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A Scotistic Cosmological Argument Remixed:

New Pathways from Cosmological Premises to the Existence of God

 

Abstract

In this paper, I’ll sketch a novel Scotistic-styled argument for theism within a contemporary metaphysical framework. I’ll draw up a map, identifying a trail from premises to conclusion. Our journey has two stages. In the first stage, I suggest pathways to the conclusion that a necessarily existing thing exists. In the second, I indicate pathways to the conclusion that the necessarily existing thing is an infinitely powerful and knowledgeable personal agent. The new routes I mark out avoid traditional obstacles between cosmological premises and theistic conclusions. I believe the map will be useful for future work on cosmological arguments of this sort.

 

 

 

 

 

 

 

 

 

 

 

 

 

§1. Introduction

In this paper, I’ll sketch a novel Scotistic-styled argument for theism within a contemporary metaphysical framework.[1] I’ll draw up a map, identifying a trail from premises to conclusion. Our journey has two stages. In the first stage, I suggest pathways to the conclusion that a necessarily existing thing exists. In the second, I indicate pathways to the conclusion that the necessarily existing thing is an infinitely powerful and knowledgeable personal agent. The new routes I mark out avoid traditional obstacles between cosmological premises and theistic conclusions. I believe the map will be useful for future work on cosmological arguments of this sort.

I’ll begin by situating the map into a contemporary metaphysical framework. Then I’ll mark out the various pathways in the two stage argument and indicate the argument’s advantages over contemporary cosmological arguments. In the final section, I’ll show how the argument survives some of the most challenging objections to be raised against cosmological arguments since the time of Hume and Kant.

§2. The Contemporary Scotistic Cosmological Argument

Scotus’s argument is out of date. In the updated version, I’ll make use of contemporary developments in logic and metaphysics. Two important products of 20th century metaphysics relevant to the argument are (i) systems of modal logic, which enable reasoning about the possible and the necessary, and (ii) theories of states of affairs, which enable thinking about non-actual situations. With respect to modal logic, I’ll assume the axioms of S5.[2] The key insight of S5 is that if it is possible that it is necessary that A, then it follows that it is simply necessary that A. For example, if it is possible that it is necessary that Goldbach’s conjecture is true, then it is necessary that Goldbach’s conjecture is true. S5 applies to broadly logical possibility—that is, to the way things could have been. I’ll make use of states of affairs and possible worlds, where a possible world is a total way things might have been (e.g., a maximal state of affairs or maximal proposition.) On to the argument. 

§2.1 Stage 1: A Necessarily Existing First Cause

Duns Scotus offers the following causal principle, “Anything to whose nature it’s

repugnant to receive existence from something else, can exist of itself if it’s able to exist at all.”[3] Scotus proceeds to argue that if it’s possible that a thing exist of itself, then it’s actual that it do so.[4] Since a necessary individual is such that if it possibly exists, then it actually exists, I will understand Scotus’ principle to be this: Any individual that can’t be caused is a necessary individual. In contemporary terms, Scotus’s causal principle can be expressed as follows:

(1)   ("x (x is an essentially uncaused individual[5]) → (x is necessary)),

 

where

 

(2)   x is necessary =def x exists in all possible worlds.

 

 (1), by contraposition, is equivelent to

 

(3)   ("x (~(x is necessary) → (~(x is an essentially uncaused individual))).

 

(3) states that necessarily, for every x, if x is contingent, then x isn’t essentially uncaused. I’ll add that (3) is only concerned with concrete individuals (what philosophers sometimes call substances) such as rocks, jellybeans, people, fundamental particles, and so on.                  

(3) appears to be a relatively modest causal principle. Cosmological arguments standardly rely on a stronger causal principle (or principle of explanation), such as Leibniz’s principle of sufficient reason. Let’s consider a few representative examples of modest causal principles in recent cosmological arguments and see how (3) compares. Consider first the causal principle offered by Richard Gale and Alexander Pruss. Their principle can be put like this:

For every contingent state of affairs S, if S obtains, it’s possible that S’s obtaining has an explanation.[6]

 

That principle has been shown to entail the principle that necessarily, if a contingent state of affairs obtains, its obtaining has an explanation—a principle that faces notoriously difficult problems, none of which threaten (3).[7]

Consider a second example of a recent, modest causal principle offered by Robert Koons:

Normally, for every wholly contingent state of affairs S, if S obtains, then S has a cause, where S is wholly contingent just in case it includes only contingent entities.[8]

 

It avoids some of the difficulties that the Gale-Pruss principle faces.[9] It’s much stronger, however, than (3), for (3) only requires that wholly contingent states of affairs of a limited variety are such that if they obtain, their obtaining is possibly caused. Also, the state of affairs consisting in a contingent individual freely performing an action appears to be a wholly contingent state of affairs. But some—especially those attracted to libertarian views of agency—may doubt that such a state of affairs could even possibly be caused to obtain. (3), by contrast, does not require that actions possibly be caused. For (3) is restricted to concrete individuals. I don’t offer a definition of a concrete individual, but I believe that we have enough grasp of concrete individuals to say that actions are not among them. So, (3) has advantages over Koons’ causal principle.

Finally, consider the principle in the Kalām cosmological argument:

Whatever begins to exist has a cause.

This causal principle faces a difficulty that’s similar to the one Koon’s principle faces. Consider the event of Paul Moser freely raising his arm. That event, supposing it existed, had a beginning. Yet it may not be the sort of thing that can have a cause. If it were, then as William Rowe observes, it seems that we must posit a further event: the event of the causing of Paul Moser freely raising his arm, and this event too would have a beginning and so require a cause. Ad infinitum.[10] (3) faces no analogous difficulty.

One might modify the causal principle so that it applies to the concrete individuals but not to events and then suppose that the universe is a concrete individual.[11] In addition to the difficulty of establishing the universe is a concrete individual that began to exist, we may ask whether it is as plausible that a universe have a cause (if it begins) as that a contingent individual possibly have a cause. It’s not easy to say which principle wins out.[12] Yet, I suspect that at least some will count (3) as the more modest principle, since it only requires that contingent individuals possibly have a cause.[13]      

Therefore, it appears that although causal principles in notable contemporary cosmological arguments are more modest than principles of earlier times, they may not exceed or even reach the level of plausibility enjoyed by the causal principle offered by Scotus in the late-thirteenth century. An argument for the existence of a necessary individual whose salient building block is (3) will, I believe, exhibit an advantage over contemporary cosmological arguments so far developed.

But how are we supposed to derive the existence of a necessarily existing first cause using (3)? Scotus combines (3) with a defense of

(4)   ◊($x (x is an essentially uncaused individual)).

It’s not hard to show that (3) and (4) together entail the existence of a necessary individual. (3) entails that necessarily, every contingent individual can have a cause, and (4) entails that an individual can exist which cannot have a cause. It follows, therefore, that an individual can exist which is not contingent—that is, it’s possible that there be a necessary individual. If we grant the S5 axioms of modal logic, then it follows that there actually is a necessary individual.[14]

            (4) may initially seem like a modest premise. After all, isn’t it intuitively plausible that it’s at least possible for there to exist an essentially uncaused individual? A couple defenders of Scotus’ argument think so.[15] However, I believe that is too quick. For there is what appears to be an equally plausible principle that is inconsistent with (4), namely:

(5)   ◊ (~$x (x is an essentially uncaused individual)).

(5) merely claims that there’s some possible world lacking an essentially uncaused individual. Thus, (5) appears to be just as plausible in its own right as (4).

But if we wish to retain (3), then either (5) or (4) must go. Here’s why. Given (3), any essentially uncaused thing must be a necessary individual. Given (5), it’s possible that there isn’t an essentially uncased individual. From these two principles it follows that it’s possible that there not exist a necessary individual. And if it is possible that there not be a necessary individual, then there really isn’t one, since if there were a necessary individual, it would be necessary that there be one (by S4). But recall that (3) and (4) jointly entail that there is a necessary individual, which contradicts the above result that there isn’t one. Therefore, (5) is inconsistent with the conjunction of (3) and (4). So, if we keep (3), then we must give up either (4) or (5).

But which one should we give up?[16] Fortunately, there’s a way to defend (4) over (5) by countenancing a tweaked version of (3). To show how, I’ll introduce a few more defintions and a new causal principle:

(6)   Producible individual =def An individual whose existence is capable of being caused.

 

(7)   Producible state of affairs S =def A possible state of affairs of producible individuals, xs, existing.[17]     

 

(8)   "x ((x is a producible state of affairs) → ◊(x’s obtaining is causally explained)).

 

I’ll say that the obtaining of S is causally explained just in case every individual in S has a cause and at least one individual in S has a cause that is not in S.[18] It seems that the existence of a bunch of individuals, no matter how many, is not explained solely by causally linking the individuals to one another. It seems, therefore, that something not included in the bunch must provide causal contribution if their joint existence is to be explained.[19] But even if it were possible for the existence of a bunch of individuals to be explained without reference to an external cause, (8) makes the modest claim that (necessarily) the existence of every bunch could have an external causal explanation.[20], [21]

Cosmological arguments traditionally rely on the intuition that the existence of contingent things cries out for an explanation. Many have thought, for example, that the fact that some contingent things exist rather than none at all cries out for an explanation. But it may be possible to make do with a more modest intuition: the existence of contingent individuals could have an explanation in terms of an external cause. More precicely put, for any given contingent individuals, the fact that those individuals exist rather than not could have an external causal explanation. (8) is still a tad more modest: for any given producible individuals, the fact that those individuals exist rather than not could have an external causal explanation.

I’ve surveyed some philosophy students and professors to see what they think about (8), and most, so far, expressed an inclination (often a very strong one) to believe it.[22] Still, some might hesitate to grant that the above principle applies to every producible state of affairs. They may be more comfortable with a defeasible version of (8):

(8N) (Normally) "x ((x is a producible state of affairs) → ◊(x’s obtaining is

       causally explained)).

 

According to (8N), for any given producible state of affairs, one may infer that its obtaining can be causally explained unless one has a good reason for thinking that the state of affairs in question is an exception to the rule. The idea is that although we may have evidence (conceptual and emperical) to support (8), perhaps someone can find evidence concerning certain cases for thinking that they are exceptions. That person may, however, find no evidence against the cases we’ll consider next—maximal producible states of affairs. She will still like our argument then, even if she doesn’t grant (8). So (8N) may be more appealing than (8). But to simplify matters, I’ll work with (8).               

            Surprisingly, (8) can be used to support (4). Here’s how. Suppose that some producible states of affairs are maximal, where one is maximal if and only it entails every producible state of affairs consistent with it. For example, the state of affairs of all possible producible individuals[23] jointly existing is maximal. It’s maximal since it entails every producible state of affairs. I’ll return to the question of whether any such maximal state of affairs is possible—can obtain. But for now, let’s assume that there is at least one maximal, producible state of affairs, M, which, since it is producible, can obtain.

Now if (8) is true, then it’s possible that M’s obtaining is causally explained. But it would be impossible for a producible individual to cause M to obtain. The reason is that any producible individual whose existence is consistent with M is included in M and so cannot (by definition) be the cause of M.[24] Therefore, if it’s possible that M’s obtaining be causally explained, then it’s possible that there is an individual that is not producible—that is, not possibly caused. Therefore, (4) follows.[25]

We’ve found a pathway from (8) to (4). That’s the good news. The bad news is that the pathway requires a somewhat precarious step. It requires that we accept that

(9)   $x (x is a maximal, producible state of affairs).

(9) may indeed be true, but I don’t know any easy way to prove it definitively. I don’t take this news as being too bad, however. First, I have a few considerations to offer in support of (9)—considerations that serve to make (9) rationally acceptable, even if not rationally compelling to everyone. Second, there are paths nearby that take us to (4) without requiring (9). The next sections, therefore, are devoted to supporting (9) and marking out alternate, nearby paths that lead to (4).

§2.1.1 Maximal Collections

Is any possible collection[26] of producible individuals maximal? That is, is there a maximal producible state of affairs? To see why we might believe so, consider more closely what denying the possibility of maximal collections amounts to. If (9) were false, then no possible collection of individuals would be a maximal one—each would be consistent with at least one other individual.[27] Here’s a thesis that follows:

(I)   No possible producible individual is radically inconsistent, that is

       inconsistent with all other possible producible individuals.

 

Suppose (I) were false and that there could be a producible individual that is radically inconsistent, call it c. Then the state of affairs of c’s existing would be a maximal producible state of affairs, since it entails every producible state of affairs consistent with it. That is, it entails c’s existing and no other producible state of affairs. So, there would exist a maximal producible state of affairs.

My plan is to indicate a path from the denial of (9) to a principle that appears to be in tension with (I). That principle is this:

(II)   Some possible producible individuals are inconsistent with some possible

         collections of producible individuals.

 

For now, I wish to point out a certain tension between (I) and (II). (II) requires that at least some individual be inconsistent with at least some possible collection of individuals, whereas (I) prohibits any individual from being inconsistent with every possible collection. But if we thought that a radically inconsistent individual were not possible, then we may feel uneasy about supposing that it is nonetheless possible for there to be an individual that is inconsistent with at least some possible collections of producible individuals. That is, we may feel uneasy about supposing that there can’t be producible individuals that are radically inconsistent and yet, by the same token, there can be ones that are inconsistent with some possible collections of producible individuals. Why should individuals be such that they can be inconsistent with some collections but can’t be inconsistent with every collection?

So here’s the situation. (I) and (II), though logically consistent, are not friendly bedfellows. If we thought that there couldn’t be radically inconsistent individuals, we may be tempted to think that individuals are (by their nature) consistent with one another—that is, no individual necessitates the non-existence of any others; and yet if we thought that individuals could be inconsistent with one another, then we may be tempted to think that there could be individuals that are (by their nature) inconsistent with every other individual (of the producible variety, at least). Thus, we want to avoid having to affirm both (I) and (II).

We already saw that if (9) is false, then (I) is true . What about (II)? Would it be true too? Well, suppose (II) were false. Then every possible producible individual would be consistent with every possible collection of producible individuals. It follows that for every possible collection of producible individuals C, there is a possible collection that contains a producible individual not in C. It also follows that for any two (or three, or four, etc.) possible collections of producible individuals that have a finite number of members, the union of those collections is also a possible collection.[28] It might be tempting, therefore, to suppose that no matter how many possible collections of producible individuals having a finite number of members you have in hand (even infinitely many), the union of all of them forms a possible collection. If one did suppose that, then one would, I think, be committed to the existense of a maximal, possible collection, namely, the union of all the possible collections of producible individuals that have a finite number of members (given the plausible assumption that every possible collection is itself a union of possible subcollections having a finite number of members).[29] So, one would be committed to thinking that if (II) is false, then (9) is true; and therefore, to thinking that the denial of (9) implies (II).   

            We should be careful about giving into temptation, however. For the denial of (II) doesn’t obviously imply that all unions of possible collections are themselves possible collections. To see why not, suppose that space is necessarily Archimedian, such that the cardinality of the set of distinct locations in space is À1. Suppose also that it’s impossible for any two objects to occupy the same region of space. Finally suppose that for every possible shape, there is a distinct possible object that can have that shape. Then, since the cardinality of the set of shapes on Archidedian space is À2, the cardinality of the set of possible spatially extended objects is À2 (at least). It follows that a collection consisting of all possible extended objects isn’t possible, even if every subset whose cardinality is finite (or even À1) is possible. There just isn’t enough space to fit in every possible extended object. So, some unions, at least, may be impossible, even if (II) is false. We might say that it’s the size of some collections that blocks them from being possible.

            Nevertheless, here’s a reason to think that size doesn’t block every maximal collection from being possible, even if it does block some. Suppose it is possible for there to be an individual o that’s infinitely extended in all possible dimensions. If so, then if (3) is true, o is possibly caused. Since o necessarily occupies all of space, the only possible cause of o must itself, while it is causing o, occupy no space.[30] Therefore, it is possible that there be an individual that doesn’t occupy space. Now it’s hard to see why there should be a size problem preventing maximal collections of unextended individuals from being possible. You can have as many angels dancing on the head of a pin as you’d like! And if one denied (II), then it would be tempting to think that all unions of unextended individuals would be possible. Here I think giving into temptation may be the right thing to do. After all, if (II) is false, then no unextended individual is inconsistent with any other or with any possible finite collection of them; and furthermore, size doesn’t seem to block infinite collections of unextended individuals from being possible.[31] But if there can be maximal collections of unextended individuals, then by adding o to one of them, we get a possible, maximal collection of producible individuals—that is, a maximal producible state of affaris.

In summary, there seems to be some support for thinking that the denial of (9) implies both (I) and (II). And there’s also some support for thinking that (I) and (II) can’t both be true. So if (9) is false, we have problem. Some may find this problem serious enough to grant (9). Yet, there may be others who would find the support I’ve offered too tenuous to yeild confidence that any maximal collection is consistent. For them, I will offer some alternative paths to consider.   

 §2.1.2 Alternate Paths

There are a couple paths in the vicinity that don’t require the possibility of a maximal collection of producible individuals. Each makes use of a slightly different causal principle. The first path I’ll mark out uses this principle:

(8II) ◊ (The obtaining of the state of affairs of there being at least one producible

           individual existing is causally explained).

 

According to (8II), it is possible for there to be a causal explanation as to why at least one producible individual exists. (8II) is an instance of this more general principle: For any sort of producible individual S, it’s possible for there to be a causal explanation of the obtaining of the state of affairs of there being at least one member of S. For example, the state of affairs of there being at least one emerald is one whose obtaining can, it seems, be causally explained. In general, the causal explanation for why there are the members of a sort that there are (e.g., why there are the emeralds that there are) may also count as the causal explanation for why there are any members of that sort (e.g., why there are any emeralds). So, (8II) doesn’t require causal explanations over and above (distinct from) those that causally explain the obtaining of a producible state of affairs. (8II) makes a relatively modest claim. It requires only that there could be a causal explanation as to why at least one producible individual exists.[32] I think at least some will find (8II), as well as the more general principle of which it’s an instance, to be plausible. 

            Now it may be plausible to think that an explanation as to why there are any members of a given sort S can’t itself be one of the members of S. For example, the explanation as to why there are any emeralds can’t itself be one (or more) of the emeralds, it seems. After all, the causal activity of an emerald will never tell us why there are any emeralds in the first place. Thus, many, I think, will be inclined to grant that

(8III) For any sort of producible individual S, the state of affairs of there being at

         least one member of S can’t be causally explained by a member of S.

 

Now the path to our destination is just a few small steps. Given (8III), it’s not possible for a producible individual to causally explain why there are any producible individuals. More precisely, there is no world in which a producible individual causally explains why the state of affairs M of there being at least one producible individual obtains. Thus, if it’s possible for M’s obtaining to be causally explained, then it’s possible for there to exist an individual that isn’t producible. So, (4) follows, which was our destination.

            Let’s turn to another route to (4). This one depends upon the following causal principle:

(8IV) ◊ (The obtaining of the state of affairs of there being at most one producible

                    individual existing is causally explained).

According to (8IV), it is possible for there to be a causal explanation as to why there is at most one producible individual. A reason one might accept (8IV) is that it’s an instance of certain general principles, each of which one may find plausible. They are these:

            (8V)  For any sort of producible individual S, ◊ (The obtaining of state of affairs of

                    there being exactly the members of S that there are is causally explained).

 

(8VI) "xy ((x and y are producible state of affairss) → ◊(the state of affairs of x’s

        obtaining and of y’s not obtaining is causally explained)).

 

Consider first, (8V). According to it, for any given collection of producible individuals of a certain sort, it’s possible to causally explain why there are exactly the members of that sort that there are. For example, let’s say that there are exactly 55 emeralds. Then according to (8V), it should be possible for there to be a causal explanation as to why there are exactly those emeralds. The explanation may simply be whatever it is that explains why there are the emeralds that there are. In general, the causal explanation for why there are the members of a sort that there are (e.g., why there are the emeralds that there are) may also count as the causal explanation for why there are the members of that sort and no more (e.g., why there are at most 55 emeralds).

            Turn to (8VI). According to it, it is possible to explain why individuals don’t exist. For example, suppose that Socrates never existed. Then it’s possible to explain why not. I won’t require that the explanation of what doesn’t exist be over and above (distinct from) the explanation of what does exist. (Nor do I require that the explanation not be distinct). Whatever individuals produced (or, perhaps, “caused” by constituting) the 55 emeralds may themselves provide the causal explanation as to why there aren’t more than 55 emeralds. They simply didn’t cause more than 55.

            If either (8V) or (8VI) are true, then so is (8IV). (8IV) is the special case of (8V) in which the sort is being a producible individual and the number of members of that sort is one. (8IV) is the special case of (8VI) in which x is any producible state of affairs and y is the state of affairs of all possible individuals not included in x existing (y may be an impossible state of affairs, but that’s no problem since (8IV) doesn’t require that y possibly obtain.)

            For those who would grant (8IV), our destination is not far off. Let M be the state of affairs of there being exactly one producible individual (or if you have doubts about whether there could be just one, let M be the state of affairs of there being exactly the producible individuals that there are in the actual world). No producible individual not included in M is consistent with M, since M entails that there only be the individuals included in M. Therefore, no producible individual could causally explain M. Therefore, if M is possibly causally explained, then it’s possible for there to be an individual that isn’t producible. Once again, (4) follows.[33]      

§2.1.3 Summing up

            By way of summary, then: I’ve marked out novel paths to Scotistic-styled causal premises: (4), recall, states that an essentially uncaused individual is possible; and (3) states that (necessarily) every contingent individual is possibly caused. These premises jointly entail the existence of a necessary individual. 

Stage II: From a Necessarily Existing First Cause to God

 

I will now propose how one might continue the journey to the conclusion that an infinitely powerful and knoweledgeable personal individual exists.

To ease our travels, it will be handy to take along a slightly more powerful causal principle. Here are definitions and the causal principle:

(10) Gridscape S =def S is a state of affairs such that, for some individuals xs  

                    and some intrinsic properties and/or relations ys, S is the 

        state of affairs of the xs instantiating the ys.

 

A picture might help:

 

 

 

 

 

 

 

(11) Wholly contingent gridscape S def= A gridscape that includes only 

        contingently instantiated properties and/or retations.    

 

(8VII) "x ((x is a wholly contingent gridscape) → ◊(x’s obtaining is causally

          explained)).

 

(8VII) basically says that the instantiation of a bunch of contingent, intrinsic  properties or relations can be causally explained. For example, redness being exemplified by John’s jellybean can be causally explained. I’ll say that the obtaining of a gridscape S is causally explained just in case for every individual x in S and every property or relation y in S, the obtaining of x’s instantiating y has a cause, and for at least one x and one y, the obtaining of x’s instantiating y has a cause that is not in S. When I say that a cause is not in S, I mean there is an individual x and a property y, such that x’s instantiating y is not in S, and x contributes to the causal explanation of S’s obtaining in virtue of instantiating y (perhaps what we have is the event of x’s instantiating y at time t). 

Coming up with a precise definition of intrinsic is notoriously difficult. Some properties seem clearly intrinsic: e.g. being colorful, being square. Others are less clear. Fortunately, I don’t believe there are unclear cases upon which the argument of this paper turns. The point of restricting the principle to intrinsic properties is to avoid certain gerrymandered properties, such as the property of being an x, such that necessarily, for all properties p, the instantiation of p by x cannot be causally explained, whose instantiation obviously can’t be causally explained. (8VII) seems unproblematic when restricted to intrinsic properties.

Some might hesitate to grant (8VII), given its complexity. Consider, however, that (8VII) is very much like (8). According to (8), the existence of a bunch of contingent individuals is possibly causally explained. (8VII) just adds that the contingent intrinsic properties and relations that individuals happen to instantiate is possibly causally explained too. I take that to be a modest addition. Note well: there is no requirement that the explanation for a thing’s having certain properties or standing in certain relations be distinct from the explanation for that thing’s existing. The causal explanation of John’s jellybean’s  existing, for example, might also be the causal explanation for his jellybean’s being red and for its standing four feet away from Eric’s blue bike. 

A motivation for (8VII) is this. What cries out for an explanation, or at least a possible explanation, is that the individuals just happen to exist or to have certain properties or to stand in certain relations—they needn’t have existed or had those properties or stood in those relations. So, it’s natural to ask, “Why do they exist or have those properties or stand in those relations?” It seems that an answer in terms of a causal explanation should be possible. Or at least, if it is possible to explain why they exist, I expect it would also be possible to explain why they have those properties that they have or stand in those relations that they stand in. I suspect, therefore, that few who accept (8) should be inclined to object to (8VII). Just as with (8), one may prefer a defeasible version of (8VII).[34] 

Using (8VII), we can construct an argument for the conclusion that if there are many necessary individuals, they form a tightly knit family—any relation between them holds necessarily unless it is the result of a freely performed action. But I wish to develop a different argument first. So for now I will assume that if there are many necessary individuals, they form a tightly knit family, call it N. I will come back to the construction of the argument for that assumption. 

§2.1.1 Infinite Power:    

I’ll offer two pathways to the conclusion that N is infinitely powerful. The first is based on a premise recommended by O’Connor[35] and inspired by Scotus’s statement, “if it is finite, it can be exceeded or excelled.”[36] Koons offers a precise formulation of the premise:

(12) For any measurable [finite] attribute A, where A consists in having

       determinable D to degree µ, and any individual x that has A, there is some

       degree such that it is possible for x to have D to degree µ - e or µ + e.[37] 

 

(12) says that if an individual has an attribute to a certain finite degree, then its having the attribute to exactly that degree is a contingent state of affairs (since it could have the attribute to slightly greater or lesser degree). Suppose that is correct. Then, we can show that N has infinite power if having power is an intrinsic property (which it appears to be).  To see how, suppose N has finite power instead. Let’s say that a power is a capacity to bring about a state of affairs or cause it to obtain. If it’s correct to say that some states of affairs require more power to bring about than others, then we can talk about degrees of power that N might have. To simplify matters, I will suppose that premise (9) is true: at least some producible states of affairs are maximal.[38] Let s be one of them. Then let S be a gridscape that includes all and only the individuals in s plus N. S consists in those individuals (the ones in s plus N) having the various degrees of power that they have (had and will have). If (12) is true, then all the properties (powers) included in S are contingent, since they are each had to a finite degree. Although N is a necessary individual(s) and S includes N, S is still a wholly contingent gridscape since it includes only contingent properties. (Note that to explain why S obtains is to explain why the individuals in S have the properties that they have, and such an explanation needn’t involve explaining why the individuals in S exist.) So, by 8VII S’s obtaining can be causally explained.

This is a problem because every possible individual consistent with S is included in S and no individual included in S can provide a causal explanation for S unless it already has power to work with. Yet S specifies how much power each and every individual in S has. So the causal explanation of S must be in terms of individuals having power to causally explain why those very individuals have the power that they do, and surely that’s not possible. Thus, there cannot be an external causal explanation of S, which contradicts (8VII). Therefore, the supposition that N is finitely powerful is false. N is infinitely powerful.

I’ll mark out an alternative path to infinite power. It’s based upon Scotus’ suggestion that an individual that can cause any collection of contingent things to exist must have infinite power to be able to do so.[39] The argument may be filled out as follows. Given the conclusion of Stage I, N can provide an external causal explanation for any and every maximal producible state of affairs.[40] That makes N rather powerful.[41] To reach the conclusion that N is infinitely powerful, one need only add that there is no upper limit on how difficult it is to bring about certain producible states of affairs. That is,

(13) For every producible state of affairs S, there is a producible state of affairs

       that requires more power to bring about than S does. 

    

If (13) is true, then N can’t be limited in power. For if it were, then N couldn’t bring about states of affairs exceeding a certain level of difficulty to bring about. That is, there would be producible states of affairs too difficult for N to bring about. But any such state of affairs s is, if any of our paths in Stage I go through, entailed by a state of affairs S that N can bring about (for example, the state of affairs of there being at least the producible individuals included in s; or a maximal, consistent state of affairs that includes the individuals included in s). And yet S should be no easier to bring about than s. So, N both can and can’t bring about S. To avoid this contradiction, we should say that N is not limited in power. N is infinitely powerful.

            (13) deserves further investigation. But it looks fairly plausible on the face of it. Consider that some states of affairs require more power to bring about than others. (Let’s suppose all producible states of affairs require only a finite amount of power to bring about, for if there are producible states of affairs that require an infinite power to bring about, then it follows immediately that N is infinitely powerful.) According to (13), there is no producible state of affairs that is most difficult to bring about, since for every producible state of affair, there will always be a state of affairs more difficult to bring about. In other words, there’s no upperbound on how difficult a producible state of affairs can be to bring about. For every state of affairs, one can always imagine a “heavier” or “bigger” state of affairs which takes more power to bring about. That seems plausible, given that any upperbound would, it seems, be arbitrary and inexplicable. Thus, (13) is a useful principle for stage II of cosmological arguments that’s worthy of further examination.       

§2.1.2 Volitional Agency:     

Let’s proceed on the route to the conclusion that N is a volitional agent(s). Scotus’ most promising argument for volition is based on the premise that

(14) (N does not possess the capacity to act freely) → (N exercises its causal

        power and thereby produces an effect).[42]

 

The intuition behind (14) is that what makes an action volitional is that it is not causally necessitated. If an individual x is not causally necessitated to exercise its causal power (either by its own nature or by the causal action of another individual), then x’s exercise

of causal power is contingent and so free. Some are content to grant (14).[43] However, a popular view among contemporary theorists is that there can be “exercises of causal power” that do not necessitate their effects (e.g. Hugh Mellor[44] and Michael Tooley[45]). These theorists typically analyze non-volitional “exercises of causal power” in terms of statistical probabilities. For example, if A causes B, then A’s existence fixes a certain probability that B exist.[46] Therefore, it would be nice if we could get away with a more modest premise: 

(15) (N is not a personal agent) → (if N brings about a state of affairs, N does

       so in virtue of exemplifying some property or properties[perhaps in

       combination with some law obtaining]).

 

According to (15), if N is not a personal agent and so cannot act volitionally, then if N causes an effect, it does so in virtue of exemplifying a property. The idea is that individuals either produce effects in virtue of volitionally