Aseity and the Bootstrapping Problem

The last two rungs kept returning to one idea without examining it. Independence from anything external generated simplicity, forced timelessness, produced impassibility, and was the thing neo-classical theism was willing to trade away. It is time to look at it directly, because when you do, a problem appears that the classical tradition did not see coming and that has occupied a substantial literature since the mid-1980s.

The problem is not raised by atheists. It is raised by theists, against other theists, and it concerns numbers.

The doctrine

Aseity is not a fringe commitment that a theist could quietly drop. It is what the creeds assert when they call God the maker of all things visible and invisible, and the prologue of John's gospel makes the same claim in the strong form, saying that everything that came to be came to be through the Word and that nothing that exists came about apart from it. It is also what the arguments of rungs 1 through 3 concluded to, since a first cause that depended on something would not be first and a necessary being that owed its nature to something else would not be the terminus of the explanation.

Two claims are bundled inside it, and separating them matters for what follows. The first is that God does not depend on anything. The second is that everything other than God depends on God. A being could satisfy the first without the second: an isolated necessary being alongside other independent things would exist from itself while not being the source of anything else. Classical theism asserts both, and it is the second that runs into trouble.

The challenge

Consider the number seven. It seems to exist. Mathematical statements about it are true, and the most natural reading of a true statement is that the things it talks about are there to be talked about. It also seems to exist necessarily, since there is no possible situation in which the sequence of natural numbers has a gap. And it does not seem to have been made by anyone, since making something takes a process and there was never a time before there were numbers.

This argument is not aimed at theism and was not devised with theism in mind. It comes from twentieth-century philosophy of mathematics, and its force is independent of anything religious. But if it succeeds, the theist has a problem, because numbers now join the inventory of what exists, and they have exactly the profile aseity reserves for God: necessary, uncreated, not dependent on anything.

Nor is the difficulty confined to mathematics. Properties, propositions, possible worlds, and sets have all been argued to exist as abstract objects, and the count runs high. Realists about properties hold that "the ball is red" is true because there is a property, redness, that the ball exemplifies. If properties are uncreated abstract objects, then God exemplifies omnipotence, goodness, and knowledge only because those properties are available to be exemplified, and God's being what he is depends on items God did not make.

Not every abstract object presses equally hard, and it is worth sorting them before looking at the responses, because the options that work for one category fail for another.

Numbers are the loudest case but arguably the easiest, because nothing about God's own nature depends on them. A theist who ends up saying that arithmetic is a useful fiction has said something many philosophers of mathematics say for reasons of their own, and has given up nothing theological.

Properties are harder, because God has them, or at least is described as having them. If exemplifying a property requires the property to be there, then the answer to what makes God omnipotent points away from God.

Propositions are harder still, because the theistic claims themselves are propositions. If the proposition that God exists is an uncreated abstract object, then something not made by God has been true from all eternity, and that truth is not one God brought about.

The worst case is God's own essence. Whatever else can be argued to be a divine product, the nature that makes God the being he is cannot plausibly be something he decided on, since deciding presupposes the nature. Anyone who takes the strong reading of aseity has to say something here, and the two available answers are that God has no nature distinct from himself, which is the simplicity doctrine of rung 4, or that God's nature is uncreated but not distinct enough from God to count as an exception. The second answer is harder to state than it sounds.

Michael Bergmann and Jeffrey Brower press this as a straightforward incompatibility, in "A Theistic Argument Against Platonism (and in Support of Truthmakers and Divine Simplicity)", published in Oxford Studies in Metaphysics volume 2 in 2006. Their claim is that no theist can consistently be a Platonist about properties, and their preferred exit is the truthmaker account that rung 4 met in the context of simplicity: predications about God are made true by God, and no distinct property is required. The two problems turn out to be the same problem approached from different sides.

Creating the abstract objects

The boldest theistic response is to accept that abstract objects exist and to bring them inside the scope of creation.

The vocabulary here is not stable, and it is worth flagging rather than papering over. Morris and Menzel introduced both terms in the same paper, later writers have used them with different scopes, and William Lane Craig has published a plea for terminological uniformity precisely because the literature had drifted. The usable distinction, and the one this rung follows, is that absolute creationism is the thesis and theistic activism is a particular mechanism for it. Someone could hold the thesis while giving a different account of the mechanism.

The appeal of the activist version is that it does not treat creation of the abstract as a strange event. Nothing is manufactured, nothing is assembled, and there is no moment before which numbers were absent. There is an eternal activity, and abstract objects are what that activity produces, in something like the way a thought's content is produced by the thinking of it. The activity being necessary, its products are necessary, which explains why mathematical truths could not have been otherwise without making them independent of God.

The circle

Then comes the objection, and it is not an objection anyone had to look hard for.

A second version runs through propositions and is harder to shrug off, because it does not depend on any assumption about what a property is. On theistic activism, the proposition that God exists is a product of God's thinking it. But God's thinking it is an activity performed by a being that exists, so the proposition is true whether or not it is thought, and its being true is not something the thinking accomplished. The activist can reply that being true and existing come apart, so that the proposition owes its existence to God's activity while owing its truth to God's existence. That reply is available. It also concedes that there is at least one thing about the abstract realm that divine activity does not settle, which is a smaller concession than the objection wanted but not nothing.

The dilemma is clean, which is why it has stuck. It is also, importantly, a problem for the theist and not for anybody else. A Platonist atheist is untroubled by uncreated properties, and a nominalist has no properties to worry about. Only someone who wants both a full inventory of abstracta and an unrestricted doctrine of divine sourcehood is caught.

Menzel returned to it thirty years later, in "Problems with the Bootstrapping Objection to Theistic Activism" in the American Philosophical Quarterly in 2016, arguing that the objection does not survive scrutiny. The defence turns on the word "prior" in the third premise. The objection needs an ordering in which God's having the property comes before God's producing it, and the activist denies that there is any such ordering: the activity is eternal, has no stages, and is not a sequence of steps in which one thing is settled and then the next. What the activist offers instead is a single necessary activity in which God's having the properties and God's producing them are two descriptions of one state of affairs rather than two events standing in a relation of dependence.

Whether this answers the objection or renames it is the live question. Critics reply that dropping temporal priority does not help, because the objection can be restated in terms of explanatory priority, which does not require time. If the fact that God has the power to create explains the fact that properties exist, and the fact that properties exist explains the fact that God has the power to create, then two facts each explain the other, and that is a vicious circle whether or not anything happens in a sequence. The activist's answer has to be that there is no explanatory priority in either direction, which amounts to declaring the whole configuration primitive. That is a coherent position. It is also a considerable retreat from the explanatory ambitions that motivated aseity in the first place.

The mind of God

A second route keeps abstract objects but denies that they are created things at all.

This has the best historical credentials of any option on the menu. Augustine's move of relocating the Platonic forms from an independent realm into the mind of God was the standard medieval settlement, and it was made for very nearly the modern reason: an independent realm of eternal exemplars is a rival to God for ultimacy. Contemporary defenders, Greg Welty among the most explicit, have argued the position in the analytic idiom, and it is one of the six positions represented in Paul Gould's Beyond the Control of God? (Bloomsbury, 2014), which sets out the main contenders and lets each answer the others.

The objections to conceptualism are of two kinds. The first is about number and identity. There are more propositions than any mind could entertain as discrete items, including infinitely many propositions about the real numbers, and a defender has to say either that God's thinking is not a matter of discrete items or that an infinite mind can have infinitely many. Neither is absurd, but both weaken the analogy with thoughts that made the position intuitive.

The second is sharper and connects to earlier rungs. Thoughts are ordinarily individuated by their contents, and contents look like exactly the abstract objects that were supposed to be explained. If God's thought that seven is prime is individuated by the proposition that seven is prime, the proposition has not been reduced to the thought; it has been presupposed by it. The conceptualist must say that divine thoughts are individuated some other way, which pushes the account toward something a good deal less like thinking than the name suggests. There is also a tension with simplicity that a classical theist has to face: a God with a plurality of distinct concepts is a God with internal multiplicity, which the previous rungs ruled out.

Brian Leftow's God and Necessity (Oxford, 2012) is the most sustained modern attempt to build a theistic account of modality that avoids these traps. Leftow's project is to ground necessary truths in God without leaving them as independent items God must conform to, and his verdict, after engaging accounts that ground modal truth in the divine nature, is that a voluntarist story in which God's will does much of the work is on balance preferable. That conclusion carries a cost the tradition will feel, since it puts a great deal of modality downstream of a divine choice, and rung 3's discussion of what the modal ontological argument needs is one place where the cost is felt.

The classical shortcut

A Thomist watching this argument will point out that it is a difficulty for a position they never held.

On the classical account there are no properties for God to exemplify, because there is nothing in God distinct from God. The question of whether omnipotence is created or uncreated does not arise, since omnipotence is not an item at all. As for the abstract objects that creatures involve, the classical tradition has a settled account: the divine ideas are exemplar causes, patterns according to which creatures are made, and they are not a population of entities God consults but the divine essence understood as imitable in various ways. A thing is a horse by resembling God in one respect and a stone by resembling God in another, and the plurality is in the resemblances rather than in God.

This is elegant, and it explains why the bootstrapping literature is dominated by philosophers who accept some version of the personalist picture from rung 5. The problem is generated by the combination of a God who has properties and a demand that nothing God has be independent of him. Remove the first and the problem does not arise.

The cost is that the shortcut is only as good as the simplicity doctrine, and rung 4 showed that the doctrine is contested from several directions at once. It also inherits the difficulty about analogy: saying that a horse resembles God in a way a stone does not requires that the respects of resemblance be real and distinct, and if they are real and distinct in God then simplicity is under pressure again, while if they are distinct only in our way of speaking then it is unclear what makes it true that horses and stones resemble God differently. The classical theist has traded a problem about abstract objects for a problem about predication, which is a good trade only if the second problem is more tractable than the first.

Denying the objects

The third route accepts the challenge as stated and rejects the first step: there are no abstract objects to account for.

This is where the theistic dispute rejoins mainstream metaphysics, since nominalism is a live position independent of any theological motivation. If "the ball is red" needs no property to be true, and if mathematical language can be understood without commitment to numbers, then aseity faces no challenge from this quarter and the entire preceding argument dissolves.

William Lane Craig's God Over All: Divine Aseity and the Challenge of Platonism (Oxford, 2016) is the fullest theistic treatment. Craig sets out the biblical and philosophical basis for aseity, formulates the challenge in terms of the indispensability argument, and then works through the realist and anti-realist responses in turn, concluding that the theist's most promising options are on the anti-realist side. The menu there is longer than most theists realise: fictionalism, on which mathematical statements are true within a story rather than true; figuralism, on which they are systematically metaphorical; and a family of views on which existential quantification simply does not carry ontological commitment, so that saying there is a prime between two and five is not saying that something exists.

That last option is the one that does the most work with the least revision, and it is also the one that draws the most fire, since it requires a substantive claim about what quantifiers mean that many philosophers of language reject. The general shape of the anti-realist strategy is worth noting: it does not solve the theological problem so much as relocate it into philosophy of mathematics, where it is fought over on entirely secular grounds. A theist who takes this route has bet aseity on the outcome of a debate that has nothing to do with God.

There is a further difficulty the anti-realist route runs into that is specific to theism. Suppose mathematical language is a useful fiction. Theistic language is not, and it quantifies over things that look abstract: God's knowing every truth requires that there be truths to be known, and God's being able to make any of several worlds requires that there be alternatives. A theist who denies that quantification carries commitment when mathematicians do it, and affirms that it does when theologians do it, needs a principled line between the cases. Some anti-realists have one. Drawing it is more work than announcing the position.

Scoring the options

Each route pays for what it buys, and the payments are in different currencies, which is why the dispute has not converged.

Absolute creationism keeps a full inventory of abstract objects and a fully unrestricted doctrine of divine sourcehood, and pays by having to declare the relation between God and his own properties primitive. That is not a refutation, since every metaphysics stops somewhere, but it stops at exactly the place the doctrine was supposed to explain.

Divine conceptualism keeps the objects and avoids any act of creation, and pays in the individuation problem and in a plurality inside God that the classical tradition ruled out. It is the most historically respectable option and the one whose modern form is furthest from what its historical proponents meant.

The classical shortcut avoids the problem entirely and pays the full price of the simplicity package, including modal collapse and the analogy difficulty. It is the only route on which the problem never arises rather than being solved.

Anti-realism keeps aseity intact at no theological cost and pays by staking the doctrine on a contested position in the philosophy of mathematics that will be settled, if it ever is, by people who have no stake in the theological question.

Restricting aseity to concrete reality costs nothing locally and weakens the arguments of rungs 1 through 3, since those arguments concluded to an unrestricted ultimate. The pattern across all five is worth noticing: nobody gets the full doctrine free, and the choice is which bill to accept.

Next

Aseity concerns where things come from. The next rung concerns what keeps them here. Classical theism holds that creation is not a single past event but a continuing dependence, so that a world left to itself would not persist but would cease. The rival thesis is that things have a tendency to stay in existence on their own, and settling between them turns out to determine how much work there is for God to do at every moment, and whether creaturely causes do any real work at all.