Problems with Earmans Attempt to Reconcile Theism with General Relativity

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PROBLEMS WITH JOHN EARMAN’S ATTEMPT TO RECONCILE THEISM WITH GENERAL RELATIVITY

ABSTRACT. Discussions of the intersection of general relativity and the philosophy of religion rarely take place on the technical level that involves the details of the mathematical physics of general relativity. John Earman’s discussion of theism and general relativity in his recent book on spacetime singularities is an exception to this tendency. By virtue of his technical expertise, Earman is able to introduce novel arguments into the debate between theists and atheists. In this paper, I state and examine Earman’s arguments that it is ration ally acceptable to believe that theism and general relativity form a mutually consistent or even mutually supportive pair. I conclude that each of his arguments is unsound.

In John Earman’s recent book, Bangs, Crunches, Whimpers, and Shrieks: Singularities and Acausalities in Relativistic Spacetimes (1995), he gives an overview, with some analytical commentary, of the literature on space- time singularities in general relativity from 1916 up to the early 1990s. In one of his main forays into philosophy, section 7.4 on “Finding God in the big bang”, Earman elaborates on some of his remarks about theism made earlier in the book. Although an atheist, Earman’s main concern in this section is to show how a theist may combine her theism with some of the more teelmical or mathematical aspects of general relativity. Discussions of the relation between theism and general relativity rarely reach the level of depth and detail in mathematical physics that is evinced in Earman’s discussion (Grtinbaum’s writings on the subject being a main exception). For this reason, Earman’s account of theism and general relativity is of interest, even though it is not a major theme of Earman’s book.

Unlike his fellow atheist Adolf Grünbaum, Earman chooses to approach the intersection of philosophy of religion and general relativity with the aim of producing arguments that the theist may use to defend the proposition that general relativity is consistent with or even supports theism. In fact, Earman has placed so much emphasis on this aim that some readers of his book have concluded (wrongly) that Earman is himself atheist. (Admittedly, it is hard to discern from some passages how or why an atheist could

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or would express himself in the manner that Earman chooses.) Earman does not explain his theory (if he has one) of the epistemology of religious beliefs, but it would be consistent to interpret his book in terms of the “rational acceptability” theory. According to this theory, it is rationally acceptable (but not rationally compelling) to be a theist, and it is rationally acceptable (but not rationally compelling) to be an atheist. This suggests that it is non-rational factors that incline one person towards theism and another towards atheism. If we see Earman’s book in this light, we may take it as a book written by an atheist who finds theism rationally accept able and who wishes to introduce some novel arguments for the rational acceptability of theism.

Earman’s emphasis on defending theism makes the natural “critic” or “opponent” of Earman’s arguments a defender of the strong atheistic position in the philosophy of religion. The strong atheistic position is that theism is rationally unacceptable and atheism rationally compelling. Adolf Griinbaum and John Mackie are examples of atheists who defend the strong position, and William Rowe and Richard Gale are examples of atheists who defend the weak position (atheism is not rationally compelling). In this paper I shall defend the strong atheistic position and argue that Earman’s arguments on behalf of the rational acceptability of theism are in each case unsuccessful.

The reader familiar with the arguments developed in the late 1 960s and 1970s that singularities are ideal points will recall that “an ideal point” does not here mean an idealization that does not really exist, but a real point that exists on the boundary of a spacetime. It exists on the boundary (rather than as a part) of the spacetime due in part to the fact that the metric tensor is not defined on this point. Earman writes: (1995: 209)

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The b-boundary (bundle-boundary) construction of singular boundary points is due to Schmidt (1971). A spacetime is b-complete if each half-curve has infinite generalized affine length. Singular spacetimes are b-incomplete. The b-incomplete curves in the original manifold M (say of our Friedmann—Robertson—Walker spacetime (M, g_ab)) have boundary points in an enlarged manifold M*; the singular points are ideal endpoints (in M*) of incomplete curves in the original manifold M. The b-boundary construction involves an extension M* of the original manifold M, with the aim of giving a topological structure to M* that delimits which points in the boundary of M* are in the neighborhoods of which points in the interior M. This is achieved by introducing a positive definite metric on the bundle of orthonormal frames of M. The Cauchy completion of this bundle is factored by the action of the Lorentz group on this bundle to obtain the original manifold M with ideal points attached. (See Schmidt (1971).)

This b-boundary construction of singular points seemed satisfactory until proven otherwise by Johnson (1977) and Geroch, Liang and Wald (1982). They demonstrated that the boundary points in M* are not Hausdorff or T1-separated from the entire spacetime (M, g_ab). Johnson has shown that in FRW (Friedmann-Robertson-Walker) spacetimes, the “b boundary M* of M is (essentially) a single point, the only neighborhood of which is M itself” (1977, p. 899). This implies the physically pathological result that each event in the, spacetime, even those in the asymptotic region, is “arbitrarily close” to the singularity.

Earman correctly notes that Johnson (1977) shows the b-boundary con struction leads to a spacetime that is not Hausdorff-separated, but we need to add that Geroch, Liang and Wald (1982) have proven the stronger result that the boundary points are not even T1-separated from the entire space time, T1 being a weaker separation condition than the T2 (Hausdorfi) separation condition. (They also show this for the g-boundary construc tion of ideal points, whose details need not detain us.) Geroch-Liang-Wald show a “singular boundary point fails to be Ti-related to an event of the

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original spacetime” (1982, p. 432). It is possible to give a brief explanation of these topological notions.

A topological space X is a T1 space if given any pair of distinct points a, b there exist open sets Oa and Ob such that a is a member of Oa and b is a member of Ob and a is not a member of Ob. X is a T2 (Hausdorff) space if given any pair of distinct points a, b there exist disjoint open sets Oa and Ob such that a is a member of Oa and a a member of Ob, See Gall (1964: 77—78).

The failure to meet these separation conditions is natural for causally pathological spacetimes, such as the Taub-NUT spacetime. The Taub NUT spacetime is non-Hausdorff but for quite different reasons than Earman’s deistic FRW spacetime. The Taub-NUT manifold has a singularity that is not due to infinite tidal gravitational forces or infinite crushing (expected for a FRW big bang singularity); rather, it has incomplete time- like geodesics which continually reenter every small neighborhood of some point of the manifold. But this esoteric example is not germane to the physical possibility of a b-boundary construction (or g-boundary construction) of a singularity in a FRW spacetime. FRW spacetime is standardly regarded as a paradigmatic case of a non-pathological spacetime. But the b-boundary construction (and every other known construction) of a FRW big bang singularity turns the FRW spacetime into a pathological space- time. The reason is that each point in the FRW spacetime — even those in the asymptotic region (!) — is “arbitrarily close” to the singularity. For example, if a is the big bang singularity and b a point on the Earth, then the failure to meet the T I condition implies that it is not the case that there are two open sets Oa and Ob that meet this condition:

This is a mathematically possible topology but not a physically possible topology of a FRW spacetime or at the very least is manifestly inconsistent with FRW spacetime in which we live. But Earman suggests that the theist

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may reasonably believe that this is a physically possible way for God to create the big bang singularity in a FRW spacetime, even if the relevant sense of “cause” is remote from the usual senses applicable to events that are parts of the spacetime. The fact that the big bang singular point is not Hausdorff-separated from interior points of M is allegedly “attractive” for the deist in particular since “although God operates at the beginning of time, He is nevertheless near every event” (Earman, 1995: 220, n. 9). I would comment that according to standard philosophies of monotheistic religions, God is “near” every event in the sense of being omnipresent, which means that God is both conscious of and causally sustains every event (See for example, Swinburne (1977: 104) and Aquinas’ Summa Theologiae Ia.8.3). It seems to be a fallacy of equivocation to relate this theological use of “near” to the thesis that God is “near” every spacetime event in the sense that he creates a non-Hausdorif spacetime with a singular point a, such that every event in the manifold is arbitrarily close to a. Would this position imply that God is not “near” (in the theological sense) every event if spacetime is Hausdorff e.g., in the case of the actual spacetime in which we exist?

Earman notes that the non-Hausdorif nature of FRW spacetimes with attached ideal points is “counterintuitive” but nonetheless allows that “Nothing prevents the theist from seeing God as operating at these ideal points” and that such divine creation is not “illegitimate” (1995: 209). But physical impossibility or illegitimacy or nonconformity with our actual FRW spacetime does prevent the theist from (justifiably) seeing this. In fact, Earman himself earlier suggests that this sort of spacetime is unacceptable. He remarks on page 59: “Because of the absence of a technique that yields intuitively satisfactory results for attaching singular points to the spacetime manifold, it is perhaps best to drop talk of spacetime singularities — which suggests localizable objects (ideal points) — in favor of talk about singular spacetimes” (my emphasis). Earman is here suggesting that the failure to satisfy the Hausdorif condition renders the belief that there are no spacetime singularities (attached ideal points) more justified than the belief that there are such points. It is more justified to talk of singular spacetimes, which are “singular” but do not have attached ideal points (Grünbaum’s case (ii) in Grünbaum (1989)). Does not this lack of justification epistemically “prevent the theist from seeing God as operating at these ideal points” and render this metaphysics epistemically “illegitimate”?

I think Earman concedes too much to the theist by allowing that such divinely created spacetimes are physically counterintuitive but metaphysically legitimate. To say they are merely “counterintuitive” is too weak a criticism (after all, even dense or continuous physical spaces have “coun

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terintuitive” features). In fact, an analysis of the support Earman offers for this metaphysical legitimacy suggests that this legitimacy is reductively analyzable into a mere mathematical consistency. The pathology of a non-Hausdorff FRW spacetime may allow a mathematically constructible abstract topological space X with corresponding features, but it is inconceivable to see how any argument can be developed to show that we live in such a spacetime or that such a spacetime is physically acceptable or “metaphysically legitimate”.

It may be thought that some of Earman’s theses can be defended, even if Earman himself does not provide such a defence. For example, one may ask why omnipresence cannot be understood or analyzed (at least in some cases) in terms of topological nearness to every point of the manifold. I think the answer is that God’s omnipresence is a mental relation of a person (God) to all physical creatures (or all creatures, or everything), whereas a topological nearness is a nonmental relation between points on the manifold.

A defender of Earman may nonetheless ask why we cannot interpret God’s ability to causally sustain every event with the help of the notion of topological nearness. I would respond that if we broadly interpret this question, then we can answer by saying that topological relations, like vectors, affine connections and metrics and many other physical attributes are helpful in obtaining a complete understanding of what it is for a universe to be causally sustained by a deity. My point is merely that the particular way in which Earman uses such notions does not result in valid or sound arguments or helpful interpretations. Earman is talking about a spacetime manifold that is not Hausdorif-separated, which is a physically pathological manifold that could not sustain living creatures or things in any familiar sense we could recognize. Earman’s attempt to unite GTR and philosophy of religion does not in this case result in any sound (or even valid) argument. It may be worthwhile to show this in more detail.

Analyzed in the most specific way possible, Earman’s account can be read as an innovative argument that a deist could use to show that a deistic God is “near” to every event, even though God causes only the big bang singular point. (Consistently with Earman’s usage, we shall say a deist holds that God causes only the first natural event or the earliest boundary of spacetime, whereas a classical theist holds that God continuously creates the universe. Following Earman, we use “theist” to refer to a deist or classical theist.) Earman is here addressing deism. Thus, in the passage in question, Earman talks of a “deistic cause” (1995: 209) and the sentence in the relevant footnote (“although God operates at the beginning of time, He is nevertheless near every event”) is naturally read as “although the

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deist God causally operates only at the beginning of time, He is nevertheless near every event”. It is this argument that I claim fails due to an equivocation on “nearness”.

A defender of Earman may argue that it is not necessary to interpret Earman’s argument as equivocating on “nearness”. I would respond that if we do not charge Earman with equivocation, we must charge him with a logical contradiction. If Earman’s argument is not read as a fallacy of equivocation on “nearness”, it would go like this:

If there is no equivocation on “near”, then premises (2) and (3) and the conclusion (4) are each implicitly self-contradictory, since (as we have seen) it is logically impossible for God to be topologically near any point. Topological nearness is a nonmental relation between points on a manifold; God is not a point on a manifold and divine omnipresence is not a nonmental relation.

If there is an equivocation in Earman’s text, then Earman’s argument (with the equivocally used terms replaced by the relevant univocal terms) would be read as follows.

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This argument is invalid since the divine attribute of omnipresence includes both divine causation and divine knowledge, and “a deist God causes point x” does not follow (contra (3a)) from “x is topologically near to a point caused by God”. Of course, one could replace “omnipresence” by “knows but does not cause everything” but this interpretation is not the intended one since this replacement would make the argument irrelevant; such a replacement would be tantamount to explaining the meaning of the phrase “a deist god” and (4a)’s truth would not need the premises (1a)—(3a). (4a) would be true by definition (of the deistic god). I think the intent (and the interest) of Earman’s argument is to show that the deistic god can be omnipresent in a hitherto unrecognized sense of “omnipresent” if we substitute some appropriate relation for the relation of causes everything (pertaining to the classical theistic notion of continuous creation) and that this new relation obtains if the deistic god creates a non-Hausdorif separated manifold. Earman thinks the topological relation of nearness can supply the extra ingredient the deist can use to argue that her god has an omnipresence in some genuine and acceptable sense. I have argued the result is merely unsound arguments, either based on fallacies of equivocation or self-contradictory premises. Earman’s argument is novel, but it is not successful.

I will briefly address one further problematic part of the passage from Earman’s (1995: 209) that I have been discussing. Earman makes another novel but unsuccessful suggestion about how a First Cause may be related to spacetimes with singularities. He suggests that God could originally create the universe at ideal points attached “at minus infinity”. “Even in models with no big bang and with time extending infinitely far into the past, ideal points corresponding to t = -∞ could be attached to the spacetime manifold and God’s helping hand could be seen at work here” (1995: 209). The fact that Penrose-diagrams can be drawn with aspects representing infinite distances does not show the notion of God creating ideal

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points at t = —00 is an intelligible notion. It would seem that one of the two most natural interpretations that spring to mind (Earman himself does not explain the sentence I quoted) is that God creates ideal points corresponding to 1 in an infinite past with the order type 1 + w* (1, ..., —3, —2, —1), where each number stands for a Planck time, 10^-43 second. At the very least, it needs to be explained how the creation of ideal points corresponding to I can have a mediated causal influence on the Planck times corresponding to any of the numbers in the subseries (..., —3, —2, —1), given that each of these Planck times is separated from the ideal points corresponding to 1 by an infinite (aleph-zero) number of intermediate Planck times. Perhaps a second interpretation of Earman’s suggestion about the creation at t = -∞ is that a Creative Force creates ideal points corresponding to some number(s) in a series with the ‘natural’ order type of an infinite past, namely, w* (..., —3, —2, —1). The question then is: exactly where in this series are the ideal points located, at minus one trillion, minus one quadrillion, minus one quintillion or at some earlier location?

If we follow Earman in his earlier chapter 2 and do not allow singularities as existent, ideal boundary points, then there is no first point that is physically uncaused. Rather, a first point or t = 0 represents a limit to a series, not something existent, and each instantaneous state of the universe in the series is an effect of earlier instantaneous states. In this case, there is no instantaneous state of the universe that lacks a physical cause. In this regard, we agree with the one of the few remarks Earman makes that belong to an atheistic philosophy of religion, viz., his remark that “the principle Every event has a cause . . is satisfied in the FRW big bang models without any help from the theists” (209). The meaning and atheistic implications of such clauses is perhaps best explicated in Grünbaum’s (1998, 1996); also see Grunbaum (1989, 1991, 1996) and Smith (1995).

But Earman’s emphasis is on showing how classical theism and deism can be defended. Let us consider another passage in chapter 7 where he seems intellectually sympathetic to a theistic theory he attributes to Willham Lane Craig. Earman states (regarding big bang models with a finite physical past) that even if there is no singular, ideal point and no first instant, God can create the universe by virtue of existing in a metaphysical time that is earlier than the physical time that runs out at the big bang. He writes (1995: 209—210). “If there is no first instant for the physical universe or no prior physical time to the big bang at which God can operate, no matter. The Creator ‘may be conceived to exist in a metaphysical time’ and thus ‘to exist temporally prior to the inception of physical time’ (Craig 1994, p. 328)”. Earman seems to identify Craig’s metaphysical time

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with his physically meaningless “mathematical time” (1995: 207) that has continuity/differentiability conditions lower than those required for a physically meaningful extension of time through the big bang. But there seem to be two problems with Earman’s account of metaphysical time.

The first problem is that it is an implicit logical contradiction to suppose that God exists in this earlier metaphysical time. If a metaphysical time t is earlier than a physical time t’, is t earlier than t’ in physical time or meta physical time? If t is earlier than t’ in metaphysical time, then t’ is a part of the metaphysical time series ordered by the metaphysical earlier than relation and thus t’ is a metaphysical time, contradicting the assumption that it is a physical rather than metaphysical time. On the other hand, if t is earlier than t’ in physical time, then t is a part of the physical time series ordered by the physical earlier than relation and thus is a physical time, contradicting the assumption that it is a metaphysical time rather than a physical time.

Can Earman be defended from this contradiction? Could one argue, for example, that if a metaphysical time t is earlier than the physical time t’ in metaphysical time, then t’ is a part of the metaphysical time series and thus t’ is a metaphysical time as well as a physical time? What prevents t’ from being a member of a metaphysical time series and a member of a physical time series?

My response is that “being a metaphysical time” and “being a physiçal time” are logically incompatible predicates and if a time t’ was a member of both time series it would satisfy incompatible predicates. A physical time is a set containing only, simultaneous physical events (relationalism) or a physical time-point (substantivalism) that can be occupied only by physical events (point-events). A metaphysical time is a set of simultaneous events some of which are nonphysical and all of which can be nonphysical (relationalism) or is a nonphysical, substantival time-point (substantivalism) that can be occupied by nonphysical or physical events. Accordingly, if time t’ were both a physical and metaphysical time, then (assuming substantivalism) t’ would have the property of being able to be occupied only by physical events and would also have the property of being able to be occupied by nonphysical events, which is an explicit logical contradiction. There are further contradictions assuming substantivalism and a series of related contradiction if we assume relationalism.

One of these contradictions concerns the issue of whether the earlier than relation Earman mentions is physical or metaphysical. If the physical time t’ is later than the metaphysical time t, it must have the relation to t of being physically later than t. This is because a physical time cannot be temporally related to something x unless it is related to x by the sort of

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relation that determines what sort of time it is (for it is the sort of temporal relations that a time t’ bears to other items that determines what sort of time t’ is — a physical time or a metaphysical time). If the physical time t’ is later than the metaphysical time t, then t’ must be physically later than t. If t’ is both a metaphysical and physical time, then it must have both a metaphysical later than relation to t and a physical later than relation to t. But by Earman’s very argument, there cannot be any time that is physically earlier than the first physical time t’.

The problems do not end here. There is a second set of problems with Earman’s theory of a pre-big bang metaphysical time in which God can exist. This set pertains to Earman’s identification of metaphysical time with a physically meaningless “mathematical time” (1995: 207). Talking of physically meaningless temporal extensions to a big bang singularity at t = 0, Earman writes “But nothing prevents God from using such a measure to peer through the big bang” (1995: 219, n. 5). This sentence appears unclear on the face of it, but if we are charitable enough, we can assign a meaning to it that is sufficiently intelligible from the context of Earman’s discussion.

When Earman is talking about “such a measure” he is referring to volume measures with respect to which a curvature scalar is locally square integrable. More precisely, Earman is referring to volume measures that al low the absolute value of the Kretschmann curvature scalar K to be locally square integrable. The volume measure belonging to the FRW metric is not integrable in this way if one tries to extend it to a big bang singularity at = 0. Other volume measures do not meet this mathematical problem but they are physically meaningless or at least are not satisfied by what physically exists. (Earman recognizes this and notes that “unless some physical significance can be assigned to such measures, the physical significance of the extension (to t = 0) remains moot” (1995: 206).) However, the fact that these mathematically unproblematic volume measures that allow time to be extended to t = 0 are not satisfied by what physically exists is precisely what prevents God “from using such a measure to peer through the big bang”, contrary to Earman’s statement that “nothing prevents God from using such a measure to peer through the big bang” (1995: 219, n. 5). If the mathematical description of such a volume measure is not satisfied by what physically exists, then the divine understanding of this description is not an understanding of a description that is satisfied by the big bang or anything that exists, and thus God cannot “peer through” the big bang or “peer” at anything that exists by virtue of grasping this description. If the physical structure of the universe does not satisfy a certain mathematical description, then it is logically impossible to grasp this structure by virtue

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of grasping the unsatisfied description. It is logically impossible to grasp or peer at a circle by virtue of grasping the description of a triangle. Rather, one must grasp the description of a circle or, in the case at hand, of the volume measure in the FRW metric of our physically existent universe. But since this volume measure precludes a big bang singularity at t = 0, no peering at the universe through a singularity at t =0 is permitted. Thus, Earman’s account of physically unsatisfied volume measures that allow a temporal extension in “mathematical time” to t = 0 does not provide a logically coherent account of how God knows the universe at a time that is earlier than physical time.

I have discussed Earman’s several arguments that it is rationally acceptable to believe that a FRW spacetime has a divine originating cause (whether this cause be construed in terms of deism or classical theism) and found them wanting. Earman’s arguments for the rational acceptability of believing that a general relativistic spacetime has a divine continuing (conserving) cause of spacetime are addressed in the next section. These arguments pertain only to classical theism.

A spacetime is maximal if and only if it is inextendible, i.e., it is not a proper subset of a larger spacetime in which it can be embedded. A FRW spacetime that begins with a big bang singularity and ends with a big crunch singularity is maximal, and a Steady State spacetime, which is spatially infinite and has an infinite past and future, is maximal. An example of a nonmaximal spacetime is our FRW spacetime with the condition that it suddenly and inexplicably ends on May 1, 2032 in a nonsingular state (not in a big crunch). Consider Earman’s metaphysical explanation of why spacetimes are maximal:

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Note that this is the first time “the Creative Force” makes an appearance in Earman’s book, so there is no background of earlier material on the Creative Force that could be used to further illuminate this passage. Note also how difficult it is to read this passage otherwise than as an espousal of a theistic metaphysics, which is one of the reasons that some readers have concluded from Earman’s book that he is a theist. (Another reason is that Earman nowhere states or implies in the book that he is an atheist or that he thinks atheism is a preferable position to theism in the philosophy of religion.) My interpretation of Earman’s actual beliefs vis a vis this passage is that he is using “the Creative Force” as an illustrative example to explain his endorsement of the principles of sufficient reason and plenitude. More precisely, I choose to read it as Earman (unclearly) suggesting that it is rationally acceptable to postulate a Creative Force and rationally compelling to adopt the metaphysical principles of sufficient reason and plenitude. I do not deny that this passage appears to be a puzzling way for an atheist to express himself on these matters and that this mode of expression makes the difficulties of interpretation all the more severe. More generally, I would even grant that a well-deserved criticism of Earman’s book is that at best he makes it extremely unclear that he is an atheist and whether or to what extent he believes the various metaphysical principles he writes as if he is endorsing. Nonetheless, as I suggested in the introduction, what is of philosophical importance are not the biographical facts as to what John Earman does or does not happen to believe, but rather the interesting and novel defenses of theism (classical theism and deism) that appear in certain passages of his book. Accordingly, I will take this passage at face value and regard it as (unclearly) suggesting that classical theism is rationally acceptable and that the metaphysical principles of sufficient reason and plenitude are rationally compelling. Given this interpretation, there are at least six problems with this passage.

First, Leibniz’s principle of sufficient reason is so far from being rationally compelling that it is not even rationally acceptable, since there are well-confirmed theories implying that many events have no sufficient reason; e.g., there is no sufficient reason why a certain alpha particle p tunnelled through the wall of the nucleus of a U²³⁸atom at time t. The weakest possible criticism that can be made in this respect is that no explanation is offered in Earman’s book of how Leibniz’s principle of sufficient reason can be reconciled with quantum mechanics, or what justification there could be for an argument of the form “the principle of sufficient reason is true a priori; therefore quantum mechanics does not describe reality”.

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Second, the advocation of Leibniz’s principle of sufficient reason is in consistent with the admission that cosmic censorship may well fail (1995: 92ff.) and that it may be the case that “classical GTR places no constraints, not even statistical ones, on what can emerge from a naked singularity” (1995: 225). For some x that “emerges” from some naked singularity, there is no sufficient reason why x “emerges”. Given this, what is the basis for a rational confidence that satisfying the principle of sufficient reason is a metaphysically necessary condition for a spacetime to be actual?

Third, the principle of plenitude is false, since it is possible for there to be many more kinds of entities than those that actually exist. Australopithicines, homo erectus, homo habilis and homo sapiens are not the only possible kinds of hominids, since there are numerous possible DNA variations that would result in different (but unactualized) species of hominids. In light of such facts as these, it is hard to see how the principle of plenitude could be rationally acceptable, let alone rationally compelling.

Fourth, the thesis that a Creative Force causes the maximality of spacetime contradicts the FRW principles that govern our spacetime. An example of a nonmaximal FRW spacetime would be our spa except that it suddenly comes to end (in a nonsingular state) on May 1, 2032. If this spacetime were not maximal, then there would be some time t such that the boundary conditions at t and the FRW laws of nature are jointly sufficient for spacetime to exist at a later time t’ but spacetime does not in fact exist at t’. But this is logically (and not just physically) impossible, for the conjunction of the premise stating the relevant boundary conditions (conditions that do not lead to a singularity) with the premise stating the FRW laws entails the conclusion that the spacetime exists at t’. For example, if a FRW universe is expanding in a non-inflationary manner at a certain rate v at time t, this is causally sufficient for the universe to be expanding at a slower rate v’ (or zero rate, if it reaches a maximum radius) at a later time t’. (Recent observations of supernovas suggest that big bang cosmology may need to be revised to allow for a cosmological constant (or something else) that causes the rate of the universe’s expansion to increase with time.) The boundary conditions and FRW laws imply that spacetime is maximal and ends in a big crunch or is maximal and expands forever. Since the maximality is causally explained within GTR, there is no causal role required or permitted for a “Creative Force”.

Fifth, the claim that “such principles” as the principle of sufficient reason and the principle of plenitude are used in Geroch (1970: 262) and Penrose (1969: 253) is not born out by the textual evidence. Penrose and Geroch are talking about contingent and a posteriori physical principles. For example, Penrose writes that an observer in a rocket ship free falls to

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the Schwarzschild radius (r = 2m) of a body and the observer’s proper time would show a finite time elapsed in the fall. “But what does the observer experience after this proper time has elapsed? Two possibilities which suggest themselves are (i) the observer encounters some form of space-time singularity — such as infinite tidal forces — which inevitably destroy him as he approaches r = 2 m; (ii) the observer enters some region of space-time not covered by the (t, r, q, j) co-ordinate system used in (l). (It would be unreasonable to suppose that the observer experiences could simply cease after some finite time, without his encountering some form of violent agency.) In the present situation, in fact, it is possibility ii) which occurs” (Penrose, 1969: 253, my italics). The italicized sentence in parentheses, which is the one Earman apparently has in mind, is not an appeal to an a priori or metaphysically necessary principle of sufficient reason. Rather, it is a physical reasonableness that Penrose is discussing, i.e., what is reasonable given the empirically confirmed theory of general relativity. The observations confirming general relativity or, more exactly, the FRW theory of our universe, all confirm the hypothesis that things cease to exist only if caused to do so. The physical reasonableness is also based on our other background empirical knowledge, e.g., our daily observations of middle-sized objects. If observations told us otherwise, Penrose would in this case not say that “it would be unreasonable to suppose that the observer’s experiences could simply cease after some finite time, without his encountering some form of violent agency”.

Similar considerations pertain to the passage in Geroch (1970: 262) that Earman mentions. Geroch writes that “We may regard inextendibility as a reasonable physical condition to be imposed on models of the universe. (Why, after all, would Nature stop building at M when She could just as well have carried on to build M’?) Furthermore an extendible spacetime provides a rather unpleasant environment for certain observers who, al though they follow geodesics, nonetheless experience only a finite proper time” (1970: 262, my italics). Apart from Geroch’s express indication that he has in mind merely a physical condition, not a metaphysical condition, it is apparent from this passage that he is presupposing the empirical confirmations of GTR. Geroch’s last sentence indicates that considerations of the pleasantness or unpleasantness of the environment presuppose that there are observers following geodesics, i.e., they presuppose the empirically confirmed theory of general relativity. There is no reason to suppose that the reasonableness of the physical condition of inextendibility is based on a priori or supernatural considerations, for Geroch talks of “Nature” and his “Nature” (unlike Earman’s “Creative Force”) can plausibly be read as referring to the totality of observed or observable natural entities.

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“Nature” can have an empirical reference even if we interpret it in terms of a posteriori, contingent background knowledge that is independent of the specific observations that confirm general relativity, e.g., knowledge that the middle-sized objects of our daily experience do not causelessly cease to exist. It seems that Geroch is suggesting that “for any x, if x is a spacetime manifold, x is inextendible” is physically necessary and is a basic law of nature.

This leads us to the sixth problem, namely, that no explanation is given of the phrase “metaphysical considerations”, let alone of where the boundary between “physical considerations” and “metaphysical considerations” is supposed to lie. Nonetheless, the contexts in which Earman uses the term “metaphysics” make his usage sufficiently clear for purposes of evaluation; usually “supernatural” and/or “synthetic a priori” can be substituted for “metaphysical”. Given Earman’s usage, a statement about God or about a synthetic a priori principle would count as a metaphysical statement. He does not appear to have in mind Plantinga’s (1970) or Kripke’s (1972) theory of a posteriori logical necessities. (For discussion, see Smith (1998d, I 998e).)

Could the problems with Earman’s theory about the role of the prin ciples of sufficient reason and plenitude in GTR be ameliorated if we redefined “metaphysical principles” to mean regulative principles, principles that in some sense “regulate” physical inquiry? Could the principle of sufficient reason play a role as a regulating principle in the construction of GTR and other physical theories? This seems false at best and self- contradictory at worst. First of all, if the principle of sufficient reason played a regulating role in the construction of physical theories then neither quantum mechanics nor big bang cosmology could ever have been constructed. For quantum mechanics (on the standard interpretation) implies that many events have no sufficient reason and big bang cosmology implies that the big bang singularity or the beginnings of singular FRW spacetimes do not have a sufficient reason in the sense of “sufficient reason” (physical sufficient reason) that is used in the construction of these theories. (Nor do they imply that the big bang singularity does or must have a sufficient reason of some sort, even if nonphysical.) Thus, it is false that the principle of sufficient reason plays a regulative role in the construction of physical theories.

Furthermore, the very notion of such regulative principles is incoherent. If we are trying to resolve the problems in Earman’s theory by considering metaphysical principles to be something other than synthetic a priori truths, then the regulative principles cannot be synthetic a priori truths. Nor are they analytic truths; it has been recognized since Hume and Kant that the

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principles of sufficient reason and plenitude are not analytically true. Nor can the regulative principles be a posteriori, synthetic and necessary truths (or any other sort of a posteriori truths), since a posteriori truths constitute the category of theses or theories whose discovery or construction is regulated by the regulative principles. (The discovery or construction of any posteriori thesis is “regulated” by a priori reflection in which the discovered or constructed thesis is compared in the relevant ways with the principles of sufficient reason and plenitude).

By process of elimination, the regulative principles must be principles that by their very nature lack a truth value (such as Wittgenstein’s “framework sentences” or Richard Taylor’s “presuppositions of reason”). However, if they are principles that lack a truth value, then we cannot appeal to such a principle to justify indefeasibly our belief in a certain theory we construct. If the indefeasible justification for the belief that p is true is based on a principle q, then q is true. Something that is not true cannot justify indefeasibly belief in what is true. Moreover, invalid inferences would appear at some point in our theory constructions, for example in an argument such as the following:

This is manifestly an invalid argument, since the (allegedly) true conclusion meets the condition of instantiating a principle mentioned in a premise but not does meet the condition of instantiating a true principle mentioned in a premise. I think it can be argued further that contemporary theories of framework or regulatory principles are self-referentially incoherent (for reasons explained in Smith, 1 997c: 58—62). Accordingly, I think that re defining “metaphysical principles” to mean regulative principles is not a promising way to salvage Earman’s metaphysical construal of GTR.

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Earman argues near end of his book that it is not necessary to have singular spacetimes in order to have rationally acceptable evidence for God’s existence. He suggests that there are scientifically inexplicable and theistically explicable natural phenomena in every scientific theory and thus that science “has a place” for a Creator. (I am here borrowing the phraseology from Hawking’s famous question, “What place, then, for a Creator?”). Earman writes: “science leaves unexplained the most fundamental laws it has been able to uncover, and it cannot say why one rather than another of the myriad histories compatible with these laws has been actualized… It strikes me as bordering on the sacrilegious to see God’s creative force as able to operate only at a singularity or ideal point. It is more to His glory if He operates everywhere and everywhen, and if He operates independently of such contingencies as whether there is an initial singularity and, if so, what type it is” (1995: 209).

One thesis that seems to be suggested by these remarks is that science cannot explain the boundary conditions of the universe, e.g., why one rather than another of the myriad histories compatible with the fundamental scientific laws is actualized. Interpreting these remarks in terms of the “rational acceptability” epistemology of religious beliefs, we may interpret Earman as suggesting that it is a rationally compelling belief that science cannot explain the boundary conditions of the universe and a rationally acceptable (but not rationally compelling) belief that God created these boundary conditions.

But this thesis is inconsistent with the research program of quantum gravity cosmology that began in the early l980s and is been actively advanced today. The wave functions of the universe developed by Hartle and Hawking, Vilenkin, Linde, and others purport to explain why one rather than another of the myriad histories compatible with the basic laws is actualized. The aim is to eliminate “brute fact” or inexplicable boundary conditions from science. For example Hawking writes that:

i) a set of differential equations that govern the variables in the theory. These are normally derived from an action principle.

ii) boundary conditions for the differential equations, or for the fields that are considered in the action principle.

One could conceive of models which did not have this division into field equations and boundary conditions .... By evaluating the path integral over compact metrics, one eliminates one of the two parts of physics, the boundary conditions. There ought to be something very special about the boundary conditions of the universe and what can be more special than the condition that there is no boundary. (1987: 162, 170)

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In the Hartle—Hawking theory, there are no boundary conditions in the sense of brute facts or unexplained initial conditions; the only boundary conditions are initial conditions explained and predicted by the basic law stating the wave function of the universe. (For discussion, see Smith (1998a, 1998b, 1997a; 1997b; 1994a). For criticism, see Craig and Smith (1993); Craig (1998; 1997; 1993); Deltete and Guy (1996, 1997)). Earman says that quantum gravity cosmologies are too speculative to be evaluated, but he refers here (1995: 58) only to Hawking’s infamous popularizer A Brief History of Time. The many technical articles on quantum gravity cosmology that Hawking authored or co-authored are not mentioned any where in Earman’s (1995), not even in his vast bibliography (pp. 228—245). The large number of workers in quantum gravity cosmology have evaluated the hundreds of technical articles developing this research program, and they do not share Earman’s hand-waving dismissal. Fang and Wu, in their introduction to a collection of some of the main technical essays on quantum gravity cosmology, evaluate this cosmology differently. “In principle, one can predict everything in the universe solely from physical laws. Thus, the long-standing ‘first cause’ problem intrinsic in cosmology has been finally dispelled” (Fang and Wu, 1987: 3). Here of course they are talking about the ideal at which this research program is aiming. At present, there are too many unsolved mathematical and interpretative problems to justify any belief that the ‘first cause’ problem has been “finally dispelled” or that we know in principle how to “predict everything in the universe solely from physical laws”. But the fact that the major physics journals, conferences and collections of essays are filled with essays on quantum gravity cosmology is but an external sign that this research program has been making considerable progress since its inception (in its modem form) in 1982—1983 by Vilenkin, Hawking and Hartle. Even the most confident proponents of quantum gravity cosmology, such as Hawking, emphasize that at present we merely have reasonable proposals about some of the general features of a complete and consistent theory. But one sign of the progress being made is that the gravest difficulty facing quantum gravity cosmology since its inception, namely, that it is perturbatively nonrenormalizable and therefore apparently mathematic ally inconsistent, has arguably been solved in the 1 990s. For example, Rivasseau (1991); Wightman (1994) have shown that perturbative normalizability is not a necessary condition of mathematical consistency. A case in point is that the Gross-Neveau model in 3 dimensions (GN) has been proved to be exactly soluble, even though it is perturbatively non renormalizable (Rivasseau, 1991; Wightman, 1994). The consequences for such recent results have been developed in Ashtekar’s important study,

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“Recent Mathematical Developments in Quantum General Relativity” (1996). It is worth quoting some of Ashtekar’s conclusions:

It is well known that quantum general relativity is perturbatively non-renormalizable. Particle theorists often take this to be a sufficient reason to abandon general relativity and seek an alternative which has a better ultraviolet behavior in perturbation theory. However, one is by no means forced to this route. For, there do exist a number of field theories which are perturbatively non-renormalizable but are exactly soluble. An outstanding ex ample is the Gross-Neveau model in 3 dimensions, (GN)₃ which was recently shown to be exactly soluble rigorously. Furthermore, the model does not exhibit any mathematical pathologies. For example, it was at first conjectured that the Wightman functions of a non-renormalizable theory would have a worse mathematical behavior. The solution to (GN)₃ showed that this is not the case; as in familiar renormalizable theories, they are tempered distributions. Thus, one can argue that, from a structural viewpoint, perturbative renormalizability is a luxury even in Minkowskian field theories. It does simplify the analysis considerably. But it is not a consistency check and should not be elevated to a viability criterion for physical theories. (Ashtekar, 1996: 75)

This suggests that the main charge against quantum gravity cosmology (specifically, the quantum general relativity theories of Hartle and Hawking, Vilenkin, Linde and others), the charge that it is “incomplete and inconsistent” is wrong, since the argument for inconsistency has been undermined. The fact that it is incomplete (and that there still remain problems of interpretation and choice of mathematical boundary conditions, etc.) are serious, but the main weight of “inconsistent because perturbative non-renormalizable” has been essentially lifted from the program. (As Ashtekar (1996) argues, one could also develop a non-perturbative quantum general relativity, but it seems to me this approach is more sketchy at present than the perturbative approaches.)

The rejection of this large research-program out of hand and the as section that no such proposals can be justifiably made or evaluated would seem to require a skeptical argument that does not imply skepticism in general, and I am unaware of any such restricted skeptical argument.

There is a further issue that needs to be pointed out to the “cautious” physicists or philosophers of physics who think that general relativity or quantum mechanics is “safe” but that quantum gravity theories are epistemically “unsafe” areas to enter. I have in mind that general relativity and quantum mechanics are logically inconsistent with each other, a fact symbolized by the reference of the time variable in the Schrodinger time dependent equation to a Newtonian absolute time. The attempt to resolve the manifold inconsistencies between GTR (general theory of relativity) and QM (quantum mechanics) by developing quantum field theories such as quantum electrodynamics only partly resolves the mutual inconsist encies, for these quantum field theories are themselves inconsistent with general relativity. For example, in QFT (quantum field theory), operators

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can be associated with spacetime regions. Operators associated with relatively spacelike regions commute, conflicting with the local nature of GTR. How could Earman feel he is on epistemically safe grounds (GTR) in the face of the facts that quantum electrodynamics has both been verified to a greater degree of predicative accuracy than general relativity and that it is inconsistent with general relativity? (The widely recognized difficulty of reconciling general relativity with the EPR correlations is only the least of the problems facing general relativity.) It seems to me that at this point in physics we can only talk about “the least unsafe grounds” and this arguably now resides in the mathematically and conceptually incomplete quantum gravity theories, since this is now the only theory that is not inconsistent with any verified theory (since it incorporates them all) and — thanks to Rivasseau, Wightman and others — can no longer be dismissed on the grounds that it is perturbatively nonrenormalizable. Roughly, the situation is that QM, QFT and GTR are more well-worked out mathematically than QG (quantum gravity) and are experimentally well-verified but both QM and QFT are inconsistent with GTR. Quantum gravity on the other hand, is not nearly as well worked out mathematically (or interpretatively) but is making progress towards unifying QM with GTR, that is, towards over coming the contradiction between the two main sorts of physical theories of the 20th century. One can no more remain content with the conjunction of extant QM and GTR, or extant QFT and GTR, than one can happily balance oneself on a round square. It is epistemically preferable to try and keep one’s balance on the storm-swept summits of QG. (For this reason, I have always found it troubling that virtually all philosophers of physics choose QM, STR or GTR as their subject of study. I have been told by some that the reason is that QG is “too difficult”. I respond that in the l920s philosophers of physics avoided GTR on the grounds that it was “too difficult”. Perhaps it is a responsibility of philosophers of physics to formulate QU in a way that makes it a more comprehensible theory. Christopher Isham (private communication of 1994) rightly suggests that this is a proper task for philosophers of physics.)

I criticized Earman for not clarifying the relationship between metaphysics and physics or explaining the criteria for determining whether a physical theory confirms theism or atheism, but up to this point I have offered no positive suggestion of my own. I have elsewhere (in Smith, 1994b; 1998c) supplied some evidence, by a method of enumerative induction, that metaphysical theses and other philosophical theses (e.g., theses in the

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philosophy of language) that have relevance to the physical universe are a part of physics (and are neither foundations of physics, nor presuppositions of physics, nor interpretations of physics, nor implications of the conjunction of physics with other principles, nor regulative principles of physical theories, nor external to physics in some other way). Specifically, metaphysics, philosophy of language, etc., are the part of physics that are involved in ontologically interpreting the constants and parameters in the mathematical formula and in interpreting the relation of the formulae to reality. This is not to stipulate (by a truth-valueless definition) that this is what “physics” or “metaphysics” means; rather, the point is to establish the truth of this thesis by showing that what have traditionally been called metaphysical or philosophical theses can be found in the writings that have traditionally been called “physics books or articles”. Towards this end, I quoted (Smith, I 994b: 3) Minkowski’s metaphysical theory that time is tenseless (the B-theory of time) and showed how it was a part of his 1908 theory, the Minkowskian or spacetime formulation of STR. And I elsewhere quoted Einstein’s thesis in the philosophy of language that both the ordinary and scientific meaning of “simultaneous” is the method of its verification (Smith, 1998c: 138—139) and indicated how this thesis is apart of STR. But this is only a beginning of what would need to be a vast task of relating metaphysical and other philosophical theses to a great variety (or all) works of physics, a task that is too large to complete but which can be approximated to some degree by way of enumerative induction.

To explain briefly the thesjs that physics includes metaphysics as a part, I can give an example that is directly pertinent to GTR. Consider one of Friedmann’s equations that defenders of classical GTR represent as describing our universe:

This equation includes the syntactic item “t”, which is generally in terpreted as a parameter (it has varying values, rather than a constant value). At least two decisions are made in providing this parameter with a more specific interpretation, interpretations that are metaphysical in nature. First, it is decided that “t” ranges over times; Second, it is decided that the times are certain physical states or features of the universe as a whole, often its radius. Christopher Isham expresses a common view when he writes: “The time variable associated with this decomposition (of a tenseless Friedmaim universe into various three dimensional spaces) is the radius of the sphere… An absolutely crucial idea here is that ‘time’ can be defined internally in terms of a particular property (i.e., radius) of the curvature of the three-dimensional space” (Isham 1988: 391). These interpretations of

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“t” constitute a certain metaphysical theory of time, namely, a relationalist (reductivist), physicalist, verificationist and tenseless theory of time. A further set of metaphysical decisions are made about what reality must be like in order for certain physical conditions (e.g., the distance between superclusters of galaxies) to be measurable manifestations of time (the radius of the universe). (For simplicity’s sake, I am here assuming a modification of the syntactic theory of science; the example could be restated in terms of a modification of the more recent semantic theory of science developed by Bas Van Fraassen, Ronald Giere and others.)

If metaphysical principles, or any philosophical principles, that are related to the physical world are a part of physics, then how should we understand the relation between theistic physics and atheistic physics? Is GTR an atheist metaphysics and is Newtonianism a theistic physics, such that the atheistic and theistic principles are included as parts of theses physics? The “received view” is that the answer is negative (“science has no implications for religion”), but the textual evidence speaks otherwise. If we take Newton’s original presentation of his theory, where absolute space is identified with God’s sensorium, then a theistic metaphysics is a part of the interpretation of any syntactic construction that refers to absolute space. It is part of Newton’s original theory, as presented in his Fundamental Principles of Natural Philosophy, that “He [God] endures forever and is everywhere present; and by existing always and everywhere, he constitutes duration and space” (Newton, 1957: 209). These may be taken as theoret ical identifications: duration is identical with God’s attribute of enduring forever and space is identical with God’s attribute of existing everywhere. (Compare with the paradigmatic contemporary example of a theoretical identification, water is identical with H By “natural philosophy” New ton means physical theory. He writes: “And thus much concerning God, to discourse of whom from the appearance of things does certainly belong to natural philosophy” (Newton, 1957: 210). However, the program that became known as “Newtonian physics” and is reproduced in contemporary undergraduate textbooks omitted the theistic part from Newton’s own version of his physics.

Copernicus’ On the Revolution of the Heavenly Bodies is also a theistic physics, defining (for example) gravity in terms of a Creator: “. . gravity is but a natural inclination, bestowed on the parts of bodies by the Creator so as to combine the parts in the form of a sphere and thus contribute to their unity and integrity” (Copernicus, 1957: 164). x is gravity if and only if x is an inclination bestowed by the Creator on the parts of bodies so as to combine the parts in the form of a sphere and thus contribute to their unity and integrity.

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Of course the position I am advocating about the relation of physics to metaphysics is not the absurd thesis that a physics book or article presents a theistic physics if the word “God” or “Creator” appears in some of its existentially generalizable sentences and is atheistic if no religious terms appear in it. The position I am advocating may be concisely and precisely put as follows. Laws of physics are interpreted mathematical equations, with the equations consisting of mathematical symbols (e.g., —3, p, =) and nonmathematical parameters or constants (e.g., t, G, p, P, a). (t, p, P and a are parameters since they have changing values and G is a constant since it has a fixed value, G = 6.67 x 10^-11.) A physics is theistic if any of the nonmathematical parameters or constants in the equations are semantically interpreted as referring to God or a divine attribute, etc. (For example, in Newton’s original theory the parameter t is interpreted as referring to a particular divine attribute and in Copernicus’ theory the gravitational constant G (which Copernicus did not assign a numerical value) is interpreted as referring to an effect of a certain sort of divine volition). More completely stated, a physics is theistic if and only if any of the basic or derived laws of nature, theoretical identifications, or definitions of constants and parameters, involve a reference to something divine. The standard contemporary view of theistic philosophers of religion (Quinn, Alston, etc.) is that references to God appear in (normally) unmentioned ceteris paribus clauses appended to statements of the laws of nature; I have argued elsewhere that this standard view is logically untenable ((Smith, 1998a, l998b, 1997a, l997c, 1996, 1995, 1994a; Craig and Smith, 1993)).

Theistic physics are not necessarily confined to the past. It is possible that a suitably revised version of Wigner’s (1961) interpretation of quantum mechanics (that only consciousness can collapse a wave function) may be combined with a complete wave function of the universe of the sort that Vilenkin (1996) or Hartle and Hawking (1983; 1996) attempt to approximate. There may be a wave function of the universe that explains everything in the universe. We may call this possible theory (no such developed theory presently exists) a Wigner quantum gravity cosmology. One may suppose a single, divine consciousness collapses the wave function of the universe, and that this wave function is a superposition of all physically or metaphysically possible universes. By collapsing this wave function, God creates our universe (Smith, 1995).

By contrast, GTR includes an atheistic metaphysics. None of the definitions, identifications or laws include a concept of God or a divine attribute, etc. GTR attaches no meaning to something not in spacetime or its boundary, and it implies its causal laws are sufficient to explain the continued existence of the universe. (See Grünbaum (1998) for a good example of

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this last point. For other arguments to this effect, see Smith (1998a, 1995) and Craig and Smith (1993).)

I think accordingly that the criteria for deciding whether a certain physical theory confirms atheism or theism requires (a) an examination of the observational evidence, (b) an examination of the consistency and completeness of the mathematical equations, (c) an examination of the metaphysical assumptions or arguments that play a part in the semantic interpretations of the nonmathematical parameters and constants in the equations, (d) an examination of the adequacy of the metaphysical content in the theory’s laws and theoretical identifications and (e) an examination of the metaphysical assumptions underlying the decision about what sort of observational evidence (experiments, ways of reading the experimental data, etc.) is to be used as confirming or disconfirming evidence for the laws, identifications and definitions. With this understanding of the relation between physics and metaphysis, I would say that the foregoing arguments I presented suggest that the metaphysical principles Earman discusses are not in fact a part of GTR and that whatever confirms GTR ipso facto con firms atheism. If theism is not to die out admist the atheistic metaphysical content of current science, it must turn to its main current hope, namely, the prospect of developing a Wigner quantum gravity cosmology.[1]

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[1] I am grateful to Adolf Grtinbaum for many helpful discussions of Earman’s (1995) and the issues discussed in this paper. I also thank two referees who wrote helpful comments about an earlier version of this paper, which enabled the paper to be improved.

One of the referees aptly noted that an adequate treatment of the subject of this paper requires discussing the general issue of how God’s causal activity pertains to the causal connectibility of physical events. I agree but would respond that this topic requires several articles or books unto themselves (e.g., see Smith (1998a, l998b, 1996, 1995) and Craig and Smith (1993)). I think the present article can stand on its own if we rely on the familiar, vague and intuitive notion of “God causes x” that is typically used in papers where the nature or definition of divine causation is not the topic of discussion. This is not to say that this familiar notion is unproblematic or even coherent; see Smith (1996) for an argument that “God causes the universe” expresses a proposition whose negation is a theorem of standard propositional logic.