A Cosmological Argument for a Self-Caused Universe (2008)

Introduction: The Meaning of "The Universe Causes Itself"

Part One: The Entailment Argument for a Self-Caused Universe

Part Two: A Universe that Causes Itself to Begin to Exist

Part Three: Complete Explanations

Appendix: The Abbreviation Argument for a Self-Caused Universe

Introduction: The Meaning of "The Universe Causes Itself"

I intend to argue for the conclusion that the universe, be it infinitely old or finitely old, causes itself. One might object that no such argument could possibly succeed, because the claim that "the universe causes itself" is incoherent. I agree that this claim is incoherent if it is understood to mean that one individual, the universe, causes that same individual to come into existence. No individual can bring about its own existence, because no individual can bring about anything unless it (already) exists. What I mean by "self-caused" in this paper is that there is a certain type of whole of parts, namely, a temporal and causal sequence of different individuals, with each individual being caused by earlier individuals in the sequence. What I mean by "the universe is self-caused" is that (a) the universe is a whole of parts, specifically, a sequence of states of the universe, with each part or state being an individual; (b) the existence of each part (state) of the universe is caused by earlier parts of the universe; and (c) the reason the universe as a whole exists is either because it is composed of or is identical with these successively caused parts.

A clear representation of these two senses of "self-caused" can be made if we use the letters x, y and z. If an individual x caused itself, this would be expressed by "x causes x." I reject the formulation, x causes x, and explain "self-cause" in a way that applies only to a sequentially extended whole of parts. The universe is a sequence of states and "the universe is self-caused" means that there are successive states of the universe x, y, z, etc., with x causing y, and y causing the later state z. The arrow means causes; x → y means that x causes y to exist. The brackets { } denote the sequence as a whole and x, y, z are successive parts of this sequence. Accordingly, if the universe sequentially causes itself to exist, this is expressed by

{. . . x → y → z . . .}

But we cannot stop here in explaining the meaning of "the universe is self-caused"; this paper's argument that the universe is self-caused is also an explanation of what "the universe is self-caused" means, and this is a progressive task.

This paper is divided into three main parts followed by an appendix. In Part One, I defend what I call the entailment argument for a universe that is self-caused in the sense just explained. Roughly, this argument claims that each part of the universe is sufficiently caused by earlier parts and the existence of the universe as a whole is entailed by the existence of all of the parts that compose this whole. The obtaining of this entailment relation between the causally explained parts and the universe they compose is the sufficient reason why the universe exists. If I am right about this, then the traditional ways of thinking about the cosmological argument for God's existence, both pro and con, are false. Defenders of the cosmological argument, going back at least as far as Leibniz and Clarke, have thought that, while the state of the universe at a time is caused by earlier states of the universe, the whole universe composed of all of its states is caused by God. Critics of the cosmological argument have claimed instead that the existence of the whole universe has no cause or explanation--its existence is just a brute fact. According to the entailment argument, both of these positions are mistaken. The universe has an explanation, but that explanation is not God or anything else distinct from the universe and its states.

In Part Two, I show that this entailment argument is consistent with a finitely old universe, and in particular with the most widely accepted cosmological theory of the universe, the Big Bang theory. In Part Three, I defend my position that the entailment argument is itself a complete explanation of the universe. Finally, in an appendix to this paper, I develop an alternative argument for a self-caused universe, one that does not assume that there is a universe distinct from all of its states. This argument is called the abbreviation argument since it assumes that the term "the universe" is used merely as an abbreviation of "all the states that exist" or other plural phrases that refer to all the states. There is no individual that is distinct from all the states and that is composed of all the states; the whole of all the states is identical with all the states, and its existence is either uncaused, or caused by God, or entailed by the existence of the states. In the abbreviation argument, the universe is "self-caused" because it is not distinct from all the states that exist and each state that exists is causally explained by earlier states. The motivation for this additional argument may be obscure to those without a background in philosophy, which is why I have placed the argument in an appendix. If the reader is not concerned about whether the universe exists as an individual distinct from all of its parts, then there is no need to read this appendix.

Part One: The Entailment Argument for a Self-Caused Universe

This argument supposes that the universe is a whole, an individual existent, that is different from all the parts of the whole. We are using "U" as the name of this whole. It is an "entailment" argument in the sense that the explanation of why the universe U exists is that its existence is entailed by the existence of its parts, each of which is causally explained in terms of earlier parts.

U, the whole of all the parts, is not causally explained by all the parts, since its parts do not cause it to exist. Rather, each part of U is caused to exist by earlier parts of U, and the causally explained existence of all the parts of the whole U logically require or entail the existence of the whole U, and in this sense the existence of the whole U is logically explained by the causally explained existence of its parts. It is a logical truth that if the parts of the whole U are caused to exist, then the whole U also exists. Once the existence of each of the parts is causally explained, the existence of the whole is logically explained, since it is a logical consequence of the existence of the parts of the whole that the whole exists.

It is either senseless or logically self-contradictory to suppose that, even if all the parts of the whole have a causal explanation of their existence, there still needs to be (or even can be) a causal explanation of the existence of their whole. There cannot be an external or divine cause of the whole, since a cause is logically "too late" in the following sense. It is logically necessary that if there exist parts of a whole, the whole exists. Each part of the whole has a sufficient cause of its existence in earlier parts. Accordingly, the existence of each part has a causal explanation and the existence of the whole has a logical explanation. Regardless of whether or not some (purported) external causal act is directed upon the whole, the whole exists because it is logically required to exist by the existence of its parts. Since this (alleged) external causal relation or causal act has no affect whatsoever on the logically necessitated existence of the whole, it is ineffective and so is not a "causal relation" in any intelligible sense of this phrase. This is stated more clearly if we say there is no such purported causal relation; there is no external cause or divine cause of the universe.

Part Two: A Universe that Causes Itself to Begin to Exist

The most widely accepted cosmological theory of the universe since the late 1960s is not the "oscillating universe" version that implies that there are infinitely many past cycles of expansion and contraction. Rather, it is the version that implies that the universe began to exist 15 billion years ago in a Big Bang singularity. To say that its beginning is a "singularity" means that the universe begins to exist but there is no first instant t=0 at which it begins. The cosmic singularity is a hypothetical time t=0 at which all the laws of nature, space and time break down. It is hypothetical or merely imaginary because if it did exist, it would be a physically impossible state, due to the breakdown of all laws, even the laws required for time to exist. This breakdown at the hypothetical t=0 implies there is no first instant t=0 of the finitely old time-series and that each instant is preceded by earlier instants. An instant is a time that is instantaneous or has zero duration. An interval is a time that is temporally extended and has a duration of a certain length, such as one hour or one minute.

Since there is a Big Bang singularity, the first interval of each length is "past-open," which means that there is no instant t that is the first instant of each earliest interval of any length, be the interval an hour, minute or second, etc. Before any instant in an earliest hour, minute, second, etc., there is an infinite number of other instants. Formulated in terms of instantaneous states of the universe, this means that before each instantaneous state of the universe, there are other instantaneous states, and each instantaneous state of the universe is caused by earlier instantaneous states. Accordingly, the universe causes or explains itself in the sense that, even though it began a finite number of years ago, say 15 billion years, each instantaneous state in any earliest interval is caused to exist and hence explained by earlier instantaneous states. In terms of the entailment argument for a self-caused universe, this means that the states are parts of a whole, the individual U, and U causes itself in the sense that (a) each instantaneous part S of the whole U is sufficiently caused by earlier instantaneous parts of U; (b) U is finitely old in the sense that there are no instantaneous parts of the whole that exist earlier than some finite number of equal-length, nonoverlapping intervals; and (c) the existence of all these parts of the whole U entails the existence of the whole U.[1]

Some philosophers have argued that if the first instant of the first hour after the Big Bang can be "deleted" (i.e., regarded as a nonexistent), then the first instant of any hour can be deleted. This would allow one to say that any hour or hour-long process has no external cause, since each of its instantaneous states is caused by earlier instantaneous states that are internal to the hour-long process. They say a cannon ball's flying through the air could then be "causally explained" without referring to the relevant external event, the explosion of the gun powder in the cannon, by saying that each instantaneous state of the ball's movement is caused by earlier instantaneous states of its movement, implying that the external event, the gun powder explosion, is not the cause of the ball's movement. 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's ball movement is externally caused by the explosion of the gunpowder.[2]

Part Three: Complete Explanations

Not every argument is an explanation, but some arguments are explanations and my entailment argument is a causal explanation of the universe's existence. The universe and its parts are contingent in the sense that they might not have existed. Since the existence of each state is caused by an earlier state, and since the existence of all these states entails the universe's existence, there is an explanation for each of these contingent beings.

Some philosophers, like Jordan Howard Sobel, maintain that, "if anything is contingent, then it is not possible that, for every fact or entity, x, there is a reason of some sort or other for x" (Sobel, 2004, p. 222). I disagree. I believe that something is contingent, but I also believe that every fact or entity x has a reason. If x is a part of the universe, it has a reason in earlier parts; if x is the universe, it has a reason for its existence in the existence of its parts. We shall shortly discuss some contingent facts or entities that some allege cannot be explained.

The entailment explanation of the universe's existence invalidates Sobel's argument that a complete explanation of the universe's existence requires that the premises all be necessary truths and that the conclusion thereby be a necessary truth. The entailment cosmological argument for a self-caused universe, for example, is a complete explanation of the universe's existence and its premises are the contingent truths that each state S contingently exists, that S's existence is sufficiently causally explained by earlier states, and that the existence of the whole universe, U, is explained by virtue of being logically necessitated by the existence of its parts, the states. This can be formulated as an argument with premises and a conclusion, such that the conclusion logically derived from these premises is the contingent truth that the universe exists. Accordingly, a complete explanation of the universe's existence does not require that the premises all be necessary truths and that the conclusion be a necessary truth.

William Rowe says that a dependent being is a being whose sufficient reason for existence lies in the causal activity of other beings. He writes that "if every being were dependent, it does seem that there would be a contingent fact without any explanation--the fact that there are dependent beings" (Rowe, 1998, p. xiii). I would ask, if every being were dependent, why would it then seem that the contingent fact that there are dependent beings has no explanation? How could one logically proceed from the premise that every being is dependent to the conclusion that there is no explanation for the fact that there are dependent beings? Rowe holds that "the sufficient reason for a fact is another fact that entails it" (Rowe, 1998, p. xvii). But it seems clear there are many facts that entail the fact that there are dependent beings. For example, the fact that there is a state of the universe S2 entails the fact that there are dependent beings; S2 is a dependent being since S2's "sufficient reason lies in the causal activity of other beings." If we interpret Rowe's sentence as meaning that a sufficient reason for a fact is an explanation for the fact, then the fact that S2 exists is an explanation of the fact that there are dependent beings.

But Rowe can be more charitably interpreted as meaning that the sufficient reason for a fact is another fact that entails it, but not every sufficient reason for a fact also explains that fact. If we adopt this interpretation, there is some further feature F that a sufficient reason must possess in order for the sufficient reason to explain the fact that it entails. But Rowe does not indicate what F is; furthermore, it is not obvious that what I called "the charitable interpretation" is what Rowe had in mind by his statement. He might be read as saying that sufficient reasons are explanations, but that some of these explanations are circular or viciously circular (and perhaps some are noncircular). Rowe offers another example of something that he believes cannot be explained. He says that the fact

t: there being positive contingent states of affairs

cannot have a sufficient reason for obtaining. However, it seems clear that this fact does have a sufficient reason for obtaining. There obtains the positive contingent state of affairs, there being an occurrence of the state of the universe S2, and this entails the fact t: there being positive contingent states of affairs. Rowe would say of a proposed explanation of this type that "such a proposed explanation is circular" (Rowe, 1998, p. xvi). But what does "circular" mean here? Rowe does not explain what he means by this word and it is hard to see why or how "circular" could mean something different than the positive theoretical virtue of being a valid argument. The premise entails the conclusion. If "circular" means that the premise entails the conclusion, then circularity is a necessary property of any deductively valid argument. However, I do not think that "circular" as this word is used in works on the logic of explanations means this; rather, it means that the conclusion of the argument not only is entailed by the premise, but also entails the premise. For example, S1's being earlier than S2 entails that S2 is later than S1. But S2's being later than S1 also entails that S1 is earlier than S2. Thus, to use one of these facts to explain the other is circular. By contrast, S2's occurrence entails the fact that there are positive contingent states, but the fact that there are positive contingent states does not entail S2's occurrence. Therefore, to use S2's occurrence to explain the fact that there are positive contingent states of affairs is not circular (unless of course one insists on calling any valid argument circular, in which case it is not "viciously circular").

But Rowe could be read as meaning that an explanation is circular if what is explained is a general fact and the explanation is a particular fact involving a being of the kind that the general fact is about. It is alleged that a general fact such as there are contingent things cannot be noncircularly explained by a particular fact about contingent things. But no justification is offered for believing this sort of explanation is "circular" in a sense of this word that implies that the explanation is defective or not very good or is in some way not satisfactory. Consider this example: Why do any red things exist? Why are there red things? Why is this general fact not explained by the particular fact that a green apple exists and that a causal process involving internal changes in the apple eventually produced a certain change of state in the apple resulting in the apple losing its green color and acquiring a red color. When the apple's red state has been caused to exist, there exists something that is red, namely, the red apple. This is a causal explanation of why there exists at least one red thing. If this is a "circular explanation" in some bad sense of "circular," then all causal scientific explanations (or almost all of them) are "circular" in a bad sense and a good or noncircular causal explanation is impossible.

The fact that the contingent being S2 is caused to exist by earlier contingent beings, each of which is also caused to exist by earlier contingent beings, explains why it is true that there is at least one contingent being. Nonetheless, the feeling still remains that something along the lines of what Rowe has in mind is true and that, whatever this is, it shows that my argument that the universe is self-caused is unsound, or else it shows that this explanation of the existence of the universe is not complete or is unsatisfactory in some respect. But what could this be? What seem to be worrisome are such questions as these: Why do these parts or states exist rather than other parts or states, or no states at all? Why does this whole exist rather than some other whole? Why does any contingent being at all exist?

Our questions can be phrased in terms of the metaphysics of possibilities. A "possible world" is a complete way things might have been. Why are these possibilities actual, rather than some other possibilities? Why, for example, is it true that our universe exists but false that there exists a universe that lasts for only one minute before ceasing to exist, and that never becomes larger than the size of the head of a pin? Regarding the false statement, the reason this is false is that nothing caused there to exist a universe of this small size and brief duration. Rather, the sequences of causes and effects has resulted (at present) in the existence of a universe that has lasted for at least 15 billion years and that is infinite in size or (talking only about the observable universe) has a radius of 13 billion light years, where one light year is 6 trillion miles. In other words, there is a concrete sequence of causes and effects that made actual the possibility mentioned, namely, that there is a universe at least 15 billion years old and at least 13 billion light years in radius, and there is no concrete sequence of causes and effects that actualized the possibility of a pinhead-sized universe that lasts for only a minute. This is why it is true that our universe exists but false that the other universe exists.[3]

Appendix: The Abbreviation Argument for a Self-Caused Universe

If we adopt the theory that there is no individual U, no universe that is a whole that is a distinct existent from all of its parts, then the reason for the universe's existence cannot be that U's existence is entailed by the existence of U's parts. There are no parts and there is no whole in the sense of "parts" and "whole" that I used in the entailment argument. Consequently, either there is a different sort of sufficient reason for the universe's existence or else there is no reason at all.

Hume and others were mistaken when they said that once each part of any whole is explained, the whole is explained. But whether or not Hume was mistaken is irrelevant to the abbreviation argument for a self-caused universe, since this argument implies that the universe is not the whole U and that there are not parts of the whole U. There is no individual, the universe U, which is a distinct existent from all of the parts of this individual. Rather, "U" or "the universe" does not refer to an individual, but is used as an abbreviation of "all the states" or "S1 and S2 and S3, and all the other states" or "S1, S2, S3, etc."

Each state includes the maximal three dimensional space that exists at a time t, and includes all the other contingent concrete beings that exist at the time t, such as galaxies and organisms as they are at the time t. The sentence "S is a part of the universe" is stipulated (in the abbreviation argument) to have the sense expressed by "S is one of all the states."

The states have various ordering relations among themselves. For example, each instantaneously existing three-dimensional space, each different maximal 3D space at each different time t, has a wider radius than all earlier 3D spaces, which is one way of suggesting a cosmological theory that space (or space-time) has been expanding since the Big Bang 15 billion years ago. Accordingly, we can have a consistent theory if we adopt the convention or stipulation that "the universe" does not refer to a distinct, individual existent, but is instead an abbreviation of "all the cosmological states." If the existence of each state has a sufficient reason by virtue of being caused by earlier states, then each state has a sufficient, causal, explanation for its existence and there is no state that is either uncaused or that has an external or divine cause of its existence.

I have adopted the convention that "the universe" is an abbreviation of such plural expressions as "S1 and S2 and S3 and so on." There is no logical or empirical contradiction or problem that results from adopting this convention and one could argue by Occam's razor (which tells us not to postulate any more individuals than is necessary) that since there is no need to postulate an individual whole U, we should not posit an individual U and instead stipulate that "U" is an abbreviation of "all the states."

Both basic and nonbasic laws of nature are dispositional properties possessed by each state and in some cases they are actualized in the form of an occurrent property or relation. For example, the law of evolution is a dispositional property of states and it was not actualized or occurrently realized until life began to exist, perhaps 4.5 billion years ago on the earth. Since these are dispositional properties of a state S, the cause of S is ipso facto the cause of the possession by S of all its dispositional properties. Since each state is caused to exist by other states, so each law, including the basic laws of nature, is caused to exist as a dispositional property of each state. These laws of nature include all the causal laws, which are causal dispositions of a state, many of which are occurrently realized. Each state has sufficiently many occurrent actualizations of causal dispositions to cause a later state to exist. Here "cause" means total cause; a state S1 causes S2 in the sense that sufficiently many causal dispositions are occurrently realized for S3 to be caused, and all of these occurrent causal relations make up the "total cause" of S3; this total cause of S3 is what I have been calling the "cause" of S3. For example, state S1 at t1 causes the state S2, which exists at t2, to actualize its disposition to cause the state S3, which exists at the later time t3.

There are no particulars, initial conditions or basic laws of nature that are causally unexplained. To say that a universe is self-caused is not only to say that each of its initial or boundary conditions or particulars are caused to exist (by earlier states), but also that all of its laws of nature are caused to exist and obtain (by earlier states).[4]

References

Clarke, Samuel (1738). A Discourse Concerning the Being and Attributes of God, 9th ed. London: Knapton Publishers.

Gale, Richard (1991). On the Existence and Nature of God. Cambridge: Cambridge University Press.

Hume, David (1779). Dialogues Concerning Natural Religion.

Leibniz, Gottfried. (1934). "On the Ultimate Origination of Things" in The Philosophical Writings of Leibniz, trans. by M. Morris. London: J. M. Dent and Sons (Everyman Library), pp. 31ff.

Rowe, William (1998). The Cosmological Argument. Fordham: Fordham University Press.

Rowe, William (1997). "Circular Explanations, Cosmological Arguments, and Sufficient Reasons." Midwest Studies in Philosophy 21: 188-201.

Smith, Quentin (1999). "The Reason the Universe Exists is that it Causes Itself to Exist." Philosophy 74: 136-146.

Sobel, Jordan Howard (2004). Logic and Theism. Cambridge: Cambridge University Press.

Notes

[1] In terms of the Abbreviation Argument for a self-caused universe, this means the universe causes itself to begin to exist in the sense that (a) each instantaneous state S is sufficiently caused by earlier states and (b) there are no instantaneous states that exist earlier than some finite number of equal-length, nonoverlapping intervals. For example, all of the states are such that each state is caused by earlier instantaneous states but no state exists earlier than 15 billion years ago.

[2] If one does not want to talk about a current scientific theory of the universe, but about mere logical possibilities, one can correctly say that it is logically possible for a universe to begin to exist with a first instantaneous state. But it is false to say that there are only two possibilities, that this state is either uncaused or caused by God (or some sort of cause external to the universe). There are instantaneous causal relations (as is shown to be the case in the actual universe by the Bell-Aspect experiments) and a self-caused universe of this sort causes itself to begin to exist in the sense that the different spatial parts of the first instantaneous state of the universe are each sufficiently caused to exist by other spatial parts of this first state. I have argued this elsewhere (Smith, 1999), but the length of the argument prevents it from being restated here.

[3] Why is the possibility that there is some contingent concrete being an actualized possibility? Why was not the possibility that there are no contingent concrete beings actualized instead? The answer is that the first possibility was caused to be actualized, leaving the second possibility unactualized. For example, the cause of the present state of the universe, the cause consisting of the various causal processes in the previous states of the universe, caused there to be a contingent concrete being, namely, the present state of the universe. Since the present state of the universe is some contingent concrete being, the explanation of why this contingent concrete being exists explains why "there is some contingent concrete being" and why "there are any contingent concrete beings at all." Suppose the possible world P is the actual world. Why is the possible world P actual rather than some other possible world Q? I will follow Adams, Pollock and others and adopt as my possible world metaphysical semantics the thesis that a possible world is a maximal proposition p, such that the actual world is a conjunction p of all and only the true propositions. For every proposition p', p includes p' as one of its conjuncts or it includes the negation of p' as one of its conjuncts. The actual world P is (identically) the actually true proposition p. Why is P actual rather than some other world, or, asking this same question but using different terminology, why is the maximal proposition p true, rather than some other maximal proposition q? Consider all the propositions that assert that some state S of the universe exists, such that each of these propositions is a long, conjunctive proposition that describes all the physical and mental events, relations, parts or properties of the state S. The proposition r asserts that the state S3 exists. Why does S3 exist? Because it was caused to exist by earlier states, states mentioned in some other conjunctive proposition t. The various conjuncts in the proposition t can be ordered as premises and inference relations. Their conclusion is that proposition r is true. The reason r is true, the reason the possibility r is actual, is because the explanatory theory or series of propositions that make up the conjunctive proposition r is true and this theory explains why t is true or why the possibility t is actual. One may take each conjunct in the actual world P and explain why it is true by some other conjunction in P. Why is the whole conjunction true? If the truth of each conjunct is explained, the truth of the entire conjunction is explained.

[4] I am grateful to Paul Draper for his significant help with this paper.