PSR Out, Entitlement In: The Armstrong–Wright Argument For The Existence Of God

1. On the Vulnerability of Cosmological Arguments

The cosmological argument has long stood as the most formidable contender as a proof for the existence of God. At present, its most discussed version is Craig & Sinclair's (2009: 101, 192) Kalām Argument. It runs as follows:

(1)

The universe began to exist.

(2)

Everything that begins to exist has a cause.

(3)

From (1) and (2), the universe has a cause.

(4)

An explanation is either scientific or personal.

(5)

The causal explanation of the origin of the universe cannot be scientific (since scientific explanations are part of the universe).

(6)

From (4) and (5), the cause of the existence of the universe is personal.

Following Rowe’s (1975:6) classification, (1)-(3) constitutes the first stage, (4)-(6) the second: the first establishes a necessary entity or a cause of the universe, the second identifies it as God. Bracketing temporal finitism — inessential, as it is not presupposed by classical versions¹ — this argument pivots on two problematic assumptions:

-

In its first stage, the principle of sufficient reason (henceforth PSR);

-

In its second, the presumption that we can know whether an entity is personal.

The PSR, which is assumed by all cosmological arguments known to me. This Protean principle has taken weaker and weaker forms to survive objections:

Causal Principle (CP). Every fact has a cause.

Limited CP (L-CP). Every fact with property x has a cause.

Weak L-CP (WL-CP). For every fact with property x, it is possible that it has a cause.

PSR. Every fact has a reason.²

Limited PSR (L-PSR). Every fact with property x has a reason.

Weak L-PSR (WL-PSR). For every fact with property x, it is possible that it has a reason.

L-CP is assumed in Plato’s Timaeus (1892: 28a), Koons (1997), Sandsmark & Megill (2010), Wahlberg (2017), Loke (2018: ch.5), and in Craig and Sinclair; Flynn & Gel (Forthcoming) derive it from the distinction between a contingent entity and its existence. WL-CP is employed by Rasmussen (2009) and Weaver (2016). L-PSR appears in Dumsday (2018) and Byerly (2019). WL-PSR is adopted by Kremer (1997), Gale (Gale & Pruss, 1999: 463) and Pruss (2010).

At present, the PSR enjoys relatively few defenders: Bourget & Chalmers (2023) report that 57.26% of metaphysicians reject it, with only 32.66% affirming it. Van Inwagen (1983: 202) argued that the PSR entails a modal collapse — and that, according to Schnieder & Steinberg (2015) and Tomaszewski (2016), is the reason behind this widespread rejection. McDaniel (2019) and Briceño (2023: §5) develop further challenges. Moreover, these criticisms may extend to limited and weak forms: in fact, Oppy (2000: §2) argued that Pruss’s WL-PSR entails the full PSR, as Pruss himself acknowledged.

Moving on to the second stage, to show that a first cause or necessary entity is God we must demonstrate that this cause or entity has at least one of the properties that distinguish God from all other causes and necessary entities. Following Theron (1987), God is defined by entitative and operative properties. Entitative properties are derived from necessity, and are therefore common to all necessary entities. Thus, God is distinguished by operative properties, i.e., his personhood. This means that God, at the very least, has a conscious mind, a subjective point of view. Aristotle’s Metaphysics already perceived this:

[I]f it thinks of nothing [...] It is just like one who sleeps. And if it thinks, but this depends on something else, then [...] it cannot be the best substance. (1924: XII, 9)

This is the minimal definition of God: a first cause or a necessary entity that is conscious. Therefore, to prove that a cause or entity is God is to prove that it is conscious. Yet, there are reasons to think that such proof may be impossible.

Consciousness is by definition subjective. Any justifier is either objective or relative to one's own subjectivity, never to the subjectivity of another. Thus, whether rocks are conscious or whether philosophical zombies exist, everything would appear the same (Chalmers, 1997: part 3). That is, consciousness is not necessarily entailed by any other fact. Hence, beliefs about the subjectivity of others cannot be justified. Following McGinn (1999), understanding consciousness may be as beyond our grasp as understanding an integral is beyond the grasp of a cow.

These difficulties do not demonstrate that the PSR or the knowability of another's mind are false beyond any reasonable doubt. However, they do make us feel the need for a cosmological argument that relies on neither the PSR nor the knowability of other minds. I aim to show that God’s existence remains defensible even on the radical assumption that the existence (or non-existence) of contingent entities cannot have a cause, reason, ground or explanation, and that it is impossible to know whether an entity is conscious.

In §2, I address the first stage of the cosmological argument by deriving the existence of necessary entities from an assumption inspired by Armstrong's metaphysics. In §3, I turn to the second stage: while it is impossible to prove that a necessary entity is God, I argue that, given Wright’s epistemology, one is nevertheless entitled to such a belief.

2. The First Stage: An Armstrongian Strategy

2.1. Nothing from Nothing?

Cosmological arguments from contingency traditionally invoke the PSR to derive, from the claim that every contingent entity requires a reason, the existence of non-contingent entities. To preserve this inferential structure, a different principle must satisfy the following requirements:

-

It does not trivially entail the PSR;

-

It is, if not unassailable, at least defensible;

-

It entails that a contingent entity requires something beyond itself.

To meet the third requirement, such a principle may deny an essential property of those entities whose existence would otherwise require nothing. Entities of this sort would be possible ex nihilo: the world containing only them would be accessible from a world devoid of entities and instantiating no positive properties whatsoever — the empty world. Thus, the following principle — which is explicitly stated by Armstrong (1989: 64) — emerges as a natural candidate:

(1)

No world is accessible from the empty world.³

As Billy Preston said, ‘Nothin’ from nothin’ leaves nothin’ / You gotta have somethin’ if you wanna be with me.’

While the PSR entails (1), the converse does not hold. The PSR posits a specific relation — cause, reason, ground, or explanation — between entities. By contrast, (1) merely posits a condition of existence. For example, all extended entities require the existence of space, yet space is not the cause, reason, ground or explanation of their existence.

In other words, given (1), a contingent entity A can exist only on the condition that some other entity B (not necessarily a specific one) already exists. Yet, if any B exists, A may come into existence as a brute fact, without cause, reason, ground or explanation.

Accordingly, the first requirement is met.

2.2. Indeed, Nothing from Nothing!

Let us now turn to the second requirement: do we have reasons to support (1)?

Armstrong regards (1) as a consequence of combinatorialism, the view that possible worlds are recombinations of actual entities and properties. Compared with the two other major theories of possible worlds, combinatorialism offers striking advantages: it does not require the bloated ontology of concretism or abstractionism, and secures a realist conception of possibility and necessity, immanently realised in actual entities. Now, in the empty world there are no entities or properties, hence no recombinations, hence no accessible worlds. Thus, whoever endorses combinatorialism thereby has reason to endorse (1).

Consider next the nature of time. According to the two major theories, either time is itself an entity (substantivalism) or it emerges from relations among entities (relationism). As Shoemaker (1969) observed, time cannot simply be reduced to change. Thus, it remains intuitive that change requires time. The emergence of an entity from nothing (i.e., accessing a non-empty world from the empty world) would constitute a change. But in the empty world there are no entities, and thus no time or entities from which it could emerge. Therefore, nothing can change. Therefore, no non-empty world can be accessible from the empty world. Thus, both substantivalism and relationism support (1).

Finally, although no philosophical principle is beyond dispute, every argument must begin somewhere. If possible, it should begin from what is most intuitive and most widely accepted. Historically, no candidate principle has enjoyed such authority as the PSR. Almost all major thinkers have taken it for granted until recently. Hamilton (2019: lect. V, part I, sec. I) ranks it as a law of thought together with the principles of identity, non-contradiction and excluded middle. Since the PSR entails (1), (1) inherits its historical popularity. Yet, since (1) does not entail the PSR, (1) remains immune to the recent attacks that have discredited it. Thus, if the intellectual contenders disagree on everything else, they may still converge on (1) as a credible point of departure.

In short, (1) finds support from multiple rational theories: it follows from combinatorialism, substantivalism and relationism, and it is implied by one of the most popular principles in the history of philosophy. Therefore, (1) is far from unfounded: it stands as strong enough to satisfy the second requirement.

2.3. From Nothing to Necessary Existence

We now come to the third requirement: showing how (1) entails the non-self-sufficiency of contingent entities.

As already noted,

(2)

If the possibility of contingent entities were unconstrained, worlds containing them would be accessible from the empty world.

Since this contradicts (1),

(3)

From (1) and (2), the possibility of contingent entities is constrained.

Now, assume that

(4)

(For reductio) There are only contingent entities.

Let $e_k$ and $e_m$ be two entities, with $e_k\ne e_m$. The path $[e_k\to e_m]$ means that the existence of $e_k$ makes $e_m$ possible, that is, $e_k$ satisfies $e_m$’s constraint. In other words, the world containing $e_m$ is accessible from a world containing other entities, and $e_k$ is any of them.

$[e_k\to e_m]$ does not mark a temporal sequence, but an ontological hierarchy. $e_k$ and $e_m$ may both begin to exist at the same instant t, yet the existence of $e_m$ at t depends on the existence of $e_k$ at t. They might even coexist throughout an infinite past, or $e_k$ may phenomenally manifest after $e_m$. Temporal order is irrelevant; what matters is that $e_m$’s possibility depends on $e_k$.⁴

Given (4), for every $e_m$, there is some $e_k$ such that $[e_k\to e_m]$. Thus, for every $e_m$, we can trace an infinite path $[...\to e_j\to e_k\to e_m]$⁵. Every infinite path results either in a circularity or in an infinite regress. In fact, either $e_m$ appears multiple times in the path or not. If it appears multiple times, we have a circularity; if not, since each entity requires another, we have an infinite regress. Hence,

(5)

From (3) and (4), every actual entity has its constraint satisfied by another entity, yielding either a circularity or an infinite regress.

In a circularity such as $[{...\to e}_k\to e_m\to e_k\to ...]$, the possibility of $e_k$ is incoherently conditional on the existence of $e_k$ itself. In an infinite regress, the possibility of each entity is conditional on the existence of another. Since in both cases the possibility of each entity is suspended upon the existence of another whose possibility is equally suspended, no entity has its constraint satisfied or is possible in its own right. Each entity should receive its possibility from another through a chain reaction that cannot begin. In other words, the regress and the circularity alike lack independent possibility. Therefore,

(6)

None of the entities of a circularity or an infinite regress can exist.

Yet

(7)

Entities exist.

Therefore,

(8)

From (6) and (7), entities do not yield a circularity or an infinite regress.

(9)

From (5) and (8), not every actual entity has its constraint satisfied by another entity.

(10)

From (4) and (9) by reductio, there is at least one necessary entity.

Thus, the third requirement is satisfied, and the first stage of the cosmological argument is complete.

As a corollary, since necessary entities exist in every possible world, metaphysical nihilism is false: the empty world is impossible. Indeed, no world is accessible from the empty world precisely because the empty world is impossible.

3. The Second Stage: A Wrightean Strategy

3.1. Reason Without Justification?

The second stage demands that we identify at least one necessary entity as God — which means proving it to be conscious. Yet, as established in §1, we operate under the assumption that such a proof is impossible. This frames the central paradox of our endeavour: how can a belief be rational when its ultimate justification is beyond our epistemic grasp?

Following Burge (2020), epistemic warrant divides into justification (through reason) and entitlement (without reason). Some beliefs, such as the belief in other minds, cannot be justified, yet remain rational because we are entitled to them. Therefore, to prove that a necessary entity is God is to prove that one is entitled to believe that it is conscious.

The most influential account of entitlement is Wright's, which I favour over the alternatives because, compared to them,

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It explicitly addresses the problem of other minds;

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It does not focus on perceptual beliefs, which are irrelevant here;

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It is modest, granting entitlement only to core beliefs;

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It is not socially relative.

According to Wright (2004: §3), I am entitled to a belief if I have no evidence against it, and it is essential for the pursuit of highly valued goals. To say a belief is essential for the pursuit of a goal means that acting as if it were true is the best way to achieve that goal, irrespective of the belief’s actual truth-value.

Yet, Wright's account seems to leave too much room for subjectivity. Although different people may indeed have opposite entitlements depending on their personal goals, the charge of radical epistemic relativism must be avoided. This can be done by placing further constraints, that is, desiderata of beliefs. This strategy has been pursued by Olhorst (2023: ch. 3) and Salvatore (n.d.).

So, which desiderata should we add? To avoid arbitrariness, we seek guidance in the classic criteria for justification: foundationalism, coherentism, and pragmatism. Foundationalism privileges beliefs formed through sensory experience or inference therefrom. Yet the existence of other minds cannot be proved this way. In coherentism, however, beliefs about other minds may be more or less coherent with other known facts; that is, they can make known facts more or less probable and help explain them. In pragmatism, in turn, these beliefs can be more or less useful from a practical standpoint. Thus, coherentism and pragmatism can supply the desiderata we seek.

Accordingly, one is entitled to believe that at least one necessary entity is conscious if

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We have no evidence against that belief;

-

That belief is essential for the pursuit of valuable goals;

-

It is pragmatically useful;

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It coheres with other known facts by making them more probable or helping explain them.

3.2. Reason Without Justification, Indeed!

3.2.1. First Requirement

First, I am invoking entitlement epistemology precisely because I assume that, whether other minds exist or not, the world would appear the same. Consequently, no data could furnish evidence either for or against their existence. By the same token, no evidence can be marshalled against the claim that a necessary entity is conscious. Hence, the first requirement is satisfied.

3.2.2. Second Requirement

Second, consider a spiritual goal: salvation from death and the attainment of theosis — that is, a personal relationship with God culminating in participation in his necessity. This goal is of supreme value to me, and the vast majority of humanity has acknowledged, in one form or another, the desirability of a blissful afterlife.

Only a conscious necessary entity — only God — could make this goal attainable. Admittedly, given our minimal definition, we are not assuming that God is omnipotent or omnibenevolent, so he might not allow such a relationship; still, only such an entity could ground a personal relation that confers participation in necessity.

Thus, if God exists, seeking communion with him is the optimal path to theosis. And if God does not exist, then theosis is impossible, so no alternative strategy could surpass this one. Acting as if God exists is therefore my dominant strategy. Hence, the second requirement is satisfied.

3.2.3. Third Requirement

Third, thousands of studies have examined the relation between belief in God and well-being. The Oxford Handbook of Religion and Health (Koenig et al., 2012: parts III-V) alone surveys more than 2,800 such investigations.

Research consistently reports positive correlations between religiosity and physical and mental health, life expectancy, quality of life, satisfaction, adaptability, and overall well-being. Nor is this merely a correlation: there is an intelligible mechanism that explains such results. The act of cultivating a personal relationship with a transcendental entity, whether illusory or not, instills hope and a sense of belonging, which in turn alleviates stress and fosters resilience.

It may be argued that if this necessary conscious entity is not conceived as omnibenevolent and omnipotent, the beneficial effect is somewhat diminished. Yet, even then, one can sustain hope in the possibility of a favourable relationship with this entity. The Tanakh presents God as at times wrathful and vengeful, and still, belief in him was a fountain of hope for its authors.

Hence, the belief in God is demonstrably useful, and the third requirement is satisfied.

3.2.4. Fourth Requirement: Miracles and Mystical Experiences

What remains is to assess whether belief in a necessary conscious entity coheres with certain known facts. I shall consider four classes of such facts that frequently arise in the debate over God's existence. I begin with miracles and mystical experiences.

Across cultures and throughout history, people have testified to miraculous events and encounters with a personal divine reality. Many of these experiences are elicited by mystical practices, which makes them at least in principle amenable to repetition and falsification — even if their precise interpretation remains debatable. Moreover, Habermas’s (2024: §§9-15) minimal facts argument demonstrates that the apostolic testimony to Jesus’ appearances exhibits features atypical of hallucinations or illusions.

If God does not exist, these experiences must be wholly non-veridical products of neurological mechanisms — however difficult some experiences may appear to be to explain. If God does exist, those mechanisms still operate, but additional, veridical encounters with the divine are possible. Consequently, whatever the baseline probability of these experiences in a godless universe, their existence is strictly more probable if God exists.⁶

3.2.5. Fourth Requirement: Deontic Facts

Most contemporary metaethicists are realists, holding that ethical facts exist. Deontic facts — those that ground duties and obligations — are a class of ethical facts. Craig (2004: 19) contends that only God provides the necessary foundation for ethical facts. Similarly, Anscombe (1958) and Adams (1987: 97-163) regard obligation as inherently theological. Why should this be so?

Following Adams, obligation is essentially social: it presupposes a relation between conscious beings. God, as a conscious necessary being, possesses a will. That will can be directed toward other persons and be expressed through commands. A command consistent with the good and issued by a legitimate authority constitutes a duty, and thereby a deontic fact. We may not know whether this minimal God is omniscient and omnibenevolent, but if he is, then he certainly is qualified as a legitimate authority whose commands are reliably aligned with the good.

If God does not exist, then all commands must be issued by conscious contingent entities. Yet the profound and persistent moral disagreement among humans makes it implausible that any contingent entity could currently serve as a legitimate authority. By contrast, if God exists, he adds to the set of conscious beings a necessary entity for whom omniscience and omnibenevolence remain live possibilities. Hence, the existence of deontic facts is more probable on the hypothesis that God exists.

3.2.6. Fourth Requirement: Formal Elegance

Leibniz (1985: 254-5) maintains that a creator God would choose to bring forth a world ‘infinitely simple and uniform, but yet of an infinite productivity’. Hence, according to him, ours is the best of all possible worlds: the one that, from the fewest principles, generates the richest variety of phenomena. In the same vein, Swinburne (2004: 150-1) argues abductively from the aesthetic qualities of the universe to the reality of God.

The preference for simplicity arises from the very nature of the mind: it allows the mind to focus using few resources. Even a mind with infinite capacity could still prefer simplicity — just as a billionaire would not pay two dollars for a coffee that costs one. We do not know whether God can shape the universe’s structure, but if he does, he would favour an elegant universe.

If God does not exist, other entities could shape the cosmos. Yet the contingent conscious entities that inhabit our universe show no power to alter its laws, and unconscious entities struggle to justify a preference for simplicity. If God exists, however, he joins the entities that might be capable of shaping the universe, and unlike these, his preference for simplicity flows directly from his conscious mind. Thus, the probability of a formally elegant universe is higher if God exists than if he does not.⁷

3.2.7. Fourth Requirement: Reason, Consciousness and Personal Continuity

Human beings manifest characteristics that pose a persistent challenge to naturalistic reduction.

Lewis (1947, §3) argued that human rationality cannot be reduced to natural processes. His challenge has been rearticulated by many philosophers, and although no formulation is unassailable (Oppy 2022), it deserves attention.

Similarly, Moreland (2008) contends that consciousness itself points beyond the natural order. He claims that the law-like correspondence between mental and neurological states is not adequately explained either by contingent correlations or by necessary emergence.

Parfit (1984: ch. 13) further shows that neither biological nor psychological continuity suffices to explain transtemporal personal identity. Still more elusive is transworld identity — personal identity across possible worlds. This led some to hypothesise unspecified further facts to account for personal continuity. Adams (1974) posited ​​a primitive thisness — an identity that does not supervene on any other fact.

If God does not exist, other entities might account for the emergence of these personal characteristics in contingent beings. However, it is not clear at all how this is possible and how likely such an emergence would be. If God exists, instead, these characteristics are not late arrivals in the cosmos, but intrinsic at the fundamental level. Thus, under the assumption of God, the probability of their existence is not merely high but maximal.

These four observations collectively satisfy the fourth requirement, entitling us to believe that at least one necessary entity is conscious — which is to say, that it is God.

3.3. Bonus Track: Theism and Its Modern Rivals

The reasoning developed so far defends the rationality of belief in God (whether this God is YHWH, the Flying Spaghetti Monster, or something else, or even whether more than one exists, is not of interest to us). It does not exclude the possibility of a symmetrical entitlement to deny God’s existence. If both theists and atheists are entitled to their respective stances, I accept this symmetry.

I acknowledge that this may render the second stage underwhelming. Since I assumed that consciousness is unprovable, I take entitlement as the only viable strategy here; it is inevitable that different individuals may hold opposing entitlements. Yet we can still ask which entitlement is more robust.

From the first stage, both theists and atheists must affirm the existence of necessary entities. Atheists, unlike agnostics, explicitly affirm that these entities are not conscious. This is a negative belief: it specifies what such entities are not, without committing to what they could be.⁸

Because consciousness is evidentially inaccessible, there can be no evidence against the thesis that no necessary entity is conscious. Hence, the atheist belief satisfies the first requirement.

A negative belief may sometimes be practically useful for the pursuit of certain goals: for example, acting as if there were no afterlife might foster prudence. Yet empirical studies on non-theistic religions reveal smaller effects on well-being (Koenig et al., 2012: parts III-V). Thus, the atheist stance seems less useful, and its capacity to fulfil the second and third requirements is at least doubtful. The reason may be structural: by affirming what reality is not, a negative belief tends to constrain rather than expand the field of action. To live as if a negative belief were true is often indistinguishable from living as if one held no beliefs on the matter at all.

Finally, positive beliefs introduce entities or properties capable of causal impact, thereby raising the probability of known facts. Negative beliefs, by contrast, tend to be neutral: they alter probabilities only by excluding alternatives, not by generating new explanatory resources. Thus, the ability of the atheist belief to meet the fourth requirement is questionable.

In conclusion, not only is the theist entitled to belief in God, that entitlement is more securely grounded than its atheistic rival.

4. Summary of the Armstrong-Wright Argument

(1)

No world is accessible from the empty world.

(2)

If the possibility of contingent entities were unconstrained, worlds containing them would be accessible from the empty world.

(3)

From (1) and (2), the possibility of contingent entities is constrained.

(4)

(For reductio) There are only contingent entities.

(5)

From (3) and (4), every actual entity has its constraint satisfied by another entity, yielding either a circularity or an infinite regress.

(6)

None of the entities of a circularity or an infinite regress can exist.

(7)

Entities exist.

(8)

From (6) and (7), entities do not yield a circularity or an infinite regress.

(9)

From (5) and (8), not every actual entity has its constraint satisfied by another entity.

(10)

From (4) and (9) by reductio, there is at least one necessary entity.

(11)

One is entitled to believe that at least one necessary entity is conscious if such a belief lacks counter-evidence, is essential to pursue valued goals, is pragmatically useful, and contributes to the explanation of known facts.

(12)

There is no evidence against the belief in a conscious necessary entity.

(13)

Acting as if there is a conscious necessary entity is essential for the pursuit of valued goals such as attaining theosis.

(14)

The belief in a conscious necessary entity is useful, as it fosters physical and mental health, longevity, well-being, satisfaction, and adaptability.

(15)

The existence of a conscious necessary entity would help explain the existence of mystical experiences, deontic facts, the formal elegance of nature, reason, consciousness, transtemporal and transworld personal identity.

(16)

From (11) and (12)-(15), one is entitled to believe that at least one necessary entity is conscious.

5. That’s Not All, Folks!

In the remaining space, let me highlight some possible developments of this line of argument.

First, several thinkers⁹ have argued that necessity entails a range of entitative and operational properties beyond consciousness. For instance, one may claim that a necessary entity is defined solely by its intrinsic, necessary, time-invariant properties; that it is without parts, immutable, concrete; and that there is exactly one necessary entity.

Second, one may argue that natural entities cannot possess these properties and are therefore contingent. For example, spacetime and fields, on a relationist account, require the existence of some relata, and thus are contingent. Natural laws and energy are not entities at all, but descriptions of how the universe changes. All known elementary particles can cease to exist through annihilation, absorption or decay, and are therefore contingent. And so on.

These two additional stages would greatly strengthen the argument. In fact, to account for the existence of necessary entities, the atheist would need to postulate a mysterious non-natural, non-conscious entity — an hypothesis that, unlike God, would hardly satisfy the requirements for entitlement.

Third, Aquinas, drawing on Aristotle’s (1924: XII, 9) definition of God as thought of thought, treats the Son as the content of God’s thought, and the Spirit as God’s loving relation with it.¹⁰ In other words, Aquinas derives the Trinity from the fact that God is conscious. Since my second stage defines God as a conscious entity, an adaptation of Aquinas's argument could naturally follow from it. In fact, God is by definition conscious and necessary. Conscious states always have content (a quale, sense-data, mental representation, or the like). Hence, God's consciousness always has content. But if that content were an entity other than himself, God would have a relation with it, and relations are contingent. Hence, in the fundamental state ontologically prior to the emergence of any contingent entity, God is both the subject and the content of his own consciousness.

Fourth, further doctrines become derivable. For example, one may be entitled to believe that God wills the good: saving us from death through resurrection and eternal life, preserving our bonds through the communion of saints, and bringing the world to perfection through redemption and the actualisation of the world to come.

With these further steps, the second stage would reveal not merely our minimal God, but none other than the Christian God, turning the argument into a springboard for a broad defence of Christianity as a whole.