Anselm's analogy

In the third chapter of the Monologium, Anselm argues that ‘there is a certain Nature through which whatever is exists and which exists through itself, and is the highest of all existing beings’ (M, III, 87). Although his argument for this conclusion is predicated upon considerations about ontological dependence, it should not be confused with his more widely known ontological argument for a necessary being in the Proslogium. Here we see Anselm arguing not for a being which merely exists necessarily, but one that exists ‘through itself’ (a se) and not through another (ab alio).

Anselm's argument takes its cue from the principle that ‘everything that is, exists either through something, or through nothing. But nothing exists through nothing. For it is altogether inconceivable that anything should not exist by virtue of something. Whatever is, then, does not exist except through something’ (M, III, 87). Clearly, for Anselm, to ‘exist through’ or ‘exist by virtue of’ something is for it to have its reason for being in something. When a exists through b, or exists by virtue of b, the reason for a's existence is b. It is inconceivable that something should exist by virtue of nothing, that is, lack a reason for its being. The main principle here, in other words, is the PSR.Footnote ²

Anselm gives several arguments for the conclusion that there must be some one thing that exists through itself as opposed to through another. What interests us is how Anselm conceives of ‘existence through itself’ (existendi per se). Towards that end, we should consider first what Anselm means by ‘existence through’ more generally. He writes:

One thing ‘exists through’ another when it derives its existence from the other. The statue's existence is derived from its matter and artificer. Furthermore, although there are different ways a thing might exist through something else (the statue depends on its matter in one sense, on its artificer in another), there are common features of derivative existence generally:

In all cases where something, a, exists through another, b, we can say: (i) a is not identical to b, (ii) a owes its existence to b in some way, and (iii) a is ontologically posterior to b. Something that does not exist through another, by contrast, lacks these features, and ‘derives existence from itself’ (M, V, 91–92). Anselm explicitly denies, however, that something's existing through itself is to be understood in terms of causing itself, efficiently, materially, or otherwise. ‘The supreme Substance’, he says ‘did not create itself, nor did it spring up as its own matter, nor did it in any way assist itself to become what it was not before’ (M, VI, 94–95). Anselm is not imagining that God pull Himself up into being by His own bootstraps, as it were.

Having clarified what it cannot mean for the supreme Substance to exist through itself, Anselm offers an analogy to help us imagine what it does mean:

One wishes that Anselm elaborated further on this analogy, but alas, this single paragraph, which is as fascinating as it is puzzling, is all we get. What can we gather from it?

As per the analogy, it is the nature of a light (noun) to be, when lit (verb), luminous (adjective). Light is what it does when it's doing it, so to speak. But what about the supreme Being is analogous? What would it mean to say that it is of the nature or essence of the supreme Being (noun) to be/exist, when it is being/existing (verb), being-y/existence-y (adjective)? Surely it would take Anselm's analogy too far to read into these verb and adjective forms of ‘being’ as having ontological significance akin to an actus purus ontology of the divine nature. Nor should we read into Anselm here an uncompromisingly strong doctrine of divine simplicity. It is of course true that Anselm thinks it is of the essence of God to exist. He takes that to be demonstrable from his ontological argument. But light is not, after all, identical to luminosity, at least as Anselm must have thought of it: for luminosity is just how bright a light appears to us.Footnote ³ He says, with that respect to the supreme Being, that essence, existence, and existing ‘bear much the same relations’ to one another as do light, being lit, and luminosity, relations he describes as mutual.

Some caution is needed here, however, because Anselm explicitly rejects the possibility that things could exist mutually through each other: ‘But that these beings exist mutually through one another, no reason can admit; since it is an irrational conception that anything should exist through a being on which it confers existence. For not even things of a relative nature exist thus mutually, the one through the other’ (M, III, 88). This seems to be a straightforward rejection of circular ontological dependence between two (or more) things. Anselm must have a different kind of mutual relation in mind, where the relata, while not identical, are also not separate in the way two wholly distinct beings are. Be that as it may, if light is distinct, even if not separable, from its being lit, there does not seem to be any mutual relation here, for light is itself caused to exist; that is, it exists through something prior to it. Light, as a substance, does not consist merely of being lit or being luminous. Those are properties light has posterior to being, even if a light, while lit, is essentially ipso facto luminous.

In the end, it's unclear what Anselm's analogy, when carried over to essence, existence, and existing, amounts to. After his own analysis, John Morreall thinks Anselm's proposal is no more than a grammatical confusion:

That ‘light’ can be used as both a noun (‘the light in the cave’) and verb (‘I light the cave’) is an artefact of language, not the metaphysics of light as some kind of dynamic substance whose being is what it does. Without the additional metaphysical resources to interpret being as act, as Aquinas found in Aristotle, Anselm's analogy of how light exists ‘through itself’ by at once being called what it does fails to illuminate how the supreme Being exists through itself.

Aquinas and the E = ∃ thesis

The first three of Aquinas’ esteemed Five Ways appeal to beings which call out for explanation: beings which change, beings which are caused to exist, and beings which are contingent, respectively. Such beings, explained as they are by other things (‘causes’), must ultimately answer to a being that answers to no other. Such a being, Aquinas says, exists not through another as its cause, but ‘through itself’ (OBE IV.7), and is ‘through itself a necessary being’ (SCG I.22.2).

But, crucially, just as we saw in Anselm, for Aquinas, to be through itself a necessary being is not the same as merely having necessary existence. The Third Way, recall, arrives at the existence of a certain kind of necessary being, one that exists by the necessity of its own nature. This is because an infinite regress of necessary beings, each depending on another, would be just as problematic as a regress of contingent beings each depending on another (OBE IV.7; ST I.2.3). There therefore must be something ‘having of itself its own necessity, and not receiving it from another, but rather causing in others their necessity’ (ST I.2.3). Thus in his masterful, wide-ranging study of Aquinas, Norman Kretzmann attributes to him the following PSR: every existing thing has a reason for its existence either in the necessity of its own nature or in the causal efficacy of some other being(s) (Kretzmann (Reference Kretzmann1999), 65–66).

The question now is what it means for something to be ‘through itself’ a necessary being, or have its ‘reason for its existence in the necessity of its own nature’. This time, however, we get some aid from the Aristotelian concepts Aquinas adopts. For a thing to be caused to exist is for it to have its existence (matter, in most cases) conjoined to an essence (form).Footnote ⁴ For a thing to undergo change or movement is for some potentiality in that thing (inherent in its form or essence) to be actualized. For a thing to be contingent is for it to be a matter-form composite, for its matter and form might never have been conjoined. Thus what the first three of Aquinas’ Five Ways take as their explananda are things whose essence is distinct from their existence. All things whose essence and existence are distinct are ontologically dependent entities whose existence is explained by prior existents (SCG I.22.2).

Given this metaphysical framework, all the arguments converge in their own way on a being (unmoved mover, uncaused cause, and necessary per se) whose essence is not distinct from its existence. What Aquinas means by a being that exists by the necessity of its own nature, then, is a being whose essence is its own unique act of existing (ipsum esse subsistens). Unlike everything else which finds its explanation in another, God is His own existence, and so has His explanation ‘in Himself’.

It may be questioned, however, whether the concept of a being whose essence is identical to its existence is coherent (hereafter I will refer to this as the ‘E = ∃ thesis’). As Aquinas says, such a being does not exist like anything else, but rather is existence itself (SCG I.22; I.38.5). This is remarkable in its oddity. Supposing that God could be pure subsistent existence is like ‘supposing that something could be a shape, without being the shape of anything but that shape, or be a shadow, without being the shadow of anything but that shadow’ (Hughes (Reference Hughes1989), 21). Just as I know what it means for things to have a shape or shadow, I know what it means for things like rocks, trees, and people to have existence, even if I don't know what the best philosophical analysis of ‘existence’ is. I know what ordinary existence claims mean well enough to offer and analyse claims about the existence of more peculiar things like numbers or subatomic particles or angles and demons. But on Aquinas’ view, God ‘exists’ in some radically different sense – so radically different that I don't know what ‘God exists’ means. And how would one argue for ‘God's existence’ if God doesn't have existence like other things do? Surely the Five Ways are meant to demonstrate that something in particular exists (‘et hoc omnes intelligunt Deum’), not just that ‘there is’ existence simpliciter,Footnote ⁵ or that some thing* exists*, the asterisks signifying reference to we know not what.

The conceptual difficulties continue. Aquinas thinks there is a real distinction between essence and existence in creatures. There is something we can refer to as a creature's essence, E, and something else we can refer to as a creature's existence, ∃. Assuming the standard view of identity, for any creature, ☐(E ≠ ∃). When it comes to God, however, ☐(E = ∃).Footnote ⁶ But if the meaning of ‘=’ in both cases is the same, the meaning of ‘E’ and ‘∃’ cannot be, since ☐(E ≠ ∃) is logically equivalent to ~◇(E = ∃). What is meant by ‘E’ and ‘∃’ when speaking about creatures, and when speaking about God, cannot be the same.Footnote ⁷ So the E = ∃ thesis is really an E* = ∃* thesis, the asterisks again signifying reference to we know not what. Alternatively, one might hold that ‘E’ and ‘∃’ are univocal, it's just that they can be identical in some cases (God's) but not others (creatures). In this case, the E = ∃ thesis is really an E =* ∃ thesis, ‘=*’ signifying reference to a non-standard view of identity. Either way, the thesis is about as clear as mud.

Wholly apart from these conceptual difficulties, it is unclear how the E = ∃ thesis is explanatory. It is widely agreed that mere identity, as a reflexive relation, is not an explanatory relation. ‘If anything has appeared obvious about explanation’, Robert Nozick writes, ‘it has been that the explanatory relation is irreflexive’ (Nozick (Reference Nozick1981), 181). This of course is a well-known problem facing reductive accounts of mental states in philosophy of mind, but it faces the E = ∃ thesis no less. Given the Aristotelian framework Aquinas adopts, it is clear how the existence of other things are explained: as matter-form composites, their existence is explained in part by their form and matter (internal causes), and in part by what conjoins them (external causes); that is, causes them to exist, ‘cause’ understood broadly to include not just efficient causes, but final causes as well (Gilson (Reference Gilson1937), 80). But when it comes to a being whose essence is existence, none of those explanatory elements are present.

In fact, Aquinas explicitly rejects the possibility that such a being – God – could depend on anything, as any form of dependence entails existing ‘through another’, be it internal or external (SCG I.13.5–10; I.22). A being that truly exists through itself, Aquinas believed, must therefore be absolutely simple, altogether lacking parts (SCG I.18; I.20–27).Footnote ⁸ Now, it is not that it's hard to see how an absolutely simple being could have an explanation of its existence; rather, it is easy to see how it couldn't. Clearly there are no explanatory resources external to it that could help, since it exists independently of anything else. Just as clearly, there are no internal explanatory resources, since there are no real distinctions between anything in an absolutely simple being. There's just nothing in there for an explanatory relation to squeeze between. An independently existing, absolutely simple being just is, and is without explanation. It is for this reason that Brian Leftow (Reference Leftow2003) argues that Aquinas should not be read as endorsing the PSR Krentzmann attributes to him; everything is explicable except God.Footnote ⁹ Either way, the explanatory demand of the PSR is not satisfied with respect to God.Footnote ¹⁰

Descartes on God's causal explanation

In the cosmological argument of Meditation III, Descartes is interested in the explanatory ground not of, say, contingent beings, but of the very idea of God. But the main structure of his argument follows a familiar pattern where chains of explanatory dependence bottom out in a being which exists per se. Descartes, however, offers a new gloss, saying such a being ‘derives its origin from itself’ and ‘possesses the virtue of self-existence’ (HR I, 169).

The fact that Descartes's own correspondents struggled to understand exactly what he meant by these descriptions bodes ill for us. Does Descartes mean to say God exists per se in the merely negative sense of being underived or uncaused, asks Caterus, or does he mean a bolder, positive sense of being ‘derived from its own self as from a cause’ or to have ‘conferred its own existence on itself’? Descartes replies with a clear-cut PSR: ‘The light of nature certainly tells us that nothing exists about which the question, why it exists, cannot be asked’ (HR II, 14). This PSR is, in fact, the first of his ten ‘axioms or common principles’, and so the existence question ‘may be asked even concerning God’ (HR II, 55). And when it is, Descartes answers:

It would seem that God, on this account, somehow preserves Himself in existence by the positive operation of His own causal power. But Descartes's understanding of ‘cause’ here is highly qualified.Footnote ¹¹ In his reply to Arnauld, Descartes also explicitly rejects the possibility that God is His own efficient cause, as if He bootstraps Himself into existence (HR II, 111). Further, God ‘does not conserve Himself by any transeunt action, or any continual reproduction of Himself’ (HR II, 108) as He would were He is own efficient cause. Again, the relevant causal concept is not ‘the peculiar and restricted meaning of efficient cause’ (HR II, 15), but is ‘another species of cause analogous to an efficient cause’ (HR II, 15). So how is the causal concept here different from, but analogous to, efficient causation?

It is different from efficient causation in two ways: the cause is not prior to its effect, and it is not distinct from its effect. Although ‘that statement is manifestly true when the meaning of efficient cause is restricted to those causes that are prior in time to their effects or different from them, yet it does not seem necessary to confine the term to this meaning in the present investigation’ (HR II, 14) – that is, investigation into what sense God is the cause of Himself. But even in ordinary cases of efficient causation, Descartes says, the cause may not be prior to its effect, at least temporally (HR II, 14). Thus, God's causing Himself need not be understood as God's somehow being prior to Himself, temporally or otherwise, for, he rhetorically asks, ‘Who does not know that the same thing can neither be prior to nor different from itself?’ (HR II, 14).

The relevant causal concept is analogous to efficient causation in that efficient causes have the power to conserve or preserve their effects in being, and God exercises such power in excelsis with respect to Himself (HR II, 14, 16). This, Descartes thinks, is the key to a positive conception of self-existence demanded by the PSR. The merely negative sense of existing per se (underived or uncaused) is fine as it goes, but

He goes on, noting that the existence of beings which clearly do not exist per se but depend on something else (such as ourselves) conceptually requires one that does exist per se, boldly announcing that ‘here I will add a statement I have not hitherto made in writing – that we cannot arrive merely at a secondary cause, but that the cause which has power sufficient to conserve a thing external to it must with all the more reason conserve itself by its own proper power, and so exist per se’ (HR II, 16). Not quite satisfied with this, Arnauld managed to draw Descartes a bit further out still. Descartes writes in response:

Having ‘pursued this topic at somewhat greater length than the subject demanded’ (HR II, 114), with a detectable note of frustration, Descartes says no more.

One gets the impression that, pressed by Caterus and Arnauld, Descartes retreats in substance, if not in word, to the Scholastic view of aseity, namely, that God's being identical to His essence makes it such that God is causeless, or perhaps better, à la Scotus, uncausable.

Impressions aside, a more wholistic interpretation would be as follows. God does not have an efficient cause in the strict sense for two reasons: first, negatively, because something being its own efficient cause is incoherent (HR II, 108); second, positively, because the ‘inexhaustible power, or immensity’ (HR II, 108) of God's essence ‘renders it independent of an efficient cause’ (HR II, 109). Yet there is something analogous to an efficient cause in God's essence, a ‘concept common to efficient and formal cause alike’ (HR II, 109), something ‘intermediate between efficient cause, in the proper sense, and no cause’ (HR II, 110). It is like an efficient cause because it is an effective power and is genuinely explanatory (the function of an efficient cause, according to Arnauld), and like a formal cause because that explanation is in terms of God's essence, which is ‘not distinguished’ from His existence.

Perhaps Descartes is right that the relevant causal concept is ‘self-evident’ to those who follow the natural light of reason (HR II, 109); I, however, feel more like I'm groping in the dark for it. There are passages that suggest Descartes thought formal causation alone would do, such as when he says in a March 1642 letter to Huygens,

But saying God is His own formal cause is not, I think, all there is to Descartes's view (contra Christofidou (Reference Christofidou2013) and McBrayer (Reference McBrayer2018) ).Footnote ¹² Despite notoriously distancing himself from Scholastic niceties, Descartes does seem to have in mind the classic Aristotelian sense of formal cause as explanation in terms of a thing's essence (‘in taking the entire essence of a thing as its formal cause here, I merely follow the footsteps of Aristotle’ (HR II, 112); see also Flage & Bonnen (Reference Flage and Bonnen1997) ). The formal cause of a statue is its shape. The formal cause of a house is its design or blueprint. But in these cases, the formal cause and the thing itself are distinct. The statue is not identical to its shape; other things could have the same shape. The house is not identical to its blueprint; the house might never have been built. Yet Descartes said God's essence and existence are ‘not distinguished’. Moreover, formal causes, in these mundane examples, do not constitute a sufficient reason for a thing's existence, but enter into a thing's total explanation along with the other Aristotelian causes. God, however, has no other causes.

If the usual concept of a formal cause by itself will not do, then we are left to conclude that he had in mind some sui generis causal concept, just as he implied in, for example, HR II, 15–16, 113. Perhaps this is why Descartes gestures towards God's essence qua formal cause as having a unique kind of power that makes God actually exist, and so is on that account akin to an efficient cause.Footnote ¹³ But, once again, Descartes takes back with one hand what he seemed to give with the other. He does appeal to God's unique power as playing some explanatory role, but denies that God's essential power to exist should be understood in terms of a positive operation of will (HR II, 14, 108, 112). Understandably so, for it is exceedingly puzzling what that could even mean. Are we to imagine God's existence being explained by a distinct formal cause in the manner of, say, Escher's famous paradoxical lithograph of two hands drawing themselves into existence? Presumably not, for there an efficient cause sneaks back into the picture (the hands themselves), rendering it viciously circular. Besides, it should not be forgotten that for Descartes, God's essence, existence, and power are not actually distinct. How, then, can there be any order of explanation between essence, existence, and power? It's as if Descartes wants to find in God's essence something as genuinely explanatory as an efficient cause without any of the properties thereof responsible for its explanatoriness – productive power and distinctness from the effect (one thing, the cause, exercising a power to produce an effect, a different thing). He wants the semblance of the thing without the thing. The goods without the cost.

In the end, we are left to understand ‘God's essence is such that He exists by His own power’ in the merely negative sense that God, unlike everything else, does not exist by the power of anything distinct and prior to Himself. The puzzling and provocative descriptions of God's being His own cause notwithstanding, Descartes gives no clear answer to the question of why God exists. But it is Spinoza even more than Descartes who is most closely associated with the claim that God is the cause of Himself.

Spinoza on God as causa sui

According to Michael Della Rocca, ‘Spinoza employs the PSR more systematically, perhaps, than has ever been done in the history of philosophy’ (Della Rocca (Reference Della Rocca2008), 30).Footnote ¹⁴ He thinks Spinoza's commitment to the PSR was so unconditional and absolute that he dubs it ‘rationalism on steroids’ (ibid., 3).

Although some dispute this reading of Spinoza (see Garber (Reference Garber2015) ), its justification is plain. The first two of his axioms in the Ethics together sound very much like a now familiar PSR: ‘Everything which exists, exists either in itself or in something else’ (Ia1); ‘That which cannot be conceived through anything else must be conceived through itself’ (Ia2). To exist ‘in’ or to be ‘conceived though’, for Spinoza, is to exhibit what Roger Scruton calls a ‘rational dependence’, where B rationally depends on A just in case A makes B's existence and nature intelligible (Scruton (Reference Scruton1986), 36–37). For our purposes it suffices simply to say that rational dependence is explanation. Thus, everything that exists has an explanation of its existence, either in itself or in something else. Leaving no room for doubt, Spinoza again asserts a clear-cut PSR in Ip11: ‘For every thing a cause or reason must be assigned either for its existence or for its nonexistence . . . Now this reason or cause must either be contained in the nature of the thing or be external to it’ (Cf. Ip8s2).

Spinoza does not, however, advance a traditional cosmological argument where a chain of beings leads to God. He rejects transitive chains of dependence that trace back to the existence of some extramundane being. But Spinoza certainly believed that there is an ultimate reason for things. Everything, he argues, necessarily depends on and is constitutive of a single infinite substance, identified as God, who is ‘the immanent, not transitive, cause of all things’ (Ip18. Cf. Ip28s) – including God Himself.Footnote ¹⁵

It is that last part, the eyebrow-raising notion of God as causa sui, which concerns us. The reason Spinoza thought of God as causa sui is straightforward: everything has an explanation. There is ultimately only one thing or substance (Ip5dem), the ‘absolutely infinite Entity or God’ (Ip11s). That thing has an explanation. But since there's nothing besides that thing, that thing's explanation cannot be in terms of anything beyond or external to it (Ip6; Ip18dem; Ip11s), nor can it ‘be produced by anything else’ (Cor. Pr. 6). We are left to conclude it ‘is therefore self-caused’ (Ip7) (cf. Scruton (Reference Scruton1986), 38).

But is not the idea of something being self-caused, to use Arthur Schopenhauer's phrase, a contradictio in adjecto, akin to a man who stands on a chair to reach the clasp on his tall hat, or worse, a man ‘on horseback and sinking into the water, gripping his horse with his thighs and lifting himself and the animal up by means of his own pigtail, with the words causa sui underneath’ (Schopenhauer (F), 21)? Della Rocca thinks this reading is unfair, and that Spinoza has an easy reply:

If we are not to equivocate something's being self-caused with its being self-explanatory, how, then, are we to understand something's being self-explanatory?

We need look no further than the opening line of the Ethics: ‘By that which is self-caused I mean that whose essence involves existence; or that whose nature can be conceived only as existing’ (Idef1). For Spinoza, as already mentioned, the ideas of substance and that which is causa sui are coextensive: since ‘substance cannot be produced by anything else (Cor. Pr. 6) and is therefore self-caused [causa sui]’, he says, it must be the case that ‘its essence necessarily involves existence; that is, existence belongs to its nature’ (Ip7dem). Hence, substance is also described as that ‘which is in itself and is conceived through itself’ (Idef3) and ‘which exists solely from the necessity of its own nature’ (Idef7).

Just as we saw in Descartes, Spinoza's initially intriguing and provocative language of something's being causa sui reduces to the old E = ∃ thesis, which Spinoza explicitly affirms (Ip20: ‘God's existence and his essence are one and the same’). Harry Wolfson comments:

Unfortunately, therefore, Spinoza's notion of God as causa sui sheds no new light on the question of how God's existence itself is explained, as required by the PSR to which he is so unconditionally and absolutely committed.

Leibniz on existence flowing from essence

The locus classicus of PSR-based cosmological arguments for the existence of God is, of course, Leibniz's. Several different versions of the PSR can be found throughout Leibniz's corpus, including the canonical ‘Everything that exists, exists through something.’ He writes, ‘If something is through something else, then it has a reason of existing outside itself; that is, it has a cause.’ But if something ‘is though itself, then its reason of existing is taken from its own nature’ (AG, 184). Thus, like others before him, Leibniz described God as not just a necessary being, but one whose reason for existing is in His own nature or essence, thereby supposedly satisfying the explanatory demands of the PSR. But, true to form, he had something unique to add.

For Leibniz, anything that exists exists because of its essence. Essences, he thinks, have a sort of built-in ‘propensity’ for existence. He writes: ‘[S]ince something rather than nothing exists, there is a certain urge for existence or (so to speak) a straining toward existence in possible things or in possibility or essence itself; in a word, essence in and of itself strives for existence’ (AG, 150). As he goes on to say, this ‘striving’ comes in degrees, the strength of which is proportionate to an essence's degree of perfection. Their degree of perfection is determined by, roughly, how many other things (‘requirements’) limit their being. By way of analogy, just as an object in motion travels uniformly unless acted upon by external forces, a thing's degree of perfection, and hence hold on reality, is limited to the extent that the same in other things are ‘in the way of’ its being (AG, 20). Nothing limits God's being, however, His essence being supremely perfect.Footnote ¹⁷ To continue the analogy, God's essence, being supremely perfect, is like an object in motion which cannot possibly be met with resistance. Its propensity for existence is therefore maximal and unabated – necessary existence follows, or perhaps better, flows from it. Accordingly, one might think Leibniz's account doesn't rely on an E = ∃ thesis as much as it does an E ⇒ ∃ thesis, where the ‘⇒’ is the special ‘flows’ relation. What to say?

First and foremost, ‘⇒’ is not to be understood along the lines of efficient causation. Only things which exist through other things have efficient causes. Rather, God's essence is a non-causal reason for God's existence.

Even so, how can God's essence be an explanatory resource for God's existence without itself existing? As Leibniz himself says, ‘existing things cannot derive from anything but existing things’ (AG, 152). Mustn't God's essence already have a ‘foothold in existence’ (to use Robert Adams’ phrase (Adams (Reference Adams1994), 176) ) before it can have a propensity to exist? Adams’ phrase is particularly apt, as on this account, thanks to His essence, God appears to bootstrap Himself into being – the same metaphysical absurdity in Spinoza which earned Schopenhauerian invective.

Adams is sensitive to the apparent absurdity. He writes: ‘It seems that he [Leibniz] explains God's existence by God's essence, and he explains the reality of all essences, including God's, as depending on God's existence’ (ibid., 176). In other words, because Leibniz also thought that all essences and necessary truths in general ultimately depend on God (e.g., AG, 218–219), the apparent circularity is that, on the one hand, essences exist because God exists, but on the other, God exists because His essence is such that He must exist. If ‘because’ and ‘dependence’ here are understood as relations of priority, the circularity is plain. And there is reason to treat them that way: to meet the explanatory demand of the PSR, they must be explanatory relations where one thing is explained by reference to something prior. So understood, I don't see any way around the vicious circularity of saying both that God's essence is prior to God's existence and that God's existence is prior to God's essence.

In defence of Leibniz, Adams cautions that ‘we must be careful . . . not to foist on Leibniz claims of priority to which he is not committed’ (ibid., 185). Adams suggests that all Leibniz needs to say here is that there is a mutual dependence between God's existence and God's essence in the same way there is between necessary truths and God's understanding. He writes:

Because anything at all entails a necessary truth, there are mutual entailment relations between necessary truths. For example, if ‘1 + 1 = 2’ and ‘whatever has a shape has a size’ are necessary truths, then each will entail, without seeming prior to, the other. Thus we find in Leibniz, according to Adams, not an E ⇒ ∃ thesis, but an E ⇔ ∃ thesis, where ‘⇔’ is something like mutual modal entailment.

Unfortunately, this sort of relation just doesn't seem robust enough to deliver the requisite explanatory goods. There remains an apparent explanatory asymmetry between God's understanding and necessary truths that is not there between ordinary cases of mutual necessary entailment. God's understanding explains what necessary truths there are, not vice versa, even if just those necessary truths modally entail that they are understood by God. The same is true of the relation between God's essence and existence, as, according to Leibniz, the divine essence's propensity for existence is supposed to explain God's existence. In both cases, the former is explanatorily prior to the latter, even if each mutually entails the other on account of their necessity. To all appearances, God's essence is ‘naturally prior’. So what, then, explains it?Footnote ¹⁸ It has a maximal propensity to exist, we are told. But it must first exist to have a propensity to exist. If, in the end, there just is no distinction between God's essence with its maximal propensity to exist and its existing, then we are once again back to the E = ∃ thesis or one similar.

The UPSR

‘If everything has a cause, then what caused God?’ So goes the common objection to ‘the’ cosmological argument that no philosopher of repute has ever defended. This fact has not deterred philosophical freshman and professional alike from triumphantly raising it, however, which has led more keen observers to label it ‘the straw man that will not die’.Footnote ¹⁹ Amazingly, the straw man has been alive and well for more than a century. One finds Richard Clarke, for instance, complaining of it in his logic text from the 1880s! In all fairness, the beloved straw man may owe its endurance in part to the wide range of meanings the word ‘cause’ has had in metaphysics generally, and in cosmological arguments in particular. There are, of course, Aristotle's four causes, but it is also not uncommon to see any of them referred to as grounds or reasons, or seemingly interchangeable uses of the terms ‘cause’, ‘ground’, and ‘reason’.Footnote ²⁰

This being the case, as Clarke goes on to clarify, the objector may be confusing the theist's appeal to a law of causality with a different law:

Everything, including God. It is no straw man, therefore, to ask ‘then what's God's explanation?’ No doubt such an unrestricted PSR (hereafter UPSR) that gives rise to our question, despite its eminent pedigree, will strike many contemporary ears as unduly strong. Indeed, it often seems as if there's a running contest to see who can articulate the most modest PSR that still has extramundane implications.Footnote ²¹ But theists – and philosophers in general – should not be so quick to distance themselves from the UPSR for several reasons.

Aristotle famously remarked in the preface to the Metaphysics that philosophy begins in wonder. As explanations are found first for ‘obvious difficulties’, we advance little by little to ‘greater matters’ such as ‘the phenomena of the moon and those of the sun and the stars, and finally about the genesis of the universe’ (982b 13–17). This quest for explanations of things doesn't diminish when applied to ‘greater matters’, it intensifies, whether you take the explanatory ultimate to be God, the universe, or something else. So it is not surprising to see the UPSR front and centre in that quest, as it is in the accounts surveyed here, among others.Footnote ²² Contemporary philosophers should keep in mind that while appealing to some restricted PSR may have certain dialectical advantages, dressing modestly is only a virtue in public. It is the UPSR that drives naked rational inquiry.Footnote ²³

Furthermore, the most common arguments for the PSR – that it is a necessary presupposition of reason, that it underlies inference to the best explanation, that it is self-evident, that it is heretofore exceptionless, that denying it entails radical scepticism – all seem wholly general, supporting not just some modest PSR, but the UPSR. It is also worth pointing out that the UPSR assumed throughout above, as formulated about the existence of things, is not subject to the problem of modal collapse which faces restricted formulations about contingently true propositions or facts.Footnote ²⁴

Moreover, if any PSR gives purchase to Leibniz's pre-eminent question ‘Why is there something rather than nothing?’, it is the UPSR. The question, after all, is not ‘Why is there something contingent rather than not?’ The proper contrast is between existence and non-existence, the former but not the latter requiring explanation, since ‘nothing is simpler and easier than something’ (AG, 210).Footnote ²⁵ Thus, interpreted prima facie, Leibniz's question is really a statement with an unrestricted universal quantifier: for any x, if x exists, there is a reason for x's existence. In this way, the UPSR is actually simpler than a restricted PSR; the latter invites the additional question of why the scope is restricted to some particular domain. Those who prefer some restricted PSR will have to answer Schopenhauer's accusation of treating the need for explanation like a taxicab to hire and dismiss when it suits one's purposes (see Gale & Pruss (Reference Gale and Pruss1999), 469). Unlike a taxicab, the canonical PSR – the UPSR – rides you along with everything else to its destination.

Explaining everything

For the sake of the metaphysically bashful, let us set aside the UPSR as a metaphysical principle. Just as a matter of good methodology of rational inquiry, positing something brute and inexplicable still carries a cost, which one may want to pay only as a last resort. We should push the chain of explanations as far as possible.

Although it is common to stop explanation at the foot of necessity, even this can be bad practice. A necessary being might well be a good ultimate explanation of the chain of contingent beings, but a chain of necessary beings will no less require ultimate explanation in something relevantly different. There is nothing about necessity just as such that is buck stopping, as made evident by the fact that attempts to explain various necessities are commonplace. Moral properties and truths, for example, are often thought to be necessary, yet they seem positively to cry out for explanation (see Adams (Reference Adams1999), Ganssle (Reference Ganssle2000) ). We recognize this even with respect to beings whose essence implies necessity. Certain abstract objects, such as numbers, are such that if they possibly exist, they necessarily exist. That is their nature. And yet, even if we infer from this that they exist, we recognize that explanations of why they exist are not thereby foreclosed. Do they exist in virtue of a certain function and properties, as Bob Hale has argued (Hale (Reference Hale2013), 175ff.) )? Are they, along with other abstracta, the by-product of God's mental and causal activities, as many theists have contended (Leftow (Reference Leftow2012) )?

The point is worth emphasizing, as it might be thought that the central problem with the accounts of Anselm et al. is whether necessary existence is coherent and intelligible. Not only would that be to misunderstand them, but philosophers have to my mind shown the concept of necessary existence to be perfectly coherent and intelligible (see Plantinga (Reference Plantinga1974) and Pruss & Rasmussen (Reference Pruss and Rasmussen2018) ).

The problem, rather, is how there can be an explanation of something which exists a se (necessity and aseity are often erroneously conflated). And it's hard to see how there can be, given precisely the structural features of explanation presupposed in arguments for a being that exists a se. All of the philosophers we looked at (with the possible exception of Spinoza), among many others, offer variants of something like the following argument. No thing can bootstrap itself into being any more than something can come from nothing; beings have explanations (UPSR). But beings can't be explained by other beings ‘all the way down’ in the manner of turtles. Nor can beings explain each other in a circle. The chain of beings explained by other beings must therefore be grounded by something whose explanation is in itself.Footnote ²⁶ QED. Note carefully how the structure of explanation here is assumed to form a strict order (it is irreflexive, asymmetric, and transitive).Footnote ²⁷ Yet when it comes to explaining the being that exists a se, all the accounts we looked at renege on this assumption. The E = ∃ thesis seems to require God's explanation to be reflexive. Anselm's mutual relations between essence, to be, and being seem to require explanation to be symmetric, as does Leibniz's E ⇔ ∃ thesis. But if we reject reflexive (bootstrapping) and symmetric (circular) explanations when explaining beings which exist ab alio, why accept them when explaining a being which exists a se?Footnote ²⁸