at arbitrary times, in arbitrary locations, in arbitrary number, or of arbitrary kind.”}$$3, so $$F: \text{“entities do not begin at arbitrary times, in arbitrary locations, in arbitrary number, or of arbitrary kind.”}$$4 remains true there as well. Either way, the counterfactual $$F: \text{“entities do not begin at arbitrary times, in arbitrary locations, in arbitrary number, or of arbitrary kind.”}$$5 fails.

The third step is explicitly explanatory. HEPP assumes that if there is no causal explanation, then there is no explanation. Linford denies that assumption. Laws, symmetries, kinematic constraints, and logical or metaphysical necessities can explain. On that basis, the absence of arbitrary beginnings need not be causally explained in order to be well explained.

6. The Consistency Principle and non-causal explanation of non-arbitrary beginnings

To articulate how non-causal explanation can do the relevant work, Linford introduces the Consistency Principle (TCP):

The Consistency Principle (TCP): Whatever begins to exist must be consistent with the full set of logical, metaphysical, and nomic principles.

TCP is intentionally schematic. Logical principles include logical necessities; metaphysical principles include necessary truths about coexistence and essential properties; nomic principles are the laws of nature, whether understood in Neo-Humean or Anti-Humean terms. The principle supplies a non-causal selection rule: even if no cause picks what begins to exist, consistency with constraints does (Linford, 15 Jul 2025).

Linford distinguishes two explanatory tasks. Preventive Facts are negative constraints: items do not begin to exist that are of arbitrary kind, in arbitrary number, and so forth. Selective Facts are positive restrictions: items begin to exist only of select kinds, times, places, or numbers. The HEPP advocate assumes that only causes can explain Preventive Facts. Linford argues instead that laws and constraints can explain both Preventive and Selective Facts non-causally.

On an Anti-Humean Neo-Russellian picture, laws govern possibilities rather than merely describe regularities. Logical and metaphysical constraints can then exclude certain beginnings outright. Linford’s example is that if Susan is essentially the only child of Tom and Mary, then Carl, who would also be essentially their only child, cannot coexist with Susan in one world; Carl’s existence is thereby logically or metaphysically prevented. Nomic constraints perform analogous work in physics. The spacetime light-cone structure of relativity forbids superluminal trajectories and thereby rules out certain “space invader” scenarios that Newtonian mechanics permits through unbounded velocities. Linford also appeals to the Glashow-Iliopoulos-Maiani mechanism as a paradigmatic explanation of why certain decays do not occur at detectable frequency; to white dwarf formation, where electron degeneracy pressure and the Pauli principle constrain stellar evolution; to French and Saatsi’s treatment of ionic and covalent bonding through multi-particle wavefunction constraints; to Noether-style symmetry-conservation links, such as phase symmetry of the electron field implying charge conservation; and to Einstein’s equations, which constrain the entire global spacetime rather than merely propagating local initial data. In each case, the explanation is presented as non-causal: what is doing the work is structure, symmetry, or constraint.

On a Neo-Humean variant, the relevant resources are different but still non-causal. The Humean Mosaic is the distribution of perfectly natural properties over spacetime, and laws are the axioms of the Best System trading off simplicity, strength, and fit. Linford formulates a Chaotic Continuation Objection according to which, if $$F: \text{“entities do not begin at arbitrary times, in arbitrary locations, in arbitrary number, or of arbitrary kind.”}$$6 were false, most continuations of a given Cauchy surface would contain arbitrary beginnings. His Neo-Humean reply has several parts: objective chances derive from the whole mosaic rather than being pre-assigned to local states; metaphysical independence of local qualities does not imply probabilistic independence; there is no well-motivated natural measure over the space of Humean Mosaics; and causation itself has no special advantage in ruling out chaotic worlds. The resulting position is that explanation eventually bottoms out somewhere, and the Neo-Humean is entitled to let it bottom out in the Best System and the actual mosaic rather than in necessary causal connections.

7. Criticism, limits, and broader implications

Linford’s criticism of HEPP is conceptual, metaphysical, and dialectical. Conceptually, HEPP conflates explanation with causation. The paper’s contrary claim is that physics already contains many non-causal explanations, especially explanations by symmetry, constraint, and conservation law. It also rejects the expectation that causeless beginnings would be unconstrained simply because they are causeless. The absence of a cause does not entail the absence of any lawlike or modal restriction. Hobbes’s stronger intuition that equal eligibility would require simultaneous realization is further criticized as “bizarre” from a contemporary modal perspective, where multiple ways something could happen are typically represented by different worlds rather than by joint realization in a single world (Linford, 15 Jul 2025).

Metaphysically, the paper argues that HEPP assumes without warrant that causation itself ensures order. Even if $$F: \text{“entities do not begin at arbitrary times, in arbitrary locations, in arbitrary number, or of arbitrary kind.”}$$7 holds, the laws could still be bizarre and yield highly disordered worlds. Conversely, HEPP ignores alternative sources of necessity: logical, metaphysical, and nomic principles can do the work of selecting and excluding. Linford also notes a possible verbal dispute. Edwards’s broad notion of cause as ground or reason might allow Neo-Russellians to concede “causes” in that expansive sense. But the disagreement is not merely verbal, because Edwards retains asymmetry, antecedence, constant conjunction, and incompatibility with indeterminism.

Dialectically, the conclusion is that HEPP does not create a new problem for Neo-Russellians. They already have independent motivation to treat $$F: \text{“entities do not begin at arbitrary times, in arbitrary locations, in arbitrary number, or of arbitrary kind.”}$$8 as false, trivial, or at least in tension with fundamental physics. And whether $$F: \text{“entities do not begin at arbitrary times, in arbitrary locations, in arbitrary number, or of arbitrary kind.”}$$9 is actual or merely true in nearby worlds, they take there to be ample non-causal explanations of $E(\cdot)$0. In that setting, the counterfactual at the heart of HEPP is false by Neo-Russellian lights.

The broader implication is that any cosmological argument relying on HEPP to motivate a strong, necessary Causal Principle loses an important support if Linford’s analysis is correct. More generally, rejection of HEPP pushes toward a pluralistic account of explanation in which causal explanation is only one species among others, while non-causal explanation by laws, symmetries, constraints, and global structures is central to fundamental physics. Linford does not claim to establish Neo-Russellianism itself. He leaves open whether law-based all-at-once accounts can be fully precisified, how non-causal explanation in philosophy of science should best be analyzed, and whether a convincing defense of causal fundamentalism can be given without HEPP-style intuitions.