[This article was originally published in Philosophical Topics, Volume 21, Number 1, Spring 1996, pp. 169-191.]

CAUSATION AND THE LOGICAL IMPOSSIBILITY OF A DIVINE CAUSE* (1996)

Quentin Smith

Western Michigan University

1. Introduction

Some interesting light is thrown on the nature of causation, the origin of the universe, and arguments for atheism if we address the question: Is it logically possible that the universe has an originating divine cause?

I think that virtually all contemporary theists, agnostics and atheists believe this is logically possible. Indeed, the main philosophical tradition from Plato to the present has assumed that the sentence, "God is the originating cause of the universe", does not express a logical contradiction, even though many philosophers have argued that this sentence either is synthetic and meaningless (e.g., the logical positivists) or states a synthetic and a priori falsehood (e.g., Kant and Moore), or states a synthetic and a posteriori falsehood (e.g., contemporary defenders of the probabilistic argument from evil).

I believe the prevalence of this assumption is due to the fact that philosophers have not undertaken the requisite sort of metaphysical investigation into the nature of causation. This investigation is the purpose of this paper; specifically, I shall argue that the thesis that the universe has an originating divine cause is logically inconsistent with all extant definitions of causality and with a logical requirement upon these and all possible valid definitions or theories of causality. I will conclude that the cosmological and teleological arguments for a cause of the universe may have some force but that these arguments, traditionally understood as arguments for the existence of God, are in fact arguments for the nonexistence of God.

2. Causal Definitions and the Notion of an Originating Divine Cause

Something is a continuing cause of the universe if and only if it causes each state of the universe. Something is an originating cause of the universe if and only if it causes the earliest state of the universe. If time is continuous, "the earliest state" may refer to an instantaneous state or (if the universe's history is half-open in the earlier direction) to a temporally extended state of some given length.

If big bang cosmology is true, the universe began to exist about 15 billion years ago with the big bang. The big bang is the earliest state of the universe; "the big bang" may be taken to refer to a singularity that constitutes the first instantaneous state of the universe or (if one "cuts out" the singularity) to an explosion that constitutes the first half-open state of some brief length, e.g. the Planck length, 10-43second. In my discussion, I shall treat the big bang as a logically possible example of an earliest state of the universe.

Considerations of agent causality are not germane to our discussion; our topic is the cause of the universe's beginning to exist, not the cause of God's act of willing that the universe begin to exist. We are not examining the relation between God (the agent) and his act of willing (the effect), but the relation between his act of willing (an event) and the beginning of the universe (another event). Thus, definitions of agent causality are irrelevant to our arguments; we are interested only in definitions of event causality, where the cause and effect are both events.

HUME'S DEFINITION OF A CAUSE

The most famous and influential definition of a cause is Hume's definition; indeed, most contemporary definitions include conditions that are similar in some respect to at least one of the three conditions included in Hume's definition:

"Contiguity in time and place is therefore a requisite circumstance to the operation of all causes...Priority in time is...another requisite circumstance in every case....[A] third circumstance [is] that of constant conjunction betwixt the cause and the effect. Every object like the cause produces always some object like the effect. Beyond these three circumstances of contiguity, priority, and constant conjunction I can discover nothing in this cause."[1]

Hume's definition includes three conditions for being a cause: temporal priority, spatio-temporal contiguity, and a nomological relation ("every object like the cause produces always some object like the effect".)

(a) TEMPORAL PRIORITY

If time began to exist with the universe, the "temporal priority" condition of Hume's definition implies that the universe cannot be caused to begin to exist since there is no earlier time at which the cause could occur.

Even if there is time before the universe, the "temporal priority" condition rules out an originating divine cause if all divine acts are timeless.

However, the "temporal priority" condition only shows the universe cannot have an originating divine cause if time began to exist with the universe or if all divine acts are timeless. It is logically possible that time preceded the beginning of the universe, even if there are no known laws of physics according to which the physical variable t can take values earlier than the time at which space and mass-energy began to exist. Further, it is logically possible that God exists in time and that a pre-universe time is occupied by God's mental life, which includes his volitions. Thus, it is logically possible for a divine volition to meet the "temporal priority" condition of Hume's definition. The intractable problems begin with the other two conditions.

(b) SPATIO-TEMPORAL CONTIGUITY

Hume's and many other definitions of causality require that the causal event is spatially in contact with, or is spatially near to, the effect. God is said to be omnipresent, but this means she is conscious of and stands in a volitional relation to each physical particular. It does not mean that divine volitions, which are non-physical, touch or are in the spatial vicinity of the physical particulars that are the objects of these volitions.

God's act of willing that the big bang occurs is not spatio-temporally contiguous with the big bang since this act of willing does not have spatial coordinates. c and e are spatio-temporally contiguous only if the spatial coordinates x, y, z that locate c on a manifold either are identical with the spatial coordinates x', y' ,z' of e, or locate c in the neighborhood of e.

(c) NOMOLOGICAL RELATEDNESS

The third feature of Hume's definition, the nomological condition ("every object like the cause produces always some object like the effect"), is also common to many definitions of causality. Hume's definition belongs to the line of reductive definitions that define causes in terms of laws of nature and a set of non-causal relations (such as temporal priority and spatio-temporal contiguity) between two particulars c and e.[2] According to these definitions, c is a cause of e only if there is a law of nature L that enables a statement that e occurs to be deduced from the premises that c occurs and that the law L obtains. For example, Carl Hempel writes[3]: "a 'cause' must be allowed to be a more or less complex set of circumstances or events, which might be described by a set of statements C1, C2, . . . Ck. ....Thus the causal explanation implicitly claims that there are general laws- -let us say, L1, L2, . . . Lk--in virtue of which the occurrence of the causal antecedents mentioned in C1, C2, . . . Ck is a sufficient condition for the occurrence of the explanadum event." A probabilistic law L may be permitted as well, in which case "to be deduced from" would be replaced by "to be inductively supported by".

However, the nomological condition for being a cause is logically inconsistent with a divine cause of the big bang, since God by definition is a supernatural being and his or her actions are not governed by laws of nature. Furthermore, the fact that God's willing is omnipotent makes "the big bang occurs" deducible from "God wills that the big bang occur" alone, without the need of any supplementary nomological premise, thus vitiating the condition that a nomological premise is a logically necessary condition for the derivation of the conclusion that the effect exists from premises one of which is that the causal event occurs.

At this point, we have already ruled out virtually every extant definition of causality, since most every definition includes either the spatio-temporal contiguity condition or the nomological condition. We are left with non-contiguity and singularist definitions of causality.

A non-contiguity definition does not mention spatio-temporal contiguity and does not require the cause to be both temporally and spatially contiguous with the effect; variants of non-contiguity definitions may allow for timeless divine acts and/or temporal divine acts that are not spatially nearby or in contact with the effect. A singularist definition allows an event to cause an effect in a single case, without the cause and effect needing to instantiate some law. However, the extant formulations that are singularist and/or noncontiguity definitions are few and far between and prove problematic for a defender of the logical possibility of an originating divine cause.

DUCASSE'S SINGULARIST DEFINITION OF A CAUSE

The most famous singularist definition of a cause is J. C. Ducasse's. Ducasse's conception "defines the cause of a particular event in terms of but a single occurrence of it, and thus in no way involves the supposition that it, or one like it, ever has occurred before or ever will again. The supposition of recurrence is thus wholly irrelevant to the meaning of cause; that supposition is relevant only to the meaning of law."[4] Since the nomological condition is explicitly rejected, it seems this definition applies to God's willing that the big bang occurs.

However, further inspection of Ducasse's definition shows it does not apply, since his definition requires spatio-temporal contiguity. Ducasse claims the cause c is a sufficient condition of the effect e and that c is sufficient for e if (i) c is a change that occurred during a time and throughout a space terminating at an instant i at a surface s of an object; (ii) the change e occurred during a time and through a space beginning at the instant i at the surface s; (iii) no change other than c occurred during the time and through the space of c, and (iv) no change other than e occurred during the time and through the space of e.[5] Thus, Ducasse's account meets the singularist criterion, but not the non-contiguity criterion. (Although Ducasse calls his account a "definition" of a cause, it is only a partial definition, since he begins his definition with "if", not "if and only if".)

THE TRANSFERENCE DEFINITION OF CAUSE

Another possible candidate for a singularist and non-contiguity definition is based on the transference definition of causation, offered by Hector-Neri Castaneda, Galen Strawson, David Fair, Jerrold Aronson and others.[6] Castaneda states that "the heart of production, or causation, seems, thus, to be transfer or transmission".[7] In the actual world, what is transferred is energy (according to Castaneda), but he uses the word "causity" as a generic term for whatever may be transferred. Can God's volition transfer causity to the big bang?

Castaneda's full theory implies a definition that includes the nomological condition: c is a cause of e if and only if (i) there is a transfer of causity from an object O1 to an object O2 in a circumstance x, with the event c being O1's transmission of causity and the event e being O2's acquisition of causity; (ii) every event of the same category as c that is in a circumstance of the same category as x is conjoined with an event of the same category as e.

Condition (ii) is intended as a nomological condition and thus rules out supernatural causes. But may we isolate (i), "the heart of causation", and successfully argue that a singularist, non-contiguity, and transference condition is satisfied by a divine volition? It appears not, since there is a problem with causity. The causity cannot be identical with energy (Castaneda's claim about the actual identity of causity), since there is no energy in God (God being nonphysical). Indeed, the causity cannot be anything physical, since God is nonphysical. Nor can the causity be anything nonphysical, since the big bang is wholly physical. Thus, there appears to be no viable candidate for the causity transferred.

COUNTERFACTUAL DEFINITIONS OF CAUSATION

David Lewis's definition imports counterfactual conditions into the definition and seems to lend itself to a non-contiguity and singularist conception. According to Lewis, c causes e if and only if (i) c and e are events and both occur and it is the case that either (ii) if c had not occurred, e would not have occurred, or (iii) there is a causal chain linking c and e and each link d in the chain is such that if d had not occurred then e would not have occurred. Since there is no causal chain between a divine volition and the big bang, condition (iii) is inapplicable and we may concentrate on (i) and (ii).

Are the divine volition and the big bang both events? According to J. Kim,[8] an event is a substance exemplifying an n-adic property at a time. Even if there no pre-universe time, this need not rule out the applicability of Kim's definition to God's volition, since we may construe God's volition as simultaneous with the big bang. We may also follow Brian Leftow[9] and allow that the logical position occupied by "at the time t" may be occupied by "at eternity" or "timelessly". Alternately, we could follow Davidson[10] and take an event as a particular that is not further definable and allow that the divine volition is an event even if timeless. This route, or, following Wolterstorff and others[11], taking an event as something's exemplification of an n-adic property (without a time specification), would allow us to consider the divine volition as an event that is either timeless, simultaneous with, or earlier than the big bang. (In these various definitions, "event" and "state" may be taken to be synonyms.)

However, Lewis's counterfactual definition is not instantiated by a divine willing of the big bang. Let c be the divine willing of the big bang and let e be the big bang. If e had not occurred, then c would not have occurred. But this implies the false proposition that e is the cause of c, since c is counterfactually dependent on e. In this case (to use Lewis's words about a problem he generally notes), "we have a spurious reverse causal dependence of c on e, contradicting our supposition that e did not cause c"[12].

Lewis solves this problem by denying the counterfactual "if e had not occurred, c would not have occurred." Lewis holds that it is instead true that "c would have occurred just as it did but would have failed to cause e"[13]. But this entails that Lewis's definition cannot be instantiated by God's willing the big bang, since if c had occurred (if God had willed the big bang) then it necessarily causes e (the big bang); God is omnipotent and his willing is necessarily effective.

In summary, the above considerations suggest that there are no extant definitions of causality that are satisfied by God's willing the big bang to occur; I believe a survey of further extant definitions would show that most of them include at least one of the above-mentioned conditions (contiguity, a nomological condition, etc.) that are violated by the divine volition. The ones that do not include one of the above-mentioned conditions include some other condition that is violated by the divine volition; for example, J. Mackie's definition of an INUS condition implies a cause c is neither necessary nor sufficient for its effect e but is instead an insufficient and non-redundant part of an unnecessary but sufficient condition for e.[14] God's willing the big bang, however, is sufficient for the occurrence of the big bang and thus violates the condition "is neither necessary nor sufficient for its effect".

3. Causes and Logically Sufficient Conditions

It may be responded at this juncture that the failure of God's creation of the big bang to satisfy any of the extant definitions of causality does not imply that God's volitional act is not a cause of the big bang. It may be that the correct definition of causality has not yet been discovered, and that God's willing the big bang satisfies this correct, undiscovered definition. My argument that God cannot be a cause of the universe is at best a "weak inductive argument" based on the definitions that have been formulated by the present point in time.

Further, the preceding considerations suggest a certain definition of causality that is satisfied by the originating divine volition, regardless of whether or not this definition has been defended by anybody. This definition reads: c is a cause of e if and only if c is a sufficient condition of e and c is earlier than e. This definition includes Hume's "temporal priority" condition, but is both singularist and noncontiguous. (A definition is contiguous only if it includes both spatial and temporal contiguity.) This definition cannot be satisfied by an originating divine volition if all divine volitions are timeless or if there is no time before the beginning of the universe. But it is logically possible that there is time before the big bang and that a temporal deity performs a volition that both occurs before the big bang and is a sufficient condition of the big bang's occurrence.

It may also be said that we need not rely on the assumption that the divine volition must satisfy a definition of a cause in order to be a cause. It is arguable that causation is a simple relation, a conceptual primitive, and thus that there is no definition that could capture its nature.[15]

These three responses to my discussion in section #2 are perhaps not unreasonable; indeed, at least the first response (about section #2 presenting an "inductive argument" based only on extant definitions) contains some truth.

However, all three responses are unavailing in face of the following crucial fact: there is an entailment relation between "c is a cause of e" and "c is not a logically sufficient condition of e". It is the case that:

(1) For any two particular events or states x and y, if x is a logically sufficient condition of y, then x is not a cause of y.

For example, a body's being in motion is a logically sufficient condition of the body occupying space, but the body's being in motion is not the cause of the body's occupation of space. However, God's willing that the big bang occurs is a logically sufficient condition of the big bang, for the propositions expressed by "God wills that the big bang occur" and "the big bang does not occur" are logically incompatible. The reason for this is that God is omnipotent and thus his willing is always successful (of logical necessity); if an omnipotent being wills x and x does not occur, then x is not omnipotent, which is a contradiction. (God can do everything that is logically possible; God cannot create a stone that is too heavy for him to lift, but creating such a stone is not a logical possibility. God would never will something to occur if the occurrence of that something were logically impossible--God is omniscient and omnibenevolent and would not knowingly engage in any futile effort.)

The variables in proposition (1) range over particular events or states; they do not range over particular events taken together with laws of nature or universal generalizations under which the particulars are subsumed. As we have seen, the nomological definitions of deterministic causation imply that a particular event c, in conjunction with a law of nature, logically necessitate the event e that is the effect. The sun's shining on a stone, in conjunction with the law that whatever is shined upon is warmed, logically necessitates that the stone is warmed. Proposition (1), however, implies only that the sun's shining on the stone does not logically necessitate the stone's being warmed. The sun's shining on the stone is a non-logically sufficient condition of the stone's being warm (it is nomologically sufficient, in that it is logically sufficient for the stone's being warm only if it is conjoined with some law of nature).

Two objections may be made to my argument that divine volitions are logically sufficient conditions and therefore are not causes.

(Obj. 1) It may be objected that every cause can be described in a way that logically implies the occurrence of its effect, and therefore that divine volitions are not dissimilar to causes. For example, the cause, the explosion that burned down the house, logically necessitates its effect, the burning down of the house, since it is a logical contradiction to assert that "there is an explosion that burned down the house and yet there is no event of the house burning down".

But this objection is fallacious since "the explosion that burned down the house" does not refer merely to the cause but also to the effect. A definite description that refers merely to the causal event can be satisfied consistently with the non-occurrence of the effect; for example, the definite description, "the explosion that occurred in the house", can be satisfied consistently with the non-satisfaction of "the burning down of the house".

The fallaciousness of this objection can be explained more precisely in terms of referentially transparent and referentially opaque contexts. The definite description, "the explosion that resulted in the burning down of the house", is a referentially transparent context; this implies that "the burning down of the house" occupies a position that is open to substitution and quantification in "the explosion that resulted in the burning down of the house. A description of the form "the explosion that resulted in the F" permits co-referring expressions to be substituted for "the F" and if a description of this form is satisfied, it follows that there is an F. Since the description of the effect, "the F", occurs in a referentially transparent context, "the explosion that resulted in the F" refers to both the cause and the effect.

By contrast, the definite description, "the divine willing that the big bang occurs", is a referentially opaque context and refers merely to the divine volition. This description is referentially opaque since it a propositional attitude construction, and positions within attitude constructions are not open to substitution and quantification.[16] Specifically, a definite description of the form, "the willing by x that the F occurs", does not permit substitutions of co-referring expressions for "the F", and "the F" is not open to quantification. This implies that if a description of the form, "the willing by x that the F occurs", is satisfied, it does not follow that there is an F. Since the description of the effect, "the F", occurs in an opaque context, "the willing by x that the F occurs" refers only to the cause.

Given this distinction, we may say that a definite description D of a cause also refers to the effect if and only if D includes a term for the effect that is open to substitution and quantification. A definite description D' of a cause does not refer to the effect if and only if D' either does not contain a term for the effect or contains a term for the effect in an opaque context.

This enables us to state our principle (1) about causes and logically sufficient conditions in semantic terms: the satisfaction of a definite description D of a cause logically implies the existence of the effect if and only if D includes a term for the effect in a referentially transparent context. Since the satisfaction of the definite description, "the divine willing that the big bang occurs", logically implies that the big bang occurs, despite the fact that "the big bang" does not occur in a referentially transparent context, it follows that this description does not refer to a cause.

The reason that the satisfaction of the description, "the divine willing that the big bang occurs", implies there is a big bang is not due to the logical form of the description (the form is opaque), but is due to the content of the description. This content is distinctive in that it makes the relevant conditionals about the divine volition and the big bang logical truths. The expression, "an omnipotent being", means in part a being whose acts of will necessarily actualize what is willed, Thus, the sentence "if an omnipotent being wills that the big bang is actualized, then the big bang is actualized" expresses the same proposition as the sentence, "if an omnipotent being, whose acts of will necessarily actualize what is willed, wills that the big bang is actualized, then the big bang is actualized", which is a truth of logic.

Principle (1) about causes and logically sufficient conditions implies that no causal conditional is a logical theorem, where a causal conditional has the form "if c occurs, then e occurs" and substitutions for "c" are expressions that refer to the cause and do not include a term for the effect in a referentially transparent context.

These restatements of principle (1) in semantic and logical terms suffice to refute the first objection to my argument that the divine volition is not a cause, the objection that "for each cause c and effect e, there is some description of c that logically implies the existence of e".

(Obj. 2) The first objection to my argument about causes and logically sufficient conditions was that divine volitions are not unique since every cause can be described in a way that logically implies the effect. A second objection is that there is some description of God's willing the big bang that does not logically imply that the big bang occurs, and therefore (for this different reason) divine volitions are not dissimilar to causes. The description, "the willing that has for its aim the actualization of the big bang", can be used as a definite description of the relevant divine volition and yet "there occurs the willing that has for its aim the actualization of the big bang, but the big bang is not actualized" is not a logical contradiction. It follows (the objection goes) that God's willing need not be regarded as a logically sufficient condition of the big bang. The objector may argue that the existence of such descriptions implies that whether or not a divine volition logically necessitates the existence of its volitional object is not a fact about the divine volition itself, but is relative to how the volition is described.

But this objection is invalid, since the existence of a description of the divine volition that does not logically imply that the big bang occurs is consistent with the divine volition necessarily possessing the relational property of being conjoined with the occurrence of the big bang. This consistency is an instance of the more general principle that "something that necessarily possesses a certain property F can be described by a definite description D that does not include F among its descriptive conditions, and D will not imply that whatever satisfies D necessarily possesses F". For example, the number nine necessarily possesses oddness and is described by "the number of planets", but since "the number of planets" does not include oddness among its descriptive conditions, it does not imply that whatever satisfies this description necessarily possesses oddness.

These responses to the two objections (Obj. 1) and (Obj. 2) help to justify my claim that the proposition,

(1) For any two particular events or states x and y, if x is a logically sufficient condition of y, then x is not a cause of y, is both true and precludes divine volitions from being causes.

SOSA'S THEORY OF CAUSATION

Does every philosopher accept that a particular event c that causes a particular event e cannot logically necessitate e? Ernest Sosa has suggested a theory of causality that might appear to be inconsistent with this thesis. Sosa distinguishes several types of causation, nomological causation, material causation, consequentialist causation, and inclusive causation. Of interest to us is Sosa's definition of consequentialist causation, since this definition is instantiated by God's willing the big bang. In cases of consequentialist causation, "the cause does entail the result or consequence"[17].

Sosa list several examples of consequentialist causation: (i) an apple's being red causes the apple to be colored; (ii) Tom's being in the room causes the general fact that there is someone in the room; (iii) Peter, Paul and Mary are tall and the only people in the room, and this causes the general fact that everyone in the room is tall; (iv) an apple's being sweet, juicy, etc., causes the apple to have the value of goodness.

Sosa acknowledges that he has no analysis or definition of consequentialist causation, but says it involves a consequence deriving necessarily from a cause "that is somehow more basic"[18].

The immediate rejoinder to Sosa's theory is that his cases of consequentialist causation are not cases of causation but cases of logical derivation, or, more exactly, cases where the instantiation of one property F logically necessitates the instantiation of a second property G, or whether the obtaining of one fact p logically necessitates the obtaining of a second fact q. When Sosa says this does "seem to be a genuine form of causation"[19], he seems to be mistaken. Indeed, the man or woman in the street, contemporary philosophers and scientists would all emphatically and correctly assert that these are not genuine cases of causation. But in fairness to Sosa, he acknowledges this very point, and makes some plausible observations in this connection:

"It might be objected that much of the foregoing is a mere terminological maneuver, that it simply takes what philosophers have long called causation, relabels it 'nomological causation', and goes on to classify it with certain wholly other relations that philosophers have not heretofore called causal relations. And it might perhaps be that the word 'cause' and its cognates have been so closely and so persistently associated with nomological causation by philosophers that they must be surrendered. But even then the basic point would remain, for nomological causation is a relation between a source and a consequence or result, and so is material causation (e.g. generation), so is consequentialist causation (e.g. the apple is chromatically colored as a result of being red) and so is inclusive causation. . . These are all source-consequence relations or result-yielding relations."[20]

Thus, we can agree with Sosa inasmuch as causation can be classified with other result-yielding relations, such as the logical necessitation of a property F by another property G, as one type of result-yielding relation, but at the same time distinguish causation from these other noncausal resultyielding relations.

4. Analogical and Literal Descriptions

I suggest that the foregoing considerations give us good reason to believe that there is no actual or possible correct theory or definition of causality that is instantiated by God's willing the big bang.

How might the defender of divine causality answer these arguments? One answer might be to grant that God's willing is not a "cause" of the universe's beginning, but instead is the "creator" or "producer" of the universe's beginning. But this change in terminology does not solve the problem; "c creates e" and "c produces e" each imply "c causes e", so the problem is not avoided. If we wish to stipulate that "c creates e" does not imply "c causes e", then we deprive the word "creates" of any apparent intelligibility. If "creates" no longer means what it normally means, then we are hard put to say what it means.

A similar problem affects an alternative solution, namely, that we say that God "wills" the universe to begin to exist, but does not "cause" it to begin to exist. I provisionally used the terminology of "God's willing" and "divine volition" in the preceding sections, but this usage calls for reevaluation. "x wills e and e occurs because of x's willing" logically implies "x's willing causes e". If God's act of willing is not an act of causation, it is difficult to say what the word "willing" means when applied to God. It does not mean what it means in such sentences as "John moved his broken limb by a sheer act of will".

Perhaps we can say that the words "willing" and "cause" are used in an analogical or metaphorical sense when applied to God. This means that God has some features that are analogous to the features we normally mean by "willing" and "cause", and also some features that are different. The analogy for "willing" would be this: If a human wills something, this willing is a mental event that has for its aim bringing another event into existence. Likewise, we may say of God that he or she experiences a mental event and that this mental event has for its aim bringing another event into existence. This is the analogy. There is also a difference, in that God's willing is a logically sufficient condition for the existence of the event that is willed, whereas a human's willing is not logically sufficient for the event that is willed.

However, this resort to the "analogical" use of words threatens to break down the intelligibility of our talk about God's willing. The explanation of the analogical meaning of these words is in terms of other words that also have an analogical meaning. We said that God's willing is a mental event that "has for its aim bringing another event into existence". However, the literal meaning of the phrase about aiming for a goal implies that "it is logically possible that this goal is not achieved". When we say that Alice has the aim of writing a book, we mean, in part, that it is logically possible that she not succeed in achieving her aim. Given the literal meaning of "aims", a statement of the form "x aims to realize F and F is realized" is neither a logical nor an analytic truth. Consequently, the explanation of the analogical meaning of "divine willing" in terms of "aiming to do something" cannot involve a literal use of "aiming to do something". But if "aiming" is used analogically, then our problem of explaining what we mean by our words reappears. This problem does not appear to have a solution; we are embarked on a regress of explaining analogically used words in terms of other analogically used words, with no way to end this regress by an explanation that involves words in their normal and literal use. This regress is vicious; in order to understand phrase #1, we need to understand phrase #2, but in order to understand phrase #2, we need to understand phrase #3, and so on. This suggests we cannot attach any definite meaning to the assertion that God causes, wills or aims to bring the universe into existence.

A LITERAL FORMULATION OF THE DIVINE RELATION TO THE BIG BANG

But this is not to say that we cannot intelligibly talk about God and her relation to the big bang. It appears that we can say at least that there is some n-adic property F exemplified by God, such that by virtue of exemplifying this property, God stands in relation to the big bang of being a logically sufficient condition of the big bang. Perhaps we can even be more precise and say F is some mental property, where "mental" is understood in terms of intentionality (in the tradition of Brentano, Husserl, Chisholm and Searle). Further, we can say this intentional act experienced by God has a certain property as its intentional object, the property, being the big bang. The property being the big bang will thereby have a second order property, viz., being the intentional object of the divine intentional act A, such that being an intentional object of A is a logically sufficient condition of being exemplified. Talk of "intentional act" may be literal here, since these are technical terms in the philosophical literature and "act" here has a different meaning than "act" in "Jane's acted quickly to remedy the situation" or "the last act of the play was a disappointment".

If it is objected that "intentional act" does not have a univocal meaning between "humans perform (embodied, non-omniscient and non-omnipotent) intentional acts" and "God performs (disembodied, omniscient and omnipotent) intentional acts", then we can resort to a more general level of talk. We can say that there is a certain relation R in which God stands to the property being the big bang, such that by virtue of God standing in R to being the big bang, it is logically necessary that being the big bang is exemplified.

In summary, we are safe in saying that God does not cause the big bang, but Rs the big bang, where "God Rs the big bang" means that God stands in a certain relation R to being the big bang, such that by virtue of standing in this relation to this property, it is logically necessary that this property is exemplified. (For ease of expression, I will sometimes talk loosely in the following sections of God standing in R to the big bang, but such talk should be strictly analyzed in the way I analyzed "God Rs the big bang".)

5. Objections to the Arguments that God Cannot be a Cause

FIRST OBJECTION

It may be objected that the divine relation R cannot merely be that of being a logically sufficient condition of the big bang. God's standing in this logical relation to the big bang is not similar to the sun's being orange standing in relation to the sun's being colored as a logically sufficient condition. The sun's exemplification of being orange does not in any sense bring about or produce the sun's exemplification of being colored. But God's exemplification of R does bring about the big bang.

But this objection is overtly question-begging. I have already argued that God's standing in relation to the big bang does not satisfy any extant definition of causation (section 2) and does not satisfy a logically necessary condition of being a cause (section 3). Thus, to introduce synonyms of "causes", such as "brings about" or "produces", etc., is simply to beg the question at issue.

It may be countered by the objector that there is an important disanalogy between the case of the relevant divine event and the case of other logically sufficient conditions, viz., that God's standing in relation to the big bang is an event, a concrete particular, and the big bang is another concrete particular, whereas the other logical relations are among abstract objects.

This countering argument is inaccurate. According to one conception of events or states, an event or state is the exemplification of a property by something. God's exemplification of the polyadic property R is a state, and so is Jane's exemplification of running and her exemplification of being alive. The concrete state of Jane's exemplification of running is a logically sufficient condition of the concrete state of Jane's exemplification of being alive. Thus, there are two concrete states standing in the relation of one being the logically sufficient condition of the other. This situation is similar in this respect to God standing to the big bang in the relevant relation.

Nonetheless, the intuition may persist that there is an important ingredient in God's relation to the big bang of logically necessitating the big bang that is not present in the sun's orangeness logically necessitating the sun's being colored, or Jane's running necessitating her being alive, an ingredient that is metaphorically captured by causal language ("produces", "brings about", etc.). The objector may simply state that it is intuitively obvious that there is this difference between the two cases, even if this difference cannot be adequately expressed in words.

But this amounts to retreating to an ineffability theory. We now have the theory: "God does not literally cause the big bang, but in some metaphorical sense causes the big bang, even though it is impossible to specify literally the analogy between causation and God's relation to the big bang that justifies the metaphor." The ineffability theory is that God's R-ing the big bang is a relation with two properties; one property of God's R-ing the big bang is that the R-ing is a logically sufficient condition of the big bang, and the second property is an indescribable property, which we may call an Xproperty, such that the X-property is a property of God's R-ing that makes the R-ing analogous in a relevant respect to a causal relation.

However, the ineffability theory fails for three reasons.

(i) If the X-property makes the R-ing analogous to a causal relation, then the X-property is some property shared in common by the causal relation and the R relation. Since the X-property belongs to the causal relation, and we can literally describe the causal relation, we should be able to literally specify the causal relation's X-property and say that it is this property that the R relation has in common with the causal relation. But the ineffability theory fails to do this.

(ii) The ineffability theory has no justification for asserting there is this X-property. The ineffability theory mentions no datum that the postulation of the X-property is used to explain, and it introduces no premises from which the presence of the X-property is deduced. The only apparent justification might be that one has had a mystical experience and directly "beheld" God R-ing the big bang and "beheld" the X-property of this R-ing, but that in reporting this intuition, one realized there are no adequate and literally used words that could describe this X-property. However, if the theory that God metaphorically causes the universe amounts to nothing more than dark sayings about what is "beheld" in an ineffable mystical experience, then this not a theory based on natural reason but is a flight into mysticism and the deliverances of "supernatural reason". It would hold no interest for a philosopher intent on constructing a world-view based on natural reason.

(iii) The best explanation of the origins of the "intuition" that God metaphorically causes the big bang, and is not merely a logically sufficient condition of the big bang, does not imply this intuition is true. The origin of this "intuition" is the long and pervasive tradition (in philosophy, religion and "ordinary language") of using causal words, "causes", "creates", "wills", etc., to describe God's relation to the beginning of the universe. The psychological associations produced by the adoption of this linguistic tradition gives rise to the "intuition" that there must be an X-property of God's relation to the big bang that grounds the metaphorical usage of "causes".

There are differences between (for example) the orange/color relation and the R relation of God to the big bang, but none are causal-like. Orange is a kind of color, but God's relation to the big bang is not a kind of big bang. Further, the orangeness is a monadic property of the same thing of which being colored is a property, but the R property is polyadic and interconnects different objects. Thirdly, being orange and being colored are both physical properties, whereas the divine relation is a mental property and being the big bang is a physical property.

We can also specify formal features of the R relation: it is asymmetric, transitive and irreflexive, but many non-causal relations also possess these formal features.

SECOND OBJECTION

The theist, agnostic or atheist who believes it is logically intelligible to say that God is an originating cause of the universe may take the bull by the horns and arrogantly assert that God's being a logically sufficient condition of the big bang is a counterexample to the extant definitions of causation discussed in section 2, and shows these definitions are wrong, and is also a valid counterexample to my principle (1) that states causes are not logically sufficient conditions. The objector proclaims: "All actual and possible contiguity or nomological definitions of causation are false. The correct definition is a non-contiguity and singularist definition that allows that some causal relations are logical relations."

The problem with this "arrogant objection" is that there is no apparent justification for the belief that there is a correct definition of causation that is non-contiguous, singularist and permits logical relations apart from God's alleged acts of causation. But these are precisely the events whose causal nature is in dispute. To assume, in face of the arguments I have given, that these acts are casual relations is a question-begging response. In order to demonstrate that the relevant divine relation is a causal relation, we must have a logically independent reason to believe there is some correct definition of causation that the divine relation R satisfies. But there is no such reason. Consider the argument:

(2) There is a sufficient reason J to believe that there is a correct definition of causation that is singularist, non-contiguous and permits logical relations.

Therefore,

(3) The divine relation R is a causal relation.

If the offered reason J is (3), then the argument that the divine relation R is a causal relation is question-begging.

It may be objected that the defender of the "there cannot be a divine cause" thesis is in a similar question-begging situation and thus that there is a "stand off". It may be said that the defender begs the question by assuming that (3) is false or cannot play the role of reason J.

This objection fails since the defender of the "there cannot be a divine cause" thesis has a non-question-begging argument for the falsity of (3). The argument is that all cases of causation that are not in dispute are inconsistent with the hypothesis that there is a correct definition of the sort mentioned in (2). Both parties to the dispute agree that physical events cause other physical events, and that the mental events of intelligent organisms cause other events (assuming an appropriate philosophy of mind), and this agreement is the common ground between the opponent and defender of the "there cannot be a divine cause" thesis. But these common grounds are inconsistent with the positive thesis, viz., that "there can be a divine cause", if only for the reason that it is a logically necessary property of the agreed upon cases of causation that the causal event is not a logically sufficient condition of the effect. Since these causal events are necessarily not logically sufficient conditions, a definition of a cause that encompassed both these causal events and God's relation to the big bang would include the contradiction "is not a logically sufficient condition and is a logically sufficient condition". The agreed upon cases may also include nomological and contiguity conditions, and consequently there may be further contradictions, e.g., "instantiates some law of nature and does not instantiate any law of nature" and "is spatially contiguous with the effect and is not spatially contiguous with the effect".

THIRD OBJECTION

It may be argued that a disjunctive definition can solve the problem . Suppose we have this disjunctive definition of causation: c is a cause of e if and only if c is either a logically sufficient condition of e, or c is not a logically sufficient condition of e and instead satisfies (say) the Humean conditions.

One problem with this disjunctive definition is that it classifies the sun's being orange as a cause of the sun's being colored. So it does not work for this reason, as well as for the other reasons mentioned in my discussion of Sosa's account of causation.

Even if we add a temporal priority condition, this disjunctive definition will not work. We may say: c is a cause of e if and only if EITHER c is both a logically sufficient condition of e and temporally prior to e OR c is not a logically sufficient condition of e and satisfies (say) the Humean conditions. However, the first disjunct is satisfied by many items that are not causes. John's being a living organism (or John's being embodied in a mortal body at time t) is both temporally prior to and is a logically sufficient condition of John's being dead, but John's being a living organism (or John's being embodied in a mortal body at time t) is not the cause of his death. His death is caused, say, by a car hitting him as he crosses the street. The concept expressed by "is a living organism" analytically includes the concept expressed by "is mortal" and the relevant logical truths (e.g., "if x is an organism that dies, then x dies") can be obtained by substituting synonyms for synonyms.

Suppose we become even more specific and say instead: c is a cause of e if and only if EITHER c is God's standing in the R relation to e OR c is not a logically sufficient condition of e and satisfies (say) the Humean conditions. But this attempt to produce a satisfactory definition fails for two interrelated reasons:

(i) A logically necessary condition of a correct definition of a purely qualitative universal, be it a monadic property or a relation (such as causation or intentionality) is that it not include a disjunct that mentions one particular case that does not meet the general conditions described in the other disjunct. A purely qualitative universal does not include any particulars as constituents. An example of an impurely qualitative universal is being taller than Mount Everest. Definitions of purely qualitative universals mention general conditions and do not include mentions of a particular case, such as the particular case of God standing in an R relation to something.

(ii) If this logical condition of correct definitions of purely qualitative universals (viz., the condition of not mentioning a particular case in a disjunct) were allowed to be violated, then the procedure of testing definitions by the counterexampling method (the standard method of testing the correctness of definitions) is no longer usable. Any counterexample to a definition could be made consistent with the definition by adding to the definition a disjunct that mentions the counterexample. To save the definition "x is a planet if and only if x is a large body that orbits a star and contains no life", we can expand it to "x is a planet if and only if EITHER x is a large body that orbits a star and contains no life OR x is the Earth". The distinction between correct definitions and ad hoc definitions would collapse.

FOURTH OBJECTION

A final argument is that philosophers from Plato to Plantinga have described God's relevant mental state as a cause of the universe, and therefore that this is an acceptable notion. There is both an established philosophical usage for calling God's relation to the universe a "causal relation" and a long and venerable tradition that held it to be coherent to describe a divine mental state as a cause.

This argument, which is in effect an "appeal to authority", is unsuccessful, since if this argument were admissable, it could be used to reject any new theory that is inconsistent with traditionally held theories. This "appeal to authority" at best motivates us to examine seriously the notion that God's mental states are causes, in deference to the fact that virtually all philosophers and laypersons have accepted this notion as logically unproblematic.

Perhaps to respond fully to this objection we also need an explanation of why this mistaken tradition has prevailed for so long and among so many philosophers. I think the main reason is that an investigation of the logical connection between what is expressed by "the universe's beginning to exist is the result of a divine act" and what is expressed by "the natural event e is the causal result of the natural event e" has not been systematically undertaken. (The main exception is the different but illuminating discussions of this connection in the recent writings of Adolf Grunbaum[21].) Most philosophers have tacitly presupposed that the thesis that "divine causation is logically possible" is unproblematic, but once this thesis is examined, the presupposition is seen to be false.

6. Conclusion: Cosmological and Teleological Arguments for God's Nonexistence

The argument of this paper might seem at first glance to tell us more about the nature of causation and the nature of God than about atheism versus theism. "A divine state cannot cause the universe to begin to exist" does not entail that God does not exist or that the big bang is not a logical result of a divine state. It merely entails that we cannot describe a divine state as the originating cause of the universe.

Nonetheless, there are important and perhaps decisive implications for the debate between theism and atheism, namely, that arguments from the necessary truth, a priori truth or empirical truth of some causal principle cannot be a relevant premise from which to deduce or induce that the big bang is the logical consequence of God standing in the relation R to the property being the big bang. Consider the following argument:

(4) Whatever begins to exist has a cause.
(5) The universe begins to exist.
Therefore,
(6) The universe has a cause.

This argument fails to support the theses that God exists or that there is a divine cause of the universe. Indeed, this argument entails that the universe's existence is the result of something other than a divine state, namely, a cause. Nor can any inductive argument based on the fact that every observed event has a cause be used to support the thesis that the big bang is the result of a divine state, since this inductive argument instead supports the thesis that the big bang is the effect of some cause.

In fact, all the various cosmological and teleological arguments for the existence of God are really arguments for God's nonexistence. These arguments are arguments for the thesis that the universe has a cause and if the universe has a cause, God does not exist. This can be demonstrated as follows:

The traditional definition of God is: x is God if and only if x is omniscient, omnipotent, omnibenevolent and is the cause of any universe that exists. We have seen that what is traditionally expressed by "God is the cause of the universe", if it is logically coherent, should be expressed instead by "God Rs the universe". Thus the correct definition of God reads: x is God if and only if x is omniscient, omnipotent, omnibenevolent and Rs any universe that exists. It follows from this definition that it is an essential property of God that he Rs any universe that exists. Since this property is essential to God, there is no possible world in which it is true both that God exists and that there is a universe to which God does not have an R relation.

Our discussion of Sosa's theory of causation suggested that the causal relation and the divine R relation are two different types of result-yielding relations, to borrow Sosa's phrase. If the universe is the result of a causal result-yielding relation, it is not the result of a R-type result-yielding relation, and if the universe is the result of a divine act of R-ing, it is not the result of a cause. If there is a possible world in which some universe is the result of a cause, it follows that God does not exist in that possible world.

This shows how a cosmological argument for God's nonexistence may be explicitly constructed. The premises and inferences are mentioned in the following argument:

(4) Whatever begins to exist has a cause.
(5) The universe begins to exist.
Therefore,
(6) The universe has a cause.
(7) If the universe is the result of a cause, it is not the result of God standing to the universe in an R relation.
(8) It is an essential property of God that he Rs any universe that exists.
Therefore [from #7 and #8],
(9) There is no possible world in which it is true both that God exists and that there is a universe which is the result of a cause.
Therefore [from #6 and #9],
(10) God does not exist.

If big bang cosmology is true (and thus #5 is true), it seems that the premise with the weakest or lowest epistemic status is the first premise, "Whatever begins to exist has a cause". But William Lane Craig says about this premise: "the first premiss is so intuitively obvious, especially when applied to the universe, that probably no one in his right mind really believes it to be false."[22] If Craig is right and my argument sound, it follows that probably no one in his right mind who believes the universe has a beginning really believes that God exists.

The same considerations apply to the teleological argument, one version of which reads:

(11) Artifacts are caused to exist by some intelligent being(s) with some purpose in mind.
(12) The universe resembles an artifact.
Therefore, it is probable that:
(13) The universe is caused to exist by some intelligent being(s) with some purpose in mind.

If this is an adequate argument from analogy, then it is probably true that the result-yielding relation that is involved in the explanation of why the universe exists is a causal relation in which some intelligent being(s) stand(s) to the universe. It follows (given propositions #7 and #9) that God probably does not exist.

Since the cosmological and teleological arguments have standardly been thought to be the strongest arguments for God's existence, and since they support atheism rather than theism, it seems now that the case for theism is very weak indeed. It is hard to imagine how one could ever inductively or deductively establish, or find self-evident, that the big bang is the logical consequence of something standing in an R relation to being the big bang. Perhaps there are some fairly plausible arguments that the big bang has a cause, but there are no extant or plausible arguments that the big bang has a logically sufficient condition in an acausal mental state. This suggests that belief in the existence of God is considerably less reasonable than even the most cautious natural theologians have standardly supposed.

NOTES

* Earlier versions of this paper were read at West Virginia University (February 1995) and at Southern Methodist University (March 1996). The philosophers at both universities offered helpful comments on these earlier versions. Mark Aronszajn and William Lane Craig wrote critical responses to earlier versions, which proved useful in writing the present draft. I am also grateful to Christopher Hill for several suggestions that enabled me to improve an earlier draft.

Research for this paper was supported by an American Council of Learned Societies Fellowship for 1996, and by a National Endowment for the Humanities Summer Stipend for 1995.

[1]. David Hume, "An Abstract of A Treatise of Human Nature', in An Inquiry Concerning Human Understanding (New York: Bobbs-Merril, 1955), pp. 186-7.

[2]. It is worth noting that Michael Tooley's theory implies that a cause requires an underlying law of nature, but that the cause is not specified solely by the law of nature and noncausal facts. Although Tooley's definition differs from the traditional reductive definitions, its inclusion of a nomological condition precludes it from being satisfied by a divine volition. See his Causation: A Realist Approach (Oxford: Clarendon Press, 1987).

[3]. Carl Hempel, Aspects of Scientific Explanation (New York: The Free Press, 1965), pp. 348-49.

[4]. C. J. Ducasse, "On the Nature and the Observability of the Causal Relation", in Causation, eds. E. Sosa and M. Tooley (Oxford: Oxford University Press, 1993), p. 129.

[5]. Ducasse, p. 127.

[6]. Hector-Neri Castaneda, "Causes, Causity, and Energy,", in Midwest Studies in Philosophy IX, eds. P. French et al (Minneapolis: University of Minnesota Press, 1984); Galen Strawson, "Realism and Causation", The Philosophical Quarterly 37 (1987), pp. 253-77; David Fair, "Causation and the Flow of Energy", Erkenntnis 14 (1979), pp. 219-50; Jerrold Aronson,"The Legacy of Hume's Analysis of Causation" Studies in the History and Philosophy of Science 7 (1971), pp. 135-36.

[7]. Castaneda, p. 22.

[8]. Jaegwon Kim, "Events as Property Exemplifications", in Action Theory, eds. M. Brand and D. Walton (Dordrecht: Reidel, 1976).

[9]. Brian Leftow, Time and Eternity (Ithaca: Cornell University Press, 1993).

[10]. Donald Davidson, "Causal Relations", in Causation, eds. Sosa and Tooley.

[11]. Nicholas Wolterstorff, "God Everlasting" in God and the Good, ed. C. Orlebeke and I. Smedes (Grand Rapids, MI: Eerdmans, 1975) 1979; Quentin Smith, Language and Time (New York: Oxford University Press, 1993).

[12]. David Lewis, Philosophical Papers, Volume II (New York: Oxford University Press, 1983), p. 170.

[13]. Lewis, p. 170.

[14]. John Mackie, The Cement of the Universe (Oxford: Clarendon Press, 1974).

[15]. I argued for this theory in "The Concept of a Cause of the Universe", Canadian Journal of Philosophy 23 (1993), pp. 1-24. In this earlier article, I claimed that cases of divine volitions are valid counterexamples to extant definitions of causality. However, I have since developed a counterargument to this claim (see section 5, Second Objection), which has led me to abandon the claim that divine volitions are causes.

[16]. More exactly, a notational occurrence of a term in a position within attitude constructions is not open to substitution and quantification; a relational occurrence of a term in this position is open to substitution and quantification. "F" occurs relationally in "y desires that there is an F" if this is read as "(Ex) Fx. y desires that: (Ex) Fx." By contrast, "F" occurs notationally if "y desires that there is an F" is read as "y desires that: (Ex) Fx." See David Kaplan, "Opacity", in The Philosophy of W.V. Quine, ed. L. Hannard and P. Schlipp (La Salle: Open Court). When I talk about "positions with attitude constructions" I have in mind only positions within attitude construction in which terms occur notationally.

[17]. Ernest Sosa, "Varieties of Causation", in Causation, eds. Sosa and Tooley, p. 240.

[18]. Sosa, p. 240.

[19]. Sosa, p. 240.

[20]. Sosa, p. 242.

[21]. Adolf Grunbaum, "The Pseudo-Problem of Creation in Physical Cosmology", in John Leslie (ed.), Philosophy and Physical Cosmology: New York: Macmillan, 1990, pp. 92-112; "Creation as a Pseudo-Explanation in Current Physical Cosmology", Erkentniss 35 (1991): 233-54.

[22]. William Lane Craig and Quentin Smith, Theism, Atheism and Big Bang Cosmology (Oxford: Clarendon Press, 1993), p. 57.

"Causation and the Logical Impossibility of a Divine Cause" is copyright © 1996 by Quentin Smith. All rights reserved.
The electronic version is copyright ©1997 by Internet Infidels with the written permission of Quentin Smith.