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Objections to Smith's Cosmological Argument (2008)

Robin Collins


          Summary of Smith's Argument
          My Response to Smith

Summary of Smith's Argument

In his opening case, Quentin Smith has presented an ingenious argument for the claim that the universe is self-caused, and hence its existence is self-explanatory. He then goes on to claim that the fact that the universe is self-caused, and hence self-explanatory, is inconsistent with theism. His main argument is based on the assumption that each temporal part of the universe has an explanation in terms of the temporal parts existing prior to it. The fundamental temporal parts that Smith uses are instantaneous universe states. Before going into Smith's argument, we need to mention two technicalities that the impatient reader may skip.

The first technicality is that according to Albert Einstein's theory of special relativity, one cannot speak of the instantaneous state of the whole universe in any absolute sense, since two spatially separated events can only be considered to occur at the same time relative to a specified inertial frame of reference. For example, consider two light bulbs that flash on for a trillionth of a second, one in the United States and one in China. The flashing of each light bulb would be an event. If these two events were simultaneous relative to a stationary observer on the ground, they would not be simultaneous relative to an observer moving in an airplane. (The ground and the airplane each constitute an "inertial frame of reference," according to the terminology of special relativity.) For the case of the universe, therefore, one must choose a particular frame of reference, and then define a set of instantaneous states with respect to that frame. If one does this, one can think of the universe as being sliced into a continuous series of instantaneous universe states (IUS)--called hypersurfaces of constant time in the literature--recognizing that the choice of the set of events that belong to those instantaneous states depends on the frame of reference one chooses to use in defining the hypersurfaces.

The second technicality involves the issue of the laws of nature being indeterministic, which is implied by the standard interpretation of quantum mechanics. This presents some difficulties for the way Smith presents his argument. If the laws of nature were deterministic, then any IUS at time t1 would completely explain an IUS at any later time t2 in the sense that the existence of the IUS at time t1 conjoined with the laws of nature would logically entail the IUS at time t2. If the universe is indeterministic, however, then in general the IUS at t1 plus the laws of nature would not entail the IUS at some later time t2. Further, it is doubtful that even all the IUS prior to time t2 plus the laws of nature would entail the IUS at t2. Thus, Smith's assumption that each IUS is causally explained by the previous IUS is at best very doubtful. For the remainder of my response, however, I will ignore the problems that indeterminism might present and accept the way Smith sets up the argument.

The key principle that Smith invokes is the following, which we will call Smith's Principle of Causal Explanation (PCE):

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."

Applying this principle to the universe, the parts of the universe are the total set of IUS defined above. The sum total of all IUS logically entails the existence of the universe, whether the universe is considered to consist simply of the sum total of all the IUS or to consist of something over and above the sum of its parts. Thus, since any IUS has a complete causal explanation in terms of a previous IUS, by PCE the existence of the universe is logically explained.

To deal with the standard Big Bang cosmology in which the universe is only a finite number of years old, Smith makes the clever move of noting that in standard Big Bang cosmology, there is no first moment to the universe, even though the universe has a "beginning" in the sense that the universe only exists after some time t0 corresponding to the initial singularity, but does not exist at the singularity. So, for any IUS at time t, there will always be an IUS existing before t, but after the singularity, indeed an infinite number of them. For instance, there will always be an IUS existing halfway between t0 and t, for any time t, and of course another IUS halfway between this halfway point (i.e., ½t) and t0, ad infinitum. He can therefore apply PCE to the universe even though it has a "beginning."

My Response to Smith

In response to Smith, I will first present a modification of the cannonball example that he considers in his opening case, where the instant containing the explosion is deleted. First, we need to introduce some terminology regarding temporal intervals. A closed interval is an interval that includes its endpoints, whereas an open interval does not include its endpoints; a half-open interval includes one of its endpoints but not the other. Thus, for example, if the gunpowder in the cannon started exploding at exactly 12:00pm, then the interval of time from 12:00pm to 12:02pm that includes both the time 12:00pm and the time 12:02pm would be a closed interval. On the other hand, the interval of time that consists of all times that are later than 12:00pm but earlier than 12:02pm (and hence contains neither the moment 12:00pm nor the moment 12:02pm) would be an open interval.

Now consider the example above in which the gunpowder explodes at 12:00pm and the cannonball hits the ground at 12:02pm. Further, consider the open interval 12:01pm to 12:02pm. Any instantaneous cannonball state in the open interval (12:01pm-12:02pm) is causally explained by the infinite set of prior instantaneous cannonball states plus environmental states within the same open interval. Thus, by PCE the entire aggregate of cannonball states in the open interval (12:01pm-12:02pm) is logically explained without reference to the exploding of the gunpowder, or even the states at or before 12:01pm. Consequently, the exploding gunpowder is not needed to explain any of the cannonball states in the open interval (12:01pm to 12:02pm).

Smith responds to a somewhat similar argument to mine involving a cannonball in his opening case. He says that

Their mistake is failing to realize that the first hour after the Big Bang lacks a first instant because of a unique circumstance, that there is a cosmic singularity. There is no cosmic singularity at the present hour or at the various hours they mention and Big Bang cosmology implies these hours or hour-long processes must have a first instant. The first instantaneous state of the cannon ball's movement is externally caused by the explosion of the gunpowder. [Italics mine]

Whatever merits this response has to the cannonball argument Smith considers, it is irrelevant to the argument I present. My argument does not depend on the cannonball's movement lacking a first instance. It only depends on there being an infinite temporally ordered continuum of cannonball states after 12:01pm; it assumes nothing about the existence of a first instant for the motion of the cannonball. In order for Smith's argument to work, however, he must assume that the universe consists of such an infinite temporally ordered continuum of states; my assumption in the cannonball example, therefore, is just a specific instance of Smith's overall assumption. If such a continuum exists, then it logically follows by the rules of mathematics that the open interval with an infinite number of cannonball states exists.

This implication of PCE means that either Smith must: (i) Deny PCE; (ii) Deny that the explosion caused the sequence of cannonball states; or (iii) Retain PCE, but claim that the explosion provides an additional explanation of the sequence of cannonball states. Presumably, Smith does not want to take either options (i) or (ii). If he takes option (iii), however, then the theist can claim that this is the sort of additional explanation that God provides for the existence of the universe. Further, insofar as the explosion is essential to providing a complete explanation of the cannonball states in the open interval (12:01pm-12:02pm), the theist could argue that God is essential to providing a complete explanation of our universe, even though the universe contains no beginning point.

I believe the above cannonball example shows the inadequacy of Smith's overall argument. Locating the exact flaw is trickier, however. The problem is that we are dealing with an infinite sequence of causes, and often paradoxes arise when dealing with infinity. To illustrate one such paradox, consider the universe as consisting of a continuous sequence of instantaneous universe states (IUS), as Smith assumes in his argument. So conceived, between any instantaneous state U(0) and a later state U(1), there will be an intermediate state, U(½), that is halfway between them. In order for U(0) to cause U(1), it must first cause U(½). But, in order for U(0) to cause U(½), it must first cause U(¼), and in order for it to cause U(¼), it must first cause U(⅛), ad infinitum. Since this sequence is never completed, it is puzzling how in the case of contiguous causation one event ever causes another. Put differently, one can never locate the direct cause of U(1).[1] No state between U(0) and U(1) is the direct cause, since it always causes U(1) via some intermediary, which in turn always causes U(1) via another intermediary, ad infinitum. The worry here is that there is what philosophers call a vicious infinite regress in which one state never manages to cause another.

One fundamental philosophical worry with Smith's explanation of the universe's existence is that it is circular. PCE asserts that the existence of the whole is explained if each of the parts is explained. But the explanation of each of the parts of the universe is in turn explained by appealing to other parts of the universe. So, the whole is effectively explained by other parts of itself: the existence of the total set of parts (all the IUS) explains the whole, and each of the parts is causally explained by temporally prior parts of the whole. Another worry is 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. In any case, whether these are the correct diagnoses of the problem with Smith's argument, I believe the cannonball case above shows that his overall argument cannot be correct.

Continue the Debate

Table of Contents


[1] Contiguous causation is causation in which there are always intermediaries between cause and effect, which is the type of causation that Smith envisions since between any two instantaneous universe states there are always an infinite number of other instantaneous universe states.

Copyright ©2008 Robin Collins. The electronic version is copyright ©2008 by Internet Infidels, Inc. with the written permission of Robin Collins. All rights reserved.