In “A Cosmological Argument for a Self-Caused Universe,” one of us (Smith) argued that the universe explains its own existence because (i) its existence is entailed by (and so explained by) the existence of the infinitely many instantaneous universe states that compose it, and (ii) each of those states is caused by (and so explained by) infinitely many earlier universe states. Moreover, (ii) is true even if the universe is finitely old because, given standard Big Bang cosmology (Friedmann cosmology), the universe does not exist at t0 (i.e., the Big Bang singularity is not real) and no matter how close some moment tn (at which the universe does exist) is to t0, there are infinitely many (indeed continuum-many) moments at which the universe exists that are even closer. Thus, even a finitely old universe has no beginning in the sense of a first moment, and hence its state at any moment is (sufficiently) caused by (all of) the universe states that precede it. Further, since this explanation of the existence of the universe is complete despite making no reference to God, and since God by definition is a part of any complete explanation of the universe, it follows that God does not exist.
Robin Collins uses the example of the flight of a cannonball in an attempt to show that this argument is flawed. The example goes like this. Suppose gunpowder explodes in a cannon at t1. Now consider the subsequent movement or “flight” of the cannonball, which we may suppose occurs during the interval of time composed of all of moments later than t1 up until the moment the cannonball lands. Notice that, prior to any particular instantaneous flight state, there are infinitely many other flight states since, if time is continuous, no matter how close some moment tn is to t1, there are infinitely many other moments at which the cannonball is in flight that are even closer. What, then, explains the flight of the cannonball? According to Collins, if we follow Smith’s reasoning, then we may say that the flight of the cannonball explains its own existence, because (i*) its existence is entailed by (and so explained by) the existence of the infinitely many instantaneous flight states that compose it, and (ii*) each of those states is (sufficiently) caused by (and so explained by) infinitely many earlier flight states. If Smith is right about the implications of (i) and (ii), then (i*) and (ii*) should prove that the explosion of gunpowder at t1 is not a part of the complete explanation of the cannonball’s flight. But obviously it is. Therefore, Collins concludes, something must be wrong with Smith’s argument, even if it is difficult to say exactly what is wrong with it.
Collins takes his cannonball case to be a counterexample to a “principle” that he calls PCE. He quotes PCE directly from “A Cosmological Argument for a Self-Caused Universe“:
PCE: “Once the existence of each of the parts is causally explained, the existence of the whole [or aggregate] is logically explained, since it is a logical consequence of the existence of the parts of the whole that the whole [or aggregate of parts] exists.”
We (Draper and Smith) believe that it is a mistake for Collins to equate PCE with some general principle to which Smith’s earlier essay is committed. To begin with, PCE is an argument—not a principle (note the premise indicator “since”). More importantly, when read in context, it should be clear that it is an argument specifically about the universe and its parts, not about all wholes and their parts.
Of course, it is still legitimate to ask whether the cannonball example threatens PCE, properly understood. To answer this question, let’s first reword PCE. This is necessary because, as it is now worded, its first clause is superfluous. The existence of the parts of the whole universe (or of the parts of the whole cannonball flight for that matter) entails and so logically explains the existence of the whole whether or not those parts are themselves causally explained. The real issue is when such an explanation is complete. Thus, PCE is better stated as follows:
PCE*: Once the existence of each of the parts (states) of the universe has a historically complete explanation in terms of (earlier) parts of the universe, the existence of the universe is completely explained, since the existence of the universe is a logical consequence of the existence of its parts.
Since the flight of the cannonball does not have a historically complete explanation in terms of earlier parts of that flight, no sound parallel argument can be constructed for the conclusion that the flight of the cannonball is completely explained by its parts and their causal relations.
Still, it would be a mistake to conclude from this that Collins’ objection has been refuted. For Collins may challenge as question-begging the assumption that, just because each universe state has a complete scientific explanation in terms of earlier states, it follows that it has a complete historical explanation in terms of those states. For even though Big Bang cosmology makes no reference to God, how can we be sure that God is not as much a part of the complete historical explanation of any universe state as the explosion of gunpowder is of any flight state?
The point of this question is not to suggest that God might be the cause of the Big Bang singularity. The universe state that would exist at t0 if there were a first moment of time would be a zero-dimensional point in which there is packed all the three-dimensional matter of the universe; this is what physicists mean when they call that point “infinitely dense.” But the existence of such a point is both a mathematical and a logical impossibility. Therefore, the singular state that supposedly would exist at t0 not only is not real but cannot be real, and thus not even God can create the universe by causing that state.
But this is not what Collins has in mind. What he means to suggest is that God’s creative act might be a part of the complete causal history of any universe state, even if the universe did not exist at t0 and so did not have any first moment of existence. (Similarly, the exploding gunpowder is a part of the complete causal history of any flight state even if the flight of the cannonball did not exist at t1 and had no first moment of existence). We should not, however, interpret Collins as suggesting that some divine act of willing that the universe exist literally occurred at t0. Such an interpretation would be uncharitable because, if there were a time t0, it would belong to the physical time series that is posited by Friedmann’s cosmology; it would be a value of the temporal variable “t” in Friedmann’s equation and this temporal variable is defined by Friedmann as ranging over physical times. Collins could best state his case by supposing that there is a metaphysical time series in which God exists and that any physical time correlates to a metaphysical time [see Smith 1993, 1998; and Craig 2001]. He could then argue that, even though there is no t0, there is a metaphysical time T0 at which there is a divine creative act that causally originates the physical time series and all the universe states in this physical time series. In other words, Collins could plausibly claim that, even if the physical causal history of the universe has no first moment, it is possible that the complete (metaphysical and physical) causal history of the universe does. But even if we admit the possibility of God being a part of a complete metaphysical explanation of the universe and so admit that Smith’s argument does not demonstrate the nonexistence of God, two important conclusions still follow.
First, Big Bang cosmology undermines one major theistic argument, namely, the kalam cosmological argument. This result is remarkable, since most defenders of the kalam argument appeal to Big Bang cosmology for support. According to the kalam argument, anything that begins to exist has a cause other than itself of its existence; therefore, since the universe began to exist, it follows that it has a cause other than itself of its existence. Suppose on the one hand that “begins to exist” means “has a first moment of its existence.” Then the second premise of this argument, the premise that the universe began to exist, should be rejected. For as explained above, Big Bang cosmology supports the view that the universe cannot exist at t0 and more generally has no earliest moment. Suppose, on the other hand, that “begins to exist” just means “is finitely old.” Then the first premise of the argument asserts that anything that is finitely old has a cause other than itself of its existence. The argument in “A Cosmological Argument for a Self-Caused Universe” shows, however, that there is no good reason to believe that this premise is true. A finitely old universe with no first moment can have a complete explanation of its existence even if it has no “external” cause.
Second, even if we cannot disprove God’s existence, we still have a powerful probabilistic argument against it, indeed one having the same logical structure as Collins’ design argument. For Smith showed in “A Cosmological Argument for a Self-Caused Universe,” not just that a self-caused universe is possible, but also that its actuality is supported by our best scientific cosmology. Surely theists should be surprised by this while metaphysical naturalists, who deny the existence of supernatural causes, should not. Granted, many naturalists believe that the existence of our universe is a “brute fact” (that is, a fact having no explanation); but the only reason they hold this belief is that they mistakenly think that a naturalistic explanation of the universe is impossible. Therefore, relying on Collins’ “likelihood principle,” we can draw the following conclusion: the fact that our best scientific theory of the origin and evolution of the universe supports the claim that the universe is self-caused is antecedently much more likely given naturalism than it is given theism and so is very strong evidence supporting naturalism over theism.
Appendix: Technicalities (by Quentin Smith)
Before responding directly to my argument, Collins raises two technical objections to some of its assumptions. The first of these objections is that the argument assumes that one can speak of the instantaneous state of the whole universe in some absolute sense; however, Collins says, Einstein’s theory of special relativity denies that this is possible, implying instead that any set of instantaneous universe states will have to be defined relative to a specific inertial frame of reference. My essay explicitly notes, however, that it assumes Friedmann’s cosmology, not special relativity. Friedmann’s cosmology is the solution of Einstein’s theory of general relativity that applies to our universe; special relativity is the “vacuum solution” of the equations of general relativity. This point about special and general relativity, which is often not recognized by philosophers, is crucial here. For Friedmann’s cosmology does admit of an absolute frame, or a “privileged frame,” as is often said (e.g., by Valentini ; and by Misner, Thorne and Wheeler ).
The second technical objection is that the universe is indeterministic, which casts doubt on my assumption that each instantaneous universe state is caused by prior instantaneous universe states. This objection is based on quantum mechanics, which is one of the many scientific theories that there was no space to discuss in “A Cosmological Argument for a Self-Caused Universe.” Collins wants to know my view; so here it is in a nutshell. I am assuming Bohmian quantum mechanics, which is causally determinist. Valentini  argues that Bohmian quantum mechanics can be integrated with Friedmann’s cosmology; the result is a causally determinist universe in which there is a universe-wide absolute simultaneity plane.
Craig, William Lane (2001). Time and the Metaphysics of Relativity. Dordrecht: Kluwer Academic Publishers.
Misner, Charles W., Kip S. Thorne, and John Archibald Wheeler (1973). Gravitation. New York: W. H. Freeman.
Smith, Quentin (1993). Language and Time. New York: Oxford University Press.
Smith, Quentin (1998). ” Absolute Simultaneity and the Infinity of Time” in Robin Le Poidevin (ed.), Questions of Time and Tense. Oxford: Oxford University Press, pp. 135-183. <http://qsmithwmu.com/absolute_simultaneity_and_the_infinity_of_time.htm>.
Smith, Quentin (2006). Chapters 3-7 in Michael Martin (ed.), The Improbability of God. Amherst, New York: Prometheus Books.
Smith, Quentin (2008). Chapter 3 in W. L. Craig and Q. Smith (eds.), Einstein, Relativity, and Absolute Simultaneity. London: Routledge.
Valentini, Antony (1996). “Pilot-Wave Theory of Fields, Gravitation and Cosmology” in James T. Cushing, Arthur Fine, and Sheldon Goldstein (eds.), Bohmian Mechanics and Quantum Theory: An Appraisal. Dordrecht: Kluwer Academic Publishers, pp. 45-66.
 Notice that, contrary to what Collins suggests at the end of “Objections to Smith’s Cosmological Argument,” this explanation is not circular. For it is the existence of all of the proper parts of the universe that (logically) explains the existence of the whole universe, and the existence of any proper part of the universe is (causally) explained by other distinct proper parts. Collins’ objection is based on conflating causal and logical explanations, and on conflating the explanation of each part by earlier parts with the explanation of the whole by all of the parts.
 Near the end of “Objections to Smith’s Cosmological Argument,” Collins suggests that the problem with Smith’s argument might be that it faces an infinite regress problem: “One part of the universe (an IUS) is explained by one or more previous parts, which in turn is explained by one or more previous parts, ad infinitum. Thus, the part of the universe one starts with is never fully explained, since the part doing the explaining always is further in need of an explanation. It is just this complete sort of explanation the theist is after.” The response to this is obvious. Since there are continuum-many universe states, each instantaneous universe state is sufficiently caused and fully explained by all of the states that precede it. Thus, there is no infinite regress of causes.
 Despite some earlier interpretations of speculative quantum gravity cosmologies (see, for example, Smith 2006, pp. 86-106) and arguments that the singularity at the physical time t0 is real (see, for example, Smith 2006, pp. 41-85), the fact remains that the mainstream belief of cosmologists is that no quantum cosmology is better supported than Friedmann’s cosmology and Friedman’s equation is inconsistent with a realist interpretation of the big bang singularity. It is also worth noting that, while Smith’s present view and those in Smith 2006 (pp. 41-86) are incompatible, it would be a mistake to think that Smith has changed his mind about the same set of ideas and arguments. Rather, further study of physical cosmology has led him to a more mathematically detailed and ontologically accurate understanding of the Friedman and Quantum Gravity cosmologies. (This sort of evolution of one’s views is much more common in physics than in a priori philosophical inquiry.) An outline of Smith’s latest views appears in Smith 2008, pp. 73-124, a typo-free version of which will soon appear at www.qsmithwmu.com.
 If Collins also wants to say that God continuously creates the universe, then this would mean that corresponding to each physical time, there is a metaphysical time that contains a divine creative act that causes the physical time and the universe state that exists at that physical time.
Copyright ©2008 Paul Draper and Quentin Smith. The electronic version is copyright ©2008 by Internet Infidels, Inc. with the written permission of Paul Draper and Quentin Smith. All rights reserved.