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The following article was originally published in DIALOGUE: CANADIAN PHILOSOPHICAL REVIEW in 1994 (Volume 33, pp. 313-323).

It is rare to find an argument for the principle that it is impossible for the universe to come to be without a cause. Typically, adherents of this principle claim that it is self-evident or, as William Lane Craig, for example, asserts, that it is “intuitively obvious.”¹ This approach is not promising since this principle is not self-evident. A principle p is self-evident if and only if everybody who understands p believes p, but many philosophers and cosmologists not only believe it possible but actual that the universe began to exist without a cause.²

However, an argument for this causal principle has recently been developed by T. D. Sullivan.³ The purpose of this paper is to examine and refute Sullivan’s argument. In the course of arguing that it is possible that the universe came to be causelessly, I shall outline an argument that it is necessary that the universe began with a big-bang singularity if it began causelessly.

I.

Before I state Sullivan’s argument, I shall define ‘comes to be’. For any x, x comes to be if and only if there is some time t at which x exists and no time earlier than t at which x exists. This allows for three possibilities: (i) that x exists at the first instant of time or (ii) that x exists throughout the first interval of time of some length or (iii) that x exists at a time that is later than a period of time during which x does not exist. Possibility (ii) differs from (i) in that (ii) alone is consistent with the first interval of time being half-open in the earlier direction; that is, (ii) alone is consistent with there being no first instant (time is dense or continuous and no instant bounds the first hour in the earlier direction). This definition allows sense to be made of time’s beginning or coming to be as well as sense to be made of the beginning or coming to be of the universe. We need not suppose, with Grünbaum,⁴ that the expression ‘time begins’ is misleading and suggests that “time exists at a time that is later than a time at which it does not exist,” since ‘time begins’ may be analyzed along the lines of (i) or (ii) as meaning there is a first instant or interval of time.⁵

With this definition of ‘coming to be’ in mind, we may proceed to examine Sullivan’s argument. Before I attempt to rebut Sullivan’s argument, I shall strengthen it, since as it stands it suffers from an unnecessary weakness. His argument is a reduction to absurdity of proposition (1) below and goes:

(1) Everything is such that (if it can come to be at all) it can come to be without a cause in any situation whatsoever.

(2) Causes are necessary conditions (in the situation in which they are causes).

(3) But at least one entity, b, has a cause, c, in situation s.

Then, from (2) and (3),

(4) Cause c is a necessary condition for b in s.

And, from (4),

(5) Without a cause c in s, it would be impossible for b to come to be in s.

This contradicts assumption (1).

Sullivan does not explain the force of ‘necessary” in (2), but he seems to mean empirical necessity, not logical necessity. It is not a logical contradiction that “John comes to be from his parents, but he might have come to be without a cause.” Rather, it is an empirical contradiction, i.e., it is inconsistent with the laws of nature that obtain. Given this, an objection can be made to Sullivan’s claim that (5) contradicts (1). For (5) means “Without a cause c in s, it would be empirically impossible for b to come to be in s.” However, that is consistent with (1) construed as the claim that “Everything is such that (if it can come to be at all) it is logically possible that it come to be without a cause in any situation whatsoever.” This construal of (1) is all that is needed for the argument that “Possibly, everything comes to be without a cause,” for ‘possibly’ here has the force of logical possibility.

But this weakness in Sullivan’s argument can be remedied if we adopt Kripke’s theory⁶ of the necessity of origins. According to Kripke, if John comes to be from the union of the egg cell E and the sperm cell S, then John necessarily comes to be from the union E and S. There is no possible world in which John comes to be but does not come to be from the union of E and S.

Admittedly, it will still not be a contradiction in the “narrowly logical” sense that John comes to be but not from the union of E and C. Something is a contradiction in the narrowly logical sense if it is inconsistent with a principle of ordinary logic (first-order predicate logic with identity). But the implications of Kripke’s ideas about the necessity of origins is that something is not really possible (possible in the metaphysical or “broadly logical”⁷ sense) just because it is logically possible in this narrow sense. Just because something is consistent with ordinary logic does not mean it can become actual. It is consistent with all the axioms and theorems of first-order predicate logic with identity that John be a block of wood, but this state of affairs cannot be actualized. The theory of the necessity of origins is that it is really (metaphysically) impossible that something come to be but not from the origins it in fact has.

Given the theory of the necessity of origins, a defender of Sullivan’s position can allow that it is narrowly logically possible for everything to come to be without a cause, but can argue that it is really (metaphysically) impossible. Sullivan’s argument can be restated so that the assumption up for reductio, assumption (1), becomes “Everything is such that (if it can come to be at all), it is metaphysically possible that it can come to be without a cause in any situation whatever.” If b stands for John and c for the union of the cells E and C, assumption (5) could be interpreted as the true statement “Without a cause c in s, it would be metaphysically impossible for b to come to be in s.” Given this, it follows that it is metaphysically impossible that each thing come to be without a cause in any situation whatsoever. However, this conclusion is consistent with the metaphysical possibility that the universe comes to be without a cause.

II

This consistency obtains, since in order to show that it is metaphysically possible that the universe comes to be without a cause, it is not necessary to show it is metaphysically possible that each thing comes to be without a cause in any situation whatsoever. It is sufficient to show that in one possible situation one thing comes to be without a cause and that every other thing is an immediate or remote effect of this one thing. For illustrative purposes, we may take the notion of “the big-bang singularity” from classical or standard hot big-bang cosmology. A finite universe is here thought of as beginning with a physical singularity that is spatially pointlike (i.e., has zero spatial dimensions), that exists for one instant only and that is not governed by any physical laws. The cosmologist Michael Berry writes that at the first instant of time “there is a finite amount of matter and radiation packed into zero initial proper volume; this ‘point’, however, includes the whole of space-there is nothing ‘outside’.”⁸ This point explodes in a “big bang,” but this explosion is not governed by any physical law. Paul Davies writes of this singularity: “Anything can come out of a naked singularity-in the case of the big bang the universe came out. Its creation represents the instantaneous suspension of physical laws, the sudden, abrupt flash of lawlessness that allowed something to come out of nothing.”⁹ The big-bang singularity explodes and becomes a three-dimensional volume of space filled with interacting particles and the universe henceforth evolves in a causally sequential manner.¹⁰

The fact that the singularity gives rise to a three-dimensional space with matter does not imply that it is a physical law that the singularity give rise to something. There is no physical law in classical big-bang cosmology of the form “If there is a singularity, it must give rise to something at a later time.” The singularity in fact gives rise to something, but this fact is unpredictable given the nature of the singularity itself. For example, there is no dispositional property of the instantaneous spatial point that manifests a physical tendency to explode into something else; the singularity could just as well have been followed by nothingness (more precisely put, it could have been the case, consistently with all the laws of classical big-bang cosmology, that the only instant that exists is the instant of the singularity).

Since no physical laws govern the singularity, it is the case that if it gives rise to something at a later time, it is most likely to give rise to random or arbitrary particle configurations (giving an overall state of maximal disorder) and is not likely to give rise to a highly ordered system such as a flower or ant. This, however, is not a physical law that governs the singularity, but is a probability calculation that is based on the fact that no physical law governs the singularity.

The proposition that this singularity came to be without a cause is consistent with the proposition that each other thing comes to be with a cause, e.g., with the proposition that I came to be from the union of an egg cell with a sperm cell in my mother’s womb. Of course, the proposition that the big-bang singularity comes to be without a cause is inconsistent with the proposition that each other thing has a causal history extending infinitely into the past, but that is not the issue. We must distinguish between propositions of the form “x has a cause” and propositions of the form “x has a causal history extending infinitely into the past.” Some propositions of the first form can be true consistently with all propositions of the second form being false. Surely, one cannot refute my claim that “Something caused me to come into existence, namely, the fertilization of my mother’s egg cell by my father’s sperm cell” by saying “That is clearly false! The big-bang singularity occurred 15 billion years ago without a cause.”

These considerations suggest that even if Sullivan’s reductio is successful, it does not refute the possibility of the universe’s coming to be without a cause. Sullivan’s argument (with the Kripkean supplementation) demonstrates the falsity of the statement “Everything is such that (if it can come to be at all) it can come to be without a cause in any situation whatsoever.” Here ‘everything’ means “each thing that exists in the history of the universe.” But the falsity of this statement is consistent with the truth of the statement that “in some possible situation, some thing begins to exist without a cause and every other thing is an immediate or remote effect of this initial thing” and this latter statement entails that it is possible for the universe to come to be without a cause.

This suggests that the underlying mistake in Sullivan’s thinking is that he invalidly infers “The universe did not come to be causelessly” from “There are some things within the universe whose coming to be was caused.” This inference would be valid if “The universe came to be causelessly” meant “Everything came to be causelessly,” where ‘Everything’ means “Each thing that exists.” But this is not what is meant by the assertion that the universe came to be without a cause. What is meant is that the history of things has a beginning and that the first phase of this history (the coming to be of the first thing, if you will) is uncaused.

If Sullivan’s argument is to bear upon the claim that the universe can begin uncaused, “everything can come to be without a cause” must be interpreted to mean “the universe can come to be without a cause” and the premise for reductio, (1), would need to be rewritten as:

(1A) The universe can come to be without a cause in at least one situation.

But on this interpretation of the premise for reductio, Sullivan’s argument is unsuccessful, since the premises of Sullivan’s argument do not establish the falsity of (1A). This is because premise (5),

(5) Without a cause c in s, it would be impossible for b to come to be in s,

does not contradict the assumption that the universe can come to be without a cause in at least one situation. This is because premise (5) does not entail the following statement is false:

(1B) In one possible situation, some thing a comes to be without a cause, with b and everything else being immediate or remote effects of a.

It is interesting to add that the defender of a possible uncaused beginning of the universe can rebut Sullivan’s argument even given the constraint that the defender must show that everything can come to be without a cause. This rebuttal requires that ‘everything’ be taken as meaning “each thing that presently exists.” Given this interpretation, “Everything is such that (if it can come to be at all) it can come to be without a cause in any situation whatsoever” becomes a present-tense statement that quantifies only over whatever exists at the present time. Right now, this statement is false. But one cannot infer from this that it is never true that “Everything is such that (if it can come to be at all) it can come to be without a cause in any situation whatever.” For example, it cannot be inferred that this statement is false when the big-bang singularity is present, since at this time the big-bang singularity is everything.

To be perfectly accurate, however, the statement in this form is not true when the big-bang singularity is present. For it is not metaphysically possible that the big-bang singularity can come to be causelessly in any situation whatsoever. It cannot come to be causelessly in a situation s that is completely governed by deterministic physical laws. The tensed statement that is true at the time of the big-bang singularity is instead that “Everything is such that (if it can come to be at all) it can come to be without a cause in some situation.” All that is required to make an uncaused beginning of the universe possible is one situation in which the big-bang singularity can come to be without a cause; it need not be the case that the singularity can come to be uncaused in any situation whatsoever. The universe can come to be uncaused if the only situation in which the big-bang singularity can exist uncaused is a situation in which there is nothing in existence apart from the singularity and the singularity exists at the first instant of time.

III.

It might be objected to this conclusion that it implies a counter-intuitive proposition, namely,

(P) One thing that comes to be can come to be without a cause, but each other thing that comes to be necessarily has a cause of its coming to be.

(P) is counterintuitive, it may be said, since it is implausible to think there is one and only one exception to the rule that everything that comes to be necessarily has a cause. Any need for things to be caused does not seem to depend on a thing’s nature but on the essential structure of a thing qua thing; if any thing that comes to be essentially has a cause, then each thing that comes to be essentially has a cause.

I do not want to endorse the claim that each thing but the big-bang singularity comes to be only if it has a cause; I have merely argued that it is possible for the universe to come to be uncaused if this is true. However, I will show how principle (P) can be made plausible. If there is a relevant difference between the big-bang singularity and other things, then (P) will be plausible.

There are two relevant differences, the first being that the singularity is the only thing whose coming to be is not governed by any laws. Each thing that exists later than the big-bang singularity, each particle, organism, etc., is governed by some laws (e.g., the super-symmetry laws, Darwinian laws, etc.). Since definitions of causality often make explicit or implicit reference to laws, it is natural to suppose that, if there is only one completely lawless thing, this thing will also be the only thing exempt from causality.

Second, the big-bang singularity is the simplest possible thing; it has zero spatial dimensions (it is pointlike), zero temporal dimensions (it is instantaneous) and is governed by zero laws. It is plausible that if only one thing can come to be without a cause, this thing will be the simplest possible thing. If this is the case and (P) is true, then the theory that the universe begins with a big-bang singularity will reflect the only metaphysically possible way in which a universe can come to be uncaused.

These considerations show how metaphysics may have a bearing on the assessment of current physical cosmologies, specifically, on the comparison of classical big-bang cosmologies with quantum cosmologies. In contradistinction to classical big-bang cosmology, the quantum cosmologies of S. W. Hawking¹¹ and A. Vilenkin¹² represent the universe as beginning uncaused but as beginning with a very complex state that is governed by physical laws (e.g., Hawking’s “wave function of the universe”). For example, Hawking’s theory is that the first state of the universe has a finite and non-zero size (namely, the same radius as the minimum radius of the universe in de Sitter’s model of the universe) and that it is governed by the various physical laws found in Wheeler’s theory of superspace, Everett’s interpretation of quantum mechanics and Feynman’s sum over histories version of quantum mechanics.¹³ Now it is possible that there are no observations that discriminate between Hawking’s theory and the theory that the universe began with a lawless singularity. That is, it is possible that these two theories are underdetermined by the observational data. If this is the case, then only theoretical considerations come into play in making a decision as to which theory is more plausible. On behalf of Hawking’s theory, it may be argued that it has greater explanatory value by virtue of specifying a law (the wave function of the universe) that governs the coming to be of the first state and its evolution into later states. This will give us a “scientific” reason to prefer Hawking’s theory (at least in the sense that this reason is of the sort that physicists such as Hawking adduce in support of the superior value of the quantum cosmological theory). However, if my arguments above and (P) are accepted, there will be a metaphysical reason to prefer the theory of the lawless singularity, namely, that the big-bang singularity but not Hawking’s first state meets the condition of exhibiting a relevant difference from all else that enables it alone to be an exception to the principle that each thing necessarily has a cause of its coming to be. Hawking’s first state is governed by laws and is not the simplest possible thing, and thus there seems to be no relevant difference between it and subsequent items that would explain how it could be an exception to the causal principle.

In defense of this metaphysical argument for the superiority of classical big-bang cosmology, it may be pointed out that certain objections to it are unsound. It has been suggested by a reader of an earlier version of this paper that the thesis that each thing (other than the big-bang singularity) has a cause, in the sense of a necessary condition, is implausible in the light of virtual particles spontaneously coming into existence in quantum mechanical vacuums and real particles popping into existence in strong electromagnetic or gravitational fields. I think, however, that such events refute the sufficient-condition theory of causality, not the necessary-condition theory of causality that is adopted in this paper. The presence of a field of a certain strength in a certain space-time region r is not sufficient to produce a particle in r, since it is only probable to a greater or lesser degree that a particle will come to be in r. However, the region r is a necessary condition of the coming to be of the particle, since the particle comes into being only by virtue of borrowing energy from the field in r. If it is objected that the precise strength of the field is not fixed (due to quantum indeterminacy), and therefore that a precise strength of the field is not a necessary condition of the particle’s coming to be, this objection may be accommodated by pointing out that the necessary condition of the particle’s coming to be is that the fields in r exist with a strength that falls within a certain range of values, rather than some given precise value.

Another objection to the causal principle (P) and the Kripkean theory that is adduced on its behalf is that the Kripkean thesis of the necessity of origins may be plausible for human beings, but is implausible for elementary particles such as electrons and protons. The Kripkean thesis is implausible for electrons, it may be argued, in that any electron is exactly like any other electron, and it seems that any given electron is not dependent for its nature upon when, where or how it came into existence. Each electron might have had a different origin.

However, the thesis of the necessity of origins for electrons can be defended if we suppose, contra Kripke, that the transworld identity of things is determined by their nature or origins rather than by sheer stipulation.¹⁴ It is a modal intuition that dthat electron (‘dthat’ being Kaplan’s rigidifying function) exists in many possible worlds. However, its nature (essential monadic properties) is not sufficient to distinguish it from all other electrons in each world in which it exists, since its nature is similar to that of all other electrons. John is unique by virtue of his nature (John and only John has a certain DNA) but not an electron. However, an electron’s transworld identity can be determined by virtue of its origin; in each possible world in which the electron e exists, it comes to be from the same origins as it actually does (e.g., from the fluctuation f in the space-time region r of a quantum mechanical vacuum). Since it is a modal intuition that dthat electron exists in many possible worlds, it is plausible to think that the support of this modal intuition is the necessity of its actual origin.

If such defenses as these can be successfully developed in every case (obviously other objections to the Kripkean and causal principles can be made),¹⁵ then there will be reason to think that there are metaphysical grounds to prefer classical big-bang cosmology over quantum cosmology.¹⁶ At the very least, defenders of quantum cosmology will be faced with the task of explaining how their complex and law-governed first state can be an exception to the causal principle.¹⁷

Notes

1. William Lane Craig, The Kalam Cosmological Argument (New York: Harper & Row, 1979), p. 141.
2. For references, see Quentin Smith, “Atheism, Theism and Big Bang Cosmology,” Australasian Journal of Philosophy, 69 (1991): 48-66; “The Uncaused Beginning of the Universe,” Philosophy of Science, 55 (1988): 39-57; and “World Ensemble Explanations,” Pacific Philosophical Quarterly, 67 (1986): 73-86.
3. T. D. Sullivan, “Coming to Be without a Cause” Philosophy, 65 (1990): 261-70.
4. Adolf Grünbaum “The Pseudo-Problem of Creation in Physical Cosmology,” in Physical Cosmology and Philosophy, edited by John Leslie (New York: Macmillan, 1990), pp. 92- 112, esp. p. 107.
5. This is further discussed in Quentin Smith, “A New Typology of Temporal and Atemporal Permanence,” Nous, 23 (1989): 307-30, and “On the Beginning of Time,” Nous, 19 (1985): 579-84.
6. Saul Kripke, Naming and Necessity (Cambridge, MA: Harvard University Press, 1980).
7. The distinction between narrow and broadly logical possibility comes from Alvin Plantinga, The Nature of Necessity (Oxford: Clarendon Press, 1974), pp. 1-2.
8. Michael Berry, Principles of Cosmology and Gravitation (Bristol: Adam Hilger, 1989), p. 156.
9. Paul Davies, The Edge of Infinity (New York: Simon and Schuster, 1981), p. 161.
10. Some theories of Inflation have modified the standard hot big-bang cosmology by supposing that a false vacuum emerged from the big-bang singularity and later gave rise to the particles in the universe. For a non-technical explanation, see Paul Davies, “What Caused the Big Bang?” in Physical Cosmology and Philosophy, edited by John Leslie, (New York: Macmillan, 1990) pp. 220-38. Quantum cosmologies have further modified the standard theory by rejecting the idea of a lawless, pointlike singularity that began the universe. For a non-technical explanation, see S. W. Hawking, “The Edge of SpaceTime,” in The New Physics, edited by Paul Davies (Cambridge: Cambridge University Press, 1989), pp. 61 -69. For a non-technical discussion of various theories of Inflation, quantum cosmology and other current cosmological ideas, see John Leslie’s Universes (New York: Routledge, 1989). For a more technical explanation of the classical theory, see Quentin Smith, “A Natural Explanation of the Existence and Laws of Our Universe,” Australasian Journal of Philosophy, 68 (1990): 22-43, and “Did the Big Bang Have a Cause?,” British Journal of the Philosophy of Science (forthcoming). For a more technical explanation of Hawking’s quantum cosmology, see the Appendix in William Lane Craig and Quentin Smith, Theism, Atheism and Big Bang Cosmology (Oxford: Clarendon, 1993).
11. S. W. Hawking, “Quantum Cosmology,” in Three Hundred Years of Gravitation, edited by S. W. Hawking and W. Israel (Cambridge: Cambridge University Press, 1987), pp. 631-51.
12. A. Vilenkin, “Creation of Universes from Nothing,” Physical Letters, 117B: 25-28.
13. Sullivan believes that Hawking’s quantum cosmology (which replaces his classical cosmology of the 1960s and 1970s) does not imply that the universe began without a cause. On p. 269 of “Coming to Be without a Cause,” Sullivan criticizes my “The Uncaused Beginning of the Universe,” Philosophy of Science (1988): 39-57, and writes (p. 269 of “Coming to Be without a Cause”): “Smith notes that some philosophers resist the implication of an uncaused beginning of the universe, but it is not only philosophers who resist the conclusion. Hawking himself now resists the implication. “It is perhaps ironic that, having changed my mind, I am now trying to convince other physicists that there was in fact no singularity at the beginning of the universe-as we shall see later, it can disappear once quantum effects are taken into account” (quoted from Hawking’s A Brief History of Time [New York: Bantam Books, 1988], p. 50). With Hawking himself against the putative implication of the Hawking-Penrose singularity theorems, why give up on causality?” I think Sullivan misunderstands Hawking’s quantum theory. Hawking’s denial of the singularity is not a denial that the universe began to exist without a cause. It merely denies that the first state of the universe has the property of being lawless. Hawking’s new theory is that there is an uncaused first state of the universe, but that it is governed by a law, the “wave function of the universe,” and therefore is not a singularity. His new theory is that “the ordinary laws of science . . . hold everywhere, including at the beginning of time” (A Brief History of Time, p. 133). Hawking emphasizes that there is not only no singularity but also no naturally unexplained boundary conditions that provide room for a supernatural causal explanation of these conditions. If his new theory were true, “there would be no singularity at which the laws of science broke down and no edge of space-time at which one would have to appeal to God . . . to set the boundary conditions for space-time” (A Brief History of Time, p. 136). Thus, Hawking’s new theory does not count as evidence against an uncaused beginning of the universe, but as evidence for it.
14. Kripke writes in Naming and Necessity: “The question of essential properties is supposed to be equivalent (and is equivalent) to the question of ‘identity across possible world’. . . . But, it’s said, the problems of giving such identity criteria are very difficult. . . . It seems to me [this is not] the right way of thinking about possible worlds. . . . There is no reason why we cannot stipulate that, in talking about what would have happened to Nixon in a certain counterfactual situation, we are talking about what would have happened to him” (pp. 42-44). Kripke’s approach seems implausible. When we have in mind Nixon as he exists in different worlds, we have in mind something in addition to Nixon qua particular that is numerically distinct from other particulars. We have in mind a particular qua determined by certain essential monadic or polyadic properties that constitute its nature and/or origin and are criteria for its transworld identity.
15. See Q. Smith, “Our Knowledge of Metaphysical Possibilities” (in preparation).
16. John Leslie writes (Universes, p. 81) that in Hawking’s model “time becomes more and more space like as the analogue of a creation point is approached; and this analogue, like a needle’s so-called point, is really only a rounded tip on which many points are more or less equally qualified for the role of ‘being where it all began’.” The fact that time is spacelike at the analogue of the creation point may be thought to be a relevant difference between the first and later states that shows how the first state can be an exception to the causal principle. However, this interpretation of Hawking implicitly presupposes that the exponential part of his wave function is to be interpreted realistically, whereas arguably only the oscillatory part is to be interpreted realistically Cf. Quentin Smith, “The Wave Function of a Godless Universe,” in Craig and Smith, Theism, Atheism and Big Bang Cosmology. On this later interpretation, the first state of the universe contains a temporal dimension that is not spacelike; the “rounded tip” part of the model, where time is spacelike, has no physical reality. Given this interpretation, there remains the problem of how the first state can be an exception to the causal principle.
17. I am grateful to William Vallicella and two referees for this journal for helpful comments on an earlier version of this paper.