1 Mooguzshura

Cosmological Argument Essay Template

The Cosmological Argument 

This argument or proof proceeds from a consideration of the existence and order of the universe.  This popular  argument for the existence of God is most commonly  known as the cosmological argument. Aristotle, much like a natural scientist, believed that we could learn about our world and the very essence of things within our world through observation. As a marine biologist might observe and catalog certain marine life in an attempt to gain insight into that specific thing's existence, so too did Aristotle observe the physical world around him in order to gain insight into his world. The very term cosmological is a reflection of Aristotle's relying upon sense data and observation. The word logos suggests a study of something while the noun cosmos means order or the way things are. Thus, a cosmological argument for the existence of God will study the order of things or examine why things are the way they are in order to demonstrate the existence of God.

For Aristotle, the existence of the universe needs an explanation, as it could not have come from nothing.  There needs to be a cause for the universe.  Nothing comes from nothing so since there is something there must have been some other something that is its cause.  Aristotle rules out an infinite progression of causes, so that led to the conclusion that there must be a First Cause.  Likewise with Motion, there must have been a First Mover.

This argument was given support by modern science with the idea of the universe originating in a BIG BANG, a single event from a single point.

A site with material on this point  You can see also Stephen Hawking and the Mind of God for another view

Thomas Aquinas offered five somewhat similar arguments using ideas of the first mover, first cause, the sustainer,  the cause of excellence, the source of harmony

 Here is a sample of the pattern:


  1. there exists a series of events

  2. the series of events exists as caused and not as uncaused(necessary)

  3. there must exist the necessary being that is the cause of all contingent being


  1. there must exist the necessary being that is the cause of the whole series of beings

 First Way: The Argument From Motion

Aquinas had Five Proofs for the Existence of God. Let us consider his First argument, the so-called Argument from Motion. Aquinas begins with an observation:

 Of the things we observe, all things have been placed in motion. No thing has placed itself in motion.

 Working from the assumption that if a thing is in motion then it has been caused to be in motion by another thing, Aquinas also notes that an infinite chain of things-in-motion and things-causing-things-to-be-in-motion can not be correct. If an infinite chain or regression existed among things-in-motion and things-causing-things-to-be-in-motion then we could not account for the motion we observe. If we move backwards from the things we observe in motion to their cause, and then to that cause of motion within those things that caused motion, and so on, then we could continuing moving backwards ad infinitum. It would be like trying to count all of the points in a line segment, moving from point B to point A. We would never get to point A. Yet point A must exist as we know there is a line segment. Similarly, if the cause-and-effect chain did not have a starting point then we could not account for the motion we observe around us. Since there is motion, the cause and effect chain (accounting for motion) must have had a starting point. We now have a second point:

 The cause and effect relationship among things-being-moved and things-moving must have a starting point. At one point in time, the relationship was set in motion. Thus, there must be a First Cause which set all other things in motion. 

What else can we know about the First Cause? The first cause must have been uncaused. If it were caused by another thing, then we have not resolved the problem of the infinite regression. So, in order to account for the motion that we observe, it is necessary to posit a beginning to the cause and effect relationship underlying the observed motion. It is also necessary to claim that the First Cause has not been caused by some other thing. It is not set in motion by another entity.

 The First Cause is also the Unmoved Mover. The Unmoved Mover is that being whom set all other entities in motion and is the cause of all other beings. For Aquinas, the Unmoved Mover is that which we call God.

For Aquinas the term motion meant not just motion as with billiard balls moving from point A to point B or a thing literally moving from one place to another. Another sense of the term motion is one that appreciates the Aristotelian sense of moving from a state of potentiality towards a state of actuality. When understood in this way, motion reflects the becoming inherent in the world around us. God as First Cause becomes that entity which designed and set in motion all things in their quest to become. In the least, it is a more poetic understanding of motion.

St. Thomas Aquinas (1224-1274) was a theologian, Aristotelian scholar, and philosopher. Called the Doctor Angelicus (the Angelic Doctor,) Aquinas is considered one the greatest Christian philosophers to have ever lived. 

Much of St. Thomas's thought is an attempt to understand Christian orthodoxy in terms of Aristotelian philosophy. His five proofs for the existence of God take "as givens" some of Aristotle's assertions concerning being and the principles of being (the study of being and its principles is known as metaphysics within philosophy). Before analyzing further the first of Aquinas' Five Ways, let us examine some of the Aristotelian underpinnings at work within St. Thomas' philosophy.

 Aristotle and Aquinas also believed in the importance of the senses and sense data within the knowing process. Aquinas once wrote nothing in the mind that was not first in the senses. Those who place priority upon sense data within the knowing process are known as empiricists. Empirical data is that which can be sensed and typically tested. Unlike Anselm, who was a rationalist, Aquinas will not rely on non-empirical evidence (such as the definition of the term "God" or "perfection") to demonstrate God's existence. St. Thomas will observe the physical world around him and, moving from effect to cause, will try try to explain why things are the way they are. He will assert God as the ultimate Cause of all that is. For Aquinas, the assertion of God as prima causa (first cause) is not so much a blind religious belief but a philosophical and theoretical necessity. God as first cause is at the very heart of St. Thomas' Five Ways and his philosophy in general.

 One last notion that is central to St. Thomas' Five Ways is the concept of potentiality and actuality. Aristotle observed that things/substances strive from an incomplete state to a complete state. Things will grow and tend to become as they exist. The more complete a thing is, the better an instance of that thing it is. We have idioms and expressions within our language that reflect this idea. For example, we might say that so-and-so has a lot of potential. We might say that someone is at the peak of their game or that someone is the best at what they do. We might say It just does not get any better than this if we are are having a very enjoyable time. Aristotle alludes to this commonly held intuition when he speaks of organisms moving from a state of potentiality to actuality. When Aquinas speaks of motion within the First Way (the cosmological argument) he is referencing the Aristotelian concepts of potentiality and actuality.

Suggested Reading:  Aquinas on God’s Existence

 Notes on the Five Ways and the associated problems

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Argument from Contingency

English theologian and philosopher Samuel Clarke set forth a second variation of the Cosmological Argument, which is considered to be a superior version.  It is called the “Argument from Contingency”.  

Clarke’s “Argument from Contingency”: 


1.     Every being that exists is either contingent or necessary.

2.     Not every being can be contingent.

3.     Therefore, there exists a necessary being on which the contingent beings depend.

4.     A necessary being, on which all contingent things depend, is what we mean by “God”.


5.     Therefore, God exists. 

However, there are several weaknesses in the Cosmological Argument, which make it unable to “prove” the existence of God by itself.  One is that if it is not possible for a person to conceive of an infinite process of causation, without a beginning, how is it possible for the same individual to conceive of a being that is infinite and without beginning?  The idea that causation is not an infinite process is being introduced as a given, without any reasons to show why it could not exist. 

Clarke (1675-1729) has offered a version of the Cosmological Argument, which many philosophers consider superior.  The “Argument from Contingency” examines how every being must be either necessary or contingent.  Since not every being can be contingent, it follow that there must be a necessary being upon which all things depend.  This being is God.  Even though this method of reasoning may be superior to the traditional Cosmological Argument, it is still not without its weaknesses.  One of its weaknesses has been called the “Fallacy of Composition”.  The form of the mistake is this:  Every member of a collection of dependent beings is accounted for by some explanation.  Therefore, the collection of dependent beings is accounted for by one explanation.  This argument will fail in trying to reason that there is only one first cause or one necessary cause, i.e. one God .

There are those who maintain that there is no sufficient reason to believe that there exists a self existent being. 


 1. If there is a cause for everything then what caused the first cause (god).

2.If the first cause can be thought to be uncaused and a necessary being existing forever, then why not consider that the universe itself has always existed and shall always exist and go through a never ending cycle of expansion and contraction and then expansion (big bang) again and again!!!

If there is to be a deity that is the exception from the requirement that all existing things need a cause then the same exception can be made for the sum of all energy that exists, considering that it manifests in different forms.

What the counter argument does is to indicate that the premises of the cosmological argument do not necessarily lead to the conclusion that there is a being that is responsible for the creation of the universe.

3) Further, even if a person wanted to accept that there was such a being there is nothing at all in the cosmological argument to indicate that the being would have any of the properties of humans that are projected into the concept of the deity of  any particular religion.  The first mover or first cause is devoid of any other characteristic.

So the cosmological argument is neither a valid argument in requiring the truth of its conclusion nor is it a satisfactory argument to prove the existence of any being that would have awareness of the existence of the universe or any event within it.

When a person asks questions such as :

1 What is the cause of the the energy or the force or the agent behind the  expansion and contraction of the energy? 
These questions are considered as "loaded questions" because they loaded or contain assumptions about what exists or is true that have not yet been established.  Why is it that the idea of a "force " or agent" is even in the question?  Why operate with the assumption that there is such or needs to be such?

We do not know that there is a force "behind" the expansion and contraction. Energy might just expand and contract and there is no force at all other than those generated by the energy-gravitational force, electro magnetic, strong and weak  forces.

In another form this is the "who made god?" question or the" who made the energy question?" question.  Such an approach to the issue of an explanation for the existence of the universe assumes that there must be an agency.  When the idea of an eternal and necessary agency is introduced it was done to provide a form for describing a being that some people wanted as the ultimate explanation- a deity.  The point of the counter arguments to the cosmological argument is that the idea of an eternal and necessary agency can as logically be expressed as energy rather than as a single being or entity.  If the uncaused cause can be thought of a a single entity then the uncaused cause can be thought of a a single process-energy.

Here is another view of this argument and the rebuttal:


  • there exists a series of events
  • the series of events exists as caused and not as uncaused (necessary)
  • there must exist the necessary being that is the cause of all contingent being

CONCLUSION: There must exist the necessary being that is the cause of the whole series of beings


1.RULE: Everything that exists must have a cause

2.the Universe (multiverse) exists

3.the universe (multiverse) must have a cause


The cause of the universe (multiverse) is GOD


1.BUT what is the cause of GOD?

2.God has no cause but is a necessary being.  GOD is an EXCEPTION to RULE !

REBUTTAL:  If GOD can be the exception then why not ENERGY???


Clarke’s “Argument from Contingency”: 

1.     Every being that exists is either contingent or necessary.

2.     Not every being can be contingent.

3.     Therefore, there exists a necessary being on which the contingent beings depend.

4.     A necessary being, on which all contingent things depend, is what we mean by “God”.

CONCLUSION:  Therefore, God exists. 


Why not have that a necessary being on which the contingent beings depend is ENERGY itself that changes its form through time?  PANTHEISM

Can there be a Creation without God ?  Well this work addresses that question.

Notes on Critiques of this Argument:  David Hume’s Critique of the Cosmological Argument  

1.      Variations on the Cosmological Argument:

The Kalam Cosmological Argument

1.                 The universe either had a beginning or it did not.

2.                 The universe had a beginning.

a)                Philosophical arguments for the impossibility of transversing an actual infinite series of events (see above).

b)                The Big Bang Theory of the Universe postulates a beginning.

(1)              This is the most widely recognized theory of the universe.

c)                 The second law of thermodynamics (entropy).

(1)              The universe is running out of energy.

(2)              If it had an infinite past, it would have run out by now. 

3.                 The beginning of the universe was either caused or uncaused.

4.                 The beginning of the universe was caused.

a)                Contra Hume, every event has a cause.

b)                God is not an event.

c)                 One might hold that some events, like quantum events, don't need causes.

(1)              If so, then this premise can be replaced with "Everything that begins to exist has a cause."

 On Kalam Argument

A Modern Version of the Cosmological Argument William Lane Craig:

The Existence of God and the Beginning of the Universe

Logic and the Cosmological Argument 

Counter Arguments to the attempts to use the Cosmological or Kalam Cosmological Argument

1. ) VIEW:  Debunking the Kalam Cosmological Argument

View also Irrefutable Refutation of the Kalam Cosmological Argument!

1. Historical Overview

Although in Western philosophy the earliest formulation of a version of the cosmological argument is found in Plato’s Laws, 893–96, the classical argument is firmly rooted in Aristotle’s Physics (VIII, 4–6) and Metaphysics (XII, 1–6). Islamic philosophy enriches the tradition, developing two types of arguments. Arabic philosophers (falasifa), such as Ibn Sina (c. 980–1037), developed the argument from contingency, which is taken up by Thomas Aquinas (1225–74) in his Summa Theologica (I,q.2,a.3) and his Summa Contra Gentiles (I, 13). Influenced by John Philoponus (5th c) (Davidson 1969) the mutakallimūm—theologians who used reason and argumentation to support their revealed Islamic beliefs—developed the temporal version of the argument from the impossibility of an infinite regress, now referred to as the kalām argument. For example, al-Ghāzāli (1058–1111) argued that everything that begins to exist requires a cause of its beginning. The world is composed of temporal phenomena preceded by other temporally-ordered phenomena. Since such a series of temporal phenomena cannot continue to infinity because an actual infinite is impossible, the world must have had a beginning and a cause of its existence, namely, God (Craig 1979: part 1). This version of the argument enters the medieval Christian tradition through Bonaventure (1221–74) in his Sentences (II Sent. D.1,p.1,a.1,q.2).

Enlightenment thinkers, such as Gottfried Wilhelm Leibniz and Samuel Clarke, reaffirmed the cosmological argument. Leibniz (1646–1716) appealed to a strengthened principle of sufficient reason, according to which “no fact can be real or existing and no statement true without a sufficient reason for its being so and not otherwise” (Monadology, §32). Leibniz uses the principle to argue that the sufficient reason for the “series of things comprehended in the universe of creatures” (§36) must exist outside this series of contingencies and is found in a necessary being that we call God. The principle of sufficient reason is likewise employed by Samuel Clarke in his cosmological argument (Rowe 1975: chap. 2).

Although the cosmological argument does not figure prominently in Asian philosophy, a very abbreviated version of it, proceeding from dependence, can be found in Udayana’s Nyāyakusumāñjali I,4. In general, philosophers in the Nyāya tradition argue that since the universe has parts that come into existence at one occasion and not another, it must have a cause. We could admit an infinite regress of causes if we had evidence for such, but lacking such evidence, God must exist as the non-dependent cause. Many of the objections to the argument contend that God is an inappropriate cause because of God’s nature. For example, since God is immobile and has no body, he cannot properly be said to cause anything. The Naiyāyikas reply that God could assume a body at certain times, and in any case, God need not create in the same way humans do (Potter 1977: 100–07).

The cosmological argument came under serious assault in the 18th century, first by David Hume and then by Immanuel Kant. Hume (1748) attacks both the view of causation presupposed in the argument (that causation is an objective, productive, necessary power relation that holds between two things) and the Causal Principle—every contingent being has a cause of its existence—that lies at the heart of the argument. Kant contends that the cosmological argument, in identifying the necessary being, relies on the ontological argument, which in turn is suspect. We will return to these criticisms below.

Both theists and nontheists in the last part of the 20th century and the first part of the 21st century generally have shown a healthy skepticism about the argument. Alvin Plantinga concludes “that this piece of natural theology is ineffective” (1967: chap. 1). Richard Gale contends, in Kantian fashion, that since the conclusion of all versions of the cosmological argument invokes an impossibility, no cosmological arguments can provide examples of sound reasoning (1991: chap. 7). (However, Gale seems to have changed his mind and in recent writings proposed and defended his own version of the cosmological argument, which we will consider below.) Similarly, Michael Martin (1990: chap. 4), John Mackie (1982: chap. 5), Quentin Smith (Craig and Smith 1993), Bede Rundle (2004), Wes Morriston (2000, 2002, 2003, 2010), and Graham Oppy (2006: chap. 3) reason that no current version of the cosmological argument is sound. Yet dissenting voices can be heard. Robert Koons (1997) employs mereology and modal and nonmonotonic logic in taking a “new look” at the argument from contingency. In his widely discussed writings William Lane Craig marshals multidisciplinary evidence for the truth of the premises found in the kalām argument. Richard Gale and Alexander Pruss propose a new version based on a so-called weak principle of sufficient reason that leads to a finite God that is not omnibenevolent, and Richard Swinburne, though rejecting deductive versions of the cosmological argument, proposes an inductive argument that is part of a larger cumulative case for God’s existence.

There is quite a chance that if there is a God he will make something of the finitude and complexity of a universe. It is very unlikely that a universe would exist uncaused, but rather more likely that God would exist uncaused. The existence of the universe…can be made comprehensible if we suppose that it is brought about by God. (1979: 131–32)

In short, contemporary philosophers continue to contribute increasingly detailed and complex arguments on both sides of the debate.

2. Typology of Cosmological Arguments

Philosophers employ diverse classifications of the cosmological arguments. Swinburne distinguishes inductive from deductive versions. Craig distinguishes three types of deductive cosmological arguments in terms of their approach to an infinite regress of causes. The first, advocated by Aquinas, is based on the impossibility of an essentially ordered infinite regress. The second, which Craig terms the kalām argument, holds that an infinite temporal regress of causes is impossible because an actual infinite is impossible, and even if it were possible it could not be temporally realized. The third, espoused by Leibniz and Clarke, is overtly founded on the Principle of Sufficient Reason (Craig 1980: 282–83). Craig notes that the distinction between these types of arguments is important because the objections raised against one version may be irrelevant to other versions. So, for example, a critique of a particular version of the Principle of Sufficient Reason (PSR), which one finds developed by William Rowe or Richard Gale, might not be telling against the Thomistic or kalām versions of the argument. Another way of distinguishing between versions of the argument is in terms of the relevance of time to the argument. In Aquinas’s version, consideration of the essential ordering of the causes or reasons proceeds independent of temporal concerns. The relationship between cause and effect is treated as real but not temporal, so that the first cause is not a first cause in time but a sustaining cause. In the kalām version, however, the temporal ordering of the causal sequence is central, introducing issues of the nature of time into the discussion.

3. Complexity of the Question

It is said that philosophy begins in wonder. So it was for the ancients, who wondered what constituted the basic stuff of the world around them, how this basic stuff changed into the diverse forms they experienced, and how it came to be. Those origination questions related to the puzzle of existence that, in its metaphysical dimensions, is the subject of our concern.

First, why is there anything at all? Why is there something, no matter what it is, even if different or even radically different from what currently exists? This question becomes clearer when put in contrastive form, Why is there something rather than nothing? We can ask this question even in the absence of contingent beings, though in this context it is likely to prove unanswerable. For example, if God or the universe is logically or absolutely necessary, something would not only exist but would have to exist even if nothing else existed. At the same time, probably no reason can be given for why logically necessary things exist.

Some doubt whether we can ask this question because there being nothing is not an option. John Heil asks, “What exactly is nothing at all? What would nothing be?” (Heil 2013: 174). He analogizes nothing with the notion of empty space, in terms of which, he thinks, we can conceptualize nothing. He reasons that we cannot achieve a notion of empty space simply by removing its contents one at a time, for space (the void) would still exist. But we need not analogize nothing in terms of empty space, and even if we do, we surely can conceive of removing space. If we think of space as a particular type of relation between objects, the removal of all objects (everything) would leave nothing, including relations. The key point is that “leaving nothing” is not to be understood in the sense that nothing is or has existence. We can easily be misled by the language of there being nothing at all, leading to the notion that nothing has being or existence. Heil suggests that nothing might be a precursor to the Big Bang. But this too is a misconception—though one widely held by those who think that the universe arose out of nothing, e.g., a vacuum fluctuation. A vacuum fluctuation is itself not nothing “but is a sea of fluctuating energy endowed with a rich structure and subject to physical laws” (Craig and Sinclair 2009: 183, 191). The contrastive question is comprehensible: “Why is there something rather than there never having been anything whatsoever?”

Rutten (2012, Other Internet Resources: 15–16), using the modal proposition S5, develops an a priori argument for the impossibility of there being nothing. Suppose that there is nothing. If there is nothing, then there are no possible states of affairs, since nothing is actual to bring them about. But since I am actual, there is at least one possible state of affairs S. But if S is possible, then by S5, necessarily, S is possible. But this contradicts the original assumption that total nothingness is metaphysically possible. Hence, total nothingness cannot be actual. Rutten’s argument rests on the Principle of Causation, about which we will have a lot more to say below.

Second, why are there contingent beings? That is, “Why does a universe exist?” Several possible responses have been given: it might not be explicable (the universe just exists; its existence is a brute fact); it has always existed, which also leaves it as a brute fact; it was brought about by the intentional act of a supernatural being. The traditional cosmological arguments consider these options and determine that the last provides the best explanation for the existence of a contingent universe.

Third, why are there these particular contingent beings? The starting point here is the existence of particular things, and the question posed asks for an explanation for there being these particular things. If we are looking for a causal explanation and accept a full explanation (in terms of contemporary or immediately prior causal conditions and the relevant natural laws or intentions that together necessitate the effect), the answer emerges from an analysis of the relevant immediate causal conditions present in each case. As Hume argues, explanation in terms of immediately conjunctory factors is satisfactory. Theists counter that if we seek a complete causal explanation where nothing of the causal event remains unexplained, the response can lead to the development of the cosmological argument.

Heil suggests that the answer depends on how one understands the Big Bang (2013: 178). If it was spontaneous, the question has no answer. If not spontaneous, there might be an answer. Theists take up the latter cause, broadening the explanatory search to include final causes or intentions appropriate to a personal cause. It leads us to ask the question, “Supposing that God exists, why did he bring about contingent beings?” This assumes that God exists and now inquires about the reasons for creation. On the one hand, we might argue that this question is unanswerable in that only God would know his reasons for bringing the universe of contingent beings into existence (O’Connor 2008). On the other hand, God acts out of his nature; Swinburne (2004: 47, 114–23) emphasizes his goodness, from which we can infer possible reasons for what he brings about. God also acts from his intentions (Swinburne 1993: 139–45; 2007: 83–84), so that God could reveal his purposes for his act of creating.

Fourth, why do things exist now or at any given point? This is the question that Thomas Aquinas posed. Aquinas was interested not in a beginning cause but in a sustaining cause, for he believed that the universe could be eternal—although he believed on the basis of revelation that it was not eternal. He constructed his cosmological arguments around the question of what sustains things in the universe in their existence.

Fifth, if the universe has a beginning, what is the cause of that beginning? This is the question that is addressed by the kalām cosmological argument, given its central premise that everything that begins to exist has a cause.

Two things should be obvious from this discussion. First, questions about existence are more nuanced than usually addressed (Heil 2013: 177). It is important to be more precise about what one is asking when one asks this broader metaphysical question about why there is something rather than nothing. Second, it becomes clear that the cosmological argument lies at the heart of attempts to answer the questions, and to this we now turn.

4. Argument for a Non-contingent Cause

Thomas Aquinas held that among the things whose existence needs explanation are contingent beings that depend for their existence upon other beings. Richard Taylor (1992: 84–94) discusses the argument in terms of the world (“everything that ever does exist, except God, in case there is a god”, 1992: 87) being contingent and thus needing explanation. Arguing that the term “universe” refers to an abstract entity or set, William Rowe rephrases the issue, “Why does that set (the universe) have the members that it does rather than some other members or none at all?” (Rowe 1975: 136). Put broadly, “Why is there anything at all?” (Smart, in Smart and Haldane, 1996: 35; Rundle 2004). The response of defenders of the cosmological argument is that what is contingent exists because of the action of a necessary being.

4.1 A Deductive Argument from Contingency

As an a posteriori argument, the cosmological argument begins with a fact known by experience, namely, that something contingent exists. We might sketch out a version of the argument as follows.

  1. A contingent being (a being such that if it exists, it could have not-existed or could cease to exist) exists.
  2. This contingent being has a cause of or explanation[1] for its existence.
  3. The cause of or explanation for its existence is something other than the contingent being itself.
  4. What causes or explains the existence of this contingent being must either be solely other contingent beings or include a non-contingent (necessary) being.
  5. Contingent beings alone cannot provide a completely adequate causal account or explanation for the existence of a contingent being.
  6. Therefore, what causes or explains the existence of this contingent being must include a non-contingent (necessary) being.
  7. Therefore, a necessary being (a being such that if it exists, it cannot not-exist) exists.
  8. The universe is contingent.
  9. Therefore, the necessary being is something other than the universe.

In the argument, steps 1–7 establish the existence of a necessary or non-contingent being; steps 8–9 attempt in some way to identify it.

Over the centuries philosophers have suggested various instantiations for the contingent being noted in premise 1. In his Summa Theologica (I,q.2,a.3), Aquinas argued that we need a causal explanation for things in motion, things that are caused, and contingent beings.[2] Others, such as Richard Swinburne (2004), propose that the contingent being referred to in premise 1 is the universe. The connection between the two is supplied by John Duns Scotus, who argued that even if the essentially ordered causes were infinite, “the whole series of effects would be dependent upon some prior cause” (Scotus [c. 1300] 1964: I,D.2,p.1,q.1,§53). Gale (1999) calls this the “Big Conjunctive Contingent Fact”). Whereas the contingency of particular existents is generally undisputed, not the least because of our mortality, the contingency of the universe deserves some defense (see section 4.2). Premise 2 invokes a moderate version of the Principle of Causation or the Principle of Sufficient Reason, according to which if something is contingent, there must be a cause of its existence or a reason or explanation why it exists rather than not exists. The point of 3 is simply that something cannot cause or explain its own existence, for this would require it to already exist (in a logical if not a temporal sense). Premise 4 is true by virtue of the Principle of Excluded Middle: what explains the existence of the contingent being either are solely other contingent beings or includes a non-contingent (necessary) being. Conclusions 6 and 7 follow validly from the respective premises.

For many critics, premise 5 (along with premise 2) holds the key to the argument’s success or failure. The truth of 5 depends upon the requirements for an adequate explanation. According to the Principle of Sufficient Reason (PSR), what is required is an account in terms of sufficient conditions that provides an explanation why the cause had the effect it did, or alternatively, why this particular effect and not another arose. Swinburne (2004: 75–79), and Alexander Pruss (2006: 16–18) after him, note diverse kinds of explanations. In a full explanation the causal factors—in scientific causation, causal conditions and natural laws; in personal causation, persons and their intentions— are sufficient for the occurrence of an event. They “together necessitate the occurrence of the effect” (Swinburne 2004: 76).

It does not allow a puzzling aspect of the explanandum to disappear: anything puzzling in the explanandum is either also found in the explanans or else explained by the explanans. (Pruss 2006: 17)

It suffices to explain why something comes about given the immediately present causal conditions, but leaves unexplained why those explanatory causal conditions and/or reasons themselves hold.

In a complete explanation, every aspect of the explanandum and explanans at the time of the occurrence is accounted for; nothing puzzling remains.

A complete explanation of the occurrence of E is a full explanation of its occurrence in which all the factors cited are such that there is no [further] explanation (either full or partial) of their existence of operation in terms of factors operative at the time of their existence or operation. (Swinburne 2004, 78)

Pruss and Swinburne argue that the kind of explanation required by the PSR is a complete explanation.

Quinn argues that an adequate explanation need not require a complete explanation (2005: 584–85); a partial explanation might do just as well, depending on the context. Among these adequate explanations of why this actual world obtains rather than another possible world (including one with no contingent beings) is that the universe is an inexplicable brute fact and that God strongly actualized the world (although not everything in it). He refuses to take sides on the debate between explanations, except to say that science cannot provide an adequate explanation if the explanatory chain is infinite, for the chain of causes is itself contingent or it ends in an initial contingency not scientifically accountable. However, not only does Quinn not clarify what constitutes an adequate explanation, but as Pruss contends, the PSR “is not compatible with an infinite chain of explanations that has no ultimate explanans” (2006: 17), for in an infinite chain something puzzling remains to be explained, with the result that the PSR would again be invoked to explain what is puzzling. But, as we will question below, is the brute fact of the universe any more unacceptable as a complete explanation than the brute fact of a necessary being?

One worry with understanding the PSR is that it may lead to a deterministic account that not only bodes ill for the success of the argument but on a libertarian account may be incompatible with the contention that God created freely. Pruss, however, envisions no such difficulty.

What gives sufficiency to explanation is that mystery is taken away, for example, through the citing of relevant reasons, not that probability is increased. (Pruss 2006: 157)

Giving reasons neither makes the event deterministic nor removes freedom.

Once we have said that \(x\) freely chose \(A\) for \(R\), then the only thing left that is unexplained is why \(x\) existed and was both free and attracted by \(R\). (2006: 158)

Finally, some (disputedly, see below) argue that explanations must be either natural (impersonal) or non-natural (personal). 8 & 9 assert that if the contingent being identified in 1 is the universe, given that the universe encompasses all natural existents and the laws and principles governing them, the explanation must be in terms of a non-natural, eternal, necessary being that provides an intentional, personal, ultimate explanation. Since the argument proceeds independent of temporal considerations, the argument does not necessarily propose a first cause in time, but rather a first or primary sustaining cause of the universe. As Aquinas noted, the philosophical arguments for God’s existence as first cause are compatible with the eternity of the universe (On the Eternity of the World).

The question whether the necessary being to which the argument concludes is God is debated. Some hold that the assertion that the first sustaining cause is God (steps 8 and 9) is not part of the cosmological argument per se; such defenders of the argument sometimes create additional arguments to identify the first cause. Others, however, contend that from the concept of a necessary being other properties appropriate to a divine being flow. O’Connor (2004) argues that being a necessary being cannot be a derivative emergent property, otherwise the being would be contingent. Likewise the connection between the essential properties must be necessary. Hence, the universe cannot be the necessary being since it is mereologically complex. Similarly, the myriad elementary particles cannot be necessary beings either, for their distinguishing distributions are externally caused and hence contingent. Rather, he contends that a more viable account of the necessary being is as a purposive agent with desires, intentions, and beliefs, whose activity is guided but not determined by its goals, a view consistent with identifying the necessary being as God. Koons (as are Craig and Sinclair 2009: 192–94) also is willing to identify the necessary being as God, constructing corollaries regarding God’s nature that follow from his construction of the cosmological argument. Oppy (1999), on the other hand, expresses significant skepticism about the possibility of such a deductive move.

Critics have objected to key premises in the argument. We will consider the most important objections and responses.

4.2 Objection 1: The Universe Just Is

Interpreting the contingent being in premise 1 as the universe, Bertrand Russell denies that the universe needs an explanation (premise 2); it just is. Russell, following Hume (1779), contends that since we derive the concept of cause from our observation of particular things, we cannot ask about the cause of something like the universe that we cannot experience. The universe needs no explanation; it is “just there, and that’s all” (Russell 1948 [1964]: 175). This view was reiterated by Hawking (1987: 651).

Swinburne replies that

uniqueness is relative to description. Every physical object is unique under some description,… yet all objects within the universe are characterized by certain properties, which are common to more than one object.… The objection fails to make any crucial distinction between the universe and other objects; and so it fails in its attempt to prevent at the outset a rational inquiry into the issue of whether the universe has some origin outside itself. (Swinburne 2004: 134–35)

We don’t need to experience every possible referent of the class of contingent things to be able to conclude that a contingent thing needs a cause. “To know that a rubber ball dropped on a Tuesday in Waggener Hall by a redheaded tuba player will fall to the ground”, I don’t need a sample that includes tuba players dropping rubber balls at this location (Koons 1997: 202).

Morriston (2002: 235) responds that although it is true that we don’t need to experience every instance to derive a general principle, the universe is a very different thing from what we experientially reference when we say that things cannot come into existence without a cause. Tuba players are not “anything remotely analogous to the ‘initial singularity’ that figures in the Big Bang theory of the origin of the universe”.

Defenders of the argument respond that there is a key similarity between the universe and the experienced content, namely, both tuba players (and the like) and the cosmos are contingent. Given our experience with contingent particulars, we do not need to experience every member of a contingent cosmos to know that it is caused.

But why should we think that the cosmos is contingent? Defenders of the view contend that if the components of the universe are contingent, the universe itself is contingent. Russell replies that the move from the contingency of the components of the universe to the contingency of the universe commits the Fallacy of Composition, which mistakenly concludes that since the parts have a certain property, the whole likewise has that property. Hence, whereas we legitimately can ask for the cause of particular things, to require a cause of the universe or the set of all contingent beings based on the contingency of its parts is mistaken.

Russell correctly notes that arguments of the part-whole type can commit the Fallacy of Composition. For example, the argument that since all the bricks in the wall are small, the wall is small, is fallacious. Yet it is an informal fallacy of content, not a formal fallacy. Sometimes the totality has the same quality as the parts because of the nature of the parts invoked—the wall is brick (composed of baked clay) because it is built of bricks (composed of baked clay). The universe’s contingency, theists argue, resembles the second case. If all the contingent things in the universe, including matter and energy, ceased to exist simultaneously, the universe itself, as the totality of these things, would cease to exist. But if the universe can cease to exist, it is contingent and requires an explanation for its existence (Reichenbach 1972: chap. 5).

Whether this argument for the contingency of the universe is similar to that advanced by Aquinas in his Third Way depends on how one interprets Aquinas’s argument. Aquinas holds that “if everything can not-be, then at one time there was nothing in existence” (ST I,q.2,a.3). Plantinga, among others, points out that this may commit a quantifier mistake (Plantinga 1967: 6; Kenny 1969: 56–66). However, Haldane (Smart and Haldane 1996: 132) defends the cogency of Aquinas’s reasoning on the grounds that Aquinas’s argument is fallacious only on a temporal reading, but Aquinas’s argument employs an atemporal ordering of contingent beings. That is, Aquinas does not hold that over time there would be nothing, but that in the per se ordering of causes, if every contingent thing in that order did not exist, there would be nothing.

William Rowe treats the argument temporally and contends (1975: 160–67) that this argument for the contingency of the universe is fallacious, for even if every contingent being were to fail to exist in some possible world, it may be the case that there is no possible world that lacks a contingent being. That is, although no being would exist in every possible world, every world would possess at least one contingent being. In such a case, although each being is contingent, it is necessary that something exist. Rowe gives the example of a horse race.

We know that although no horse in a given horse race necessarily will be the winner, it is, nevertheless, necessary that some horse in the race will be the winner. (1975: 164)

Rowe’s example will work only if it is necessary that some horse will finish the race, for otherwise it is possible that all the horses break a leg and none finishes the race—a condition he notes in that “it is necessary that there exists at least one member of the collection”. So why should we think that it is necessary that something exist, even if it is contingent? Rowe does not say why, but one argument given in defense of this thesis is that the existence of one contingent being may be necessary for the nonexistence of some other contingent being. But although the fact that something’s existence is necessary for the non-existence of something else holds for certain relational properties (for example, the existence of a spouse is necessary for a man not to be a bachelor), it is doubtful that something’s existence is necessary for the non-existence of something else per se, which is what is needed to support the argument that denies the contingency of the universe.

Rowe (1975: 166) develops a different argument to support the thesis that the universe must be contingent. He argues that it is necessary that if God exists, then it is possible that no dependent beings exist. Since it is possible that God exists, it is possible that it is possible that no dependent beings exist. (This conclusion is licensed by the modal principle: If it is necessary that if \(p\) then \(q\), then if it is possible that \(p\), it is possible that \(q\).) Hence, it is possible that there are no dependent beings; that is, that the universe is contingent. Rowe takes the conditional as necessarily true in virtue of the classical concept of God, according to which God is free to decide whether or not to create dependent beings.

To avoid any hint of the Fallacy of Composition and to avoid its complications, Koons (1997: 198–99) formulates the argument for the contingency of the universe as a mereological argument. If something is contingent, it contains a contingent part. The whole and part overlap and, by virtue of overlapping, have a common part. Since the part in virtue of which they overlap is wholly contingent, the whole likewise must be contingent.

One might approach Russell’s thesis regarding the universe from a different direction. If theists are willing to accept the existence of God as the necessary being as a brute fact, why cannot nontheists accept the existence of the universe as a brute fact, as a necessary being? Bede Rundle, for example, argues that what has necessary existence is causally independent. Matter has necessary existence, for although it undergoes change as manifested in particular bits of matter, the given volume of matter found in the universe persists, and as persisting matter/energy does not have or need a cause. This accords with the Principle of Conservation of Mass-Energy, according to which matter and energy are never lost but rather transmute into each other. As indestructible, matter/energy is the necessary being. Consequently, although the material components of the universe are contingent vis-à-vis their form, they are necessary vis-à-vis their existence. On this reading, there is not one but there are many necessary beings, all internal to the universe. Their particular configurations are contingent, but since matter/energy is conserved it cannot be created or lost.

Interestingly enough, this approach was anticipated by Aquinas in his third way in his Summa Theologica (I,q.2,a.3). Once Aquinas concludes that necessary beings exist, he then goes on to ask whether these beings have their existence from themselves or from another. If from another, then we have an unsatisfactory infinite regress of explanations. Hence, there must be something whose necessity is uncaused. As Kenny points out, Aquinas understands this necessity in terms of being unable to cease to exist (Kenny 1969: 48). Although Aquinas understands the uncaused necessary being to be God, Rundle takes this to be matter/energy itself.

One question that arises with Rundle’s view is whether there could have been more or less matter/energy than there is. That is, if there is \(n\) amount of matter/energy in the world, could there be a possible world with \(+n\) or \(-n\) amounts of matter/energy? We do not know how much matter/energy existed in the first \(10^{-35}\) seconds of the universe. Even if the universe currently operates according to the principle of the Conservation of Matter and Energy, Rundle’s thesis depends on the contention that during the very early phase of rapid expansion, a period of time we know little about, this principle held. A second significant problem concerns what follows from the existence of necessary beings. If the matter/energy nexus constitutes the necessary being, what causally follows from that nexus is itself necessary, and contingency, even in the composing relations within the universe, would disappear. Everything in the universe would be necessary, which is a disquieting position. Third, O’Connor (2004) argues that since the necessary being provides the ultimate explanation, there is no explanation of the differentiation of the kinds of matter or of contingencies that matter/energy causally undergo, for example, in terms of space-time location. Perhaps one way to rescue Rundle’s thesis would be to invoke an indeterministic presentation of quantum phenomena, which would allow contingency of individual phenomena but not of the overall probabilistic structure.

4.3 Objection 2: Explaining the Individual Constituents Is Sufficient

Whereas Russell argued that the universe just is, David Hume held that when the parts are explained the whole is explained.

But the whole, you say, wants a cause. I answer that the uniting of these parts into a whole… is performed merely by an arbitrary act of the mind, and has no influence on the nature of things. Did I show you the particular causes of each individual in a collection of twenty particles of matter, I should think it very unreasonable should you afterwards ask me what was the cause of the whole twenty. This is sufficiently explained in explaining the parts. (Hume 1779: part 9)

Hume contends that uniting the parts or individual constituents into a whole is a mental act. In reality, all that exist are individual, causally-related events, not whole sets of events. When we have provided an account of each of these individual, causally-related events we have explained the whole. We don’t need anything more.

Rowe objects to what he terms the Hume-Edwards principle—that by explaining the parts we have explained the whole:

When the existence of each member of a collection is explained by reference to some other member of that very same collection, then it does not follow that the collection itself has an explanation. For it is one thing for there to be an explanation of the existence of each dependent being and quite another thing for there to be an explanation of why there are dependent beings at all. (Rowe 1975: 264)

Pruss (1999) expands on Rowe’s argument. An explanation of the parts may provide a partial but not a complete explanation. The explanation in terms of parts may fail to explain why these parts exist rather than others, why they exist rather than not, or why the parts are arranged as they are. Each member or part will be explained either in terms of itself or in terms of something else that is contingent. The former would make them necessary, not contingent, beings. If they are explained in terms of something else, they still remain unaccounted for, since the explanation would invoke either an infinite regress of causes or a circular explanation. Pruss employs the chicken/egg sequence: chickens account for eggs, which account for chickens, and so on where the two are paired. But appealing to an infinite chicken/egg regress or else arguing in a circle explains neither any given chicken nor egg.

Richard Swinburne notes that an explanation is complete when “any attempt to go beyond the factors which we have would result in no gain of explanatory power or prior probability” (2004: 89). But explaining why something exists rather than something else or than nothing and why it is as it is gives additional explanatory power in explaining why a universe exists at all. Gale (1991: 257–58) concludes that if we are to explain the parts of the universe and their particular concatenation, we must appeal to something other than those parts.

4.4 Objection 3: The Principles of Causation and of Sufficient Reason Are Suspect

Critics of the cosmological argument contend that the Causal Principle or, where applicable, the broader Principle of Sufficient Reason (PSR) that underlies versions of the argument, is suspect. As Hume argued, there is no reason for thinking that the Causal Principle is true a priori, for we can conceive of events occurring without conceiving of their being caused, and what is conceivable is possible in reality (1748: IV). Neither can an argument for the application of the Causal Principle to the universe be drawn from inductive experience. Even if the Causal Principle applies to events in the world, we cannot extrapolate from the way the world works to the world as a whole (Mackie 1982: 85).

Several replies are in order. First, Hume’s conceivability to possibility argument is unsound. For one thing, whose conceivability is being appealed to here? For another, someone who fails to understand a necessarily true proposition might conceive of it being false, but from this it does not follow that it possibly is false. A person might think (wrongly) that pi is a determinate number, but it does not follow that it is so. In the phenomenology of conceivability, what is really conceivable is difficult if not impossible to differentiate from what some might think is conceivable. And even if something is conceivable, say in a logical sense, it does not follow that it is metaphysically or factually possible. One might conceive that, since heads can be distinguished from tails on a coin, they can actually be separated, but metaphysically such is impossible. What is distinguishable is not necessarily separable. Hume, it seems, confuses epistemic with ontological conditions. Hence, the argument based on conceivability is suspect (Reichenbach 1972: 57–60).

Second, there is reason to think that the Causal and Sufficient Reason principles are true. Some suggest a pragmatic-type of argument: the principles are necessary to make the universe intelligible. Critics reply that the principles then only have methodological or practical and not ontological justification. As John Mackie argues, we have no right to assume that the universe complies with our intellectual preferences for causal order. We can simply work with brute facts. Perhaps so, but without such principles, science itself would be undercut. As Pruss (2006: 255) points out, “Claiming to be a brute fact should be a last resort. It would undercut the practice of science”. Utilization of the principles best accounts for the success of science, indeed, for any investigatory endeavor (Koons 1997; see also Koons 2008: 111–12, where he argues that it is “a subjectively required presumption for needed for immunity to internal defeaters”). The best explanation of the success of science and other such rational endeavors is that the principles are really indicative of how reality operates.

Pruss goes further to suggest that the PSR in particular is “self-evident, obvious, intuitively clear, in no need of argumentative support” (2006: 189). For example, he holds that the principle of sufficient reason—“necessarily, every contingently true proposition has an explanation” (he defers on whether the principle also applies to necessarily true propositions)—is self-evident in the sense that anyone who understands it correctly understands that it is true. These persons might not know it to be self-evidently true, but they do understand it to be true. This is consistent with other persons denying it is self-evident, for those who deny it might misunderstand the principle in various ways. They might experience a conceptual blindness to the nature of contingency or they might be “talked out of” understanding the principle because of its controversial implications (e.g., the existence of a necessary being).

The problem with the claim of self-evidence is that it is a conversation ender, not a starter. One who denies its self-evidence might think that those who hold to it are the ones who experience conceptual blindness. In contrast to analyticity, self-evidence holds in relation to the knowers themselves, and here diversity of intuitions varies, perhaps according to philosophical or other types of perspectives. Furthermore, if the principle truly is self-evident, it would be strange to respond to skeptics by attempting to give reasons to support that contention, and were such demanded, the request would itself invoke the very principle in question.

Pruss responds that being self-evident is not incompatible with providing arguments for self-evident propositions, and he thinks that arguments can show the truth of the PSR to those who deny its self-evidence. Among the numerous arguments he advances is a modal argument employing a Weak Principle of Sufficient Reason, according to which “every contingent proposition possibly has a complete explanation” (Pruss 2006: 234–35). We will develop this in section 5.

Peter van Inwagen (1983: 202–04) argues that the PSR must be rejected. If the PSR is true, every contingent proposition has an explanation. Suppose P is the conjunction of all contingent true propositions. Suppose also that there is a state of affairs S that provides a sufficient reason for P. S cannot itself be contingent, for then it would be a conjunct of P and entailed by P, and as both entailing and entailed by P would be P, so that it would be its own sufficient reason. But no contingent proposition can explain itself. Neither can S be necessary, for from necessary propositions only necessary propositions follow. Necessary propositions cannot explain contingent propositions, for if x sufficiently explains y, then x entails y, and if x is necessary so is y. So \(S\) cannot be either contingent or necessary, and hence the PSR is false. Thus, if the cosmological argument appeals to the PSR to establish the existence of a necessary being whose existence is expressed by a necessary proposition as an explanation for contingent beings, it fails in that it cannot account for the contingent beings it purportedly explains. But, as Pruss notes (2006: chaps. 6 & 7),

The word sufficient can be read in two different ways: the reason given can be logically sufficient for the explanandum, or it can sufficiently explain the explanandum. (2006: 103)

We need not hold to the strong claim of logical sufficiency about the relation between explaining and entailment in cases where the explanation is brought about by libertarian free agency. Although God is a necessary being, his connection with the world is through his free agency, and free actions explain but do not entail the existence of particular contingent states.

Clearly, the soundness of the deductive version of the cosmological argument hinges on whether principles such as that of Causation or Sufficient Reason are more than methodologically true and on the extent to which these principles can be applied to individual things or to the universe. Critics of the argument will be skeptical regarding the universal application of the principles; defenders of the argument generally not so. Perhaps the best one can say, with Taylor, is that even those who critique the PSR invoke it when they suggest that defenders have failed to provide a sufficient reason for thinking it is true.

The principle of sufficient reason can be illustrated in various ways,…but it cannot be proved…. If one were to try proving it, he would sooner or later have to appeal to considerations that are less plausible than the principle itself. Indeed, it is hard to see how one could even make an argument for it without already assuming it. For this reason it might properly be called a presupposition of reason itself. (1992: 87)

We will return to the Principle of Causation below with respect to the kalām argument.

4.5 Objection 4: Problems with the Concept of a Necessary Being

Immanuel Kant objected to the use of “necessary being” throughout the cosmological argument, and hence to the conclusion that a necessary being exists. Kant held that the cosmological argument, in concluding to the existence of an absolutely necessary being, attempts to prove the existence of a being whose nonexistence “is impossible”, is “absolutely inconceivable” (Critique B621). Kant indicates that what he has in mind by an “absolutely necessary being” is a being whose existence is logically necessary, where to deny its existence is contradictory. The only being that meets this condition is the most real or maximally excellent being—a being with all perfections, including existence. This concept lies at the heart of the ontological argument (see entry on ontological arguments). Although in the ontological argument the perfect being is determined to exist through its own concept, in fact nothing can be determined to exist in this manner; one has to begin with existence. In short, the cosmological argument presupposes the cogency of the ontological argument. But since the ontological argument is defective for the above (and other) reason, the cosmological argument that depends on or invokes it likewise must be defective (Critique B634).

Kant’s contention that the necessity found in “necessary being” is logical necessity was common up through the 1960s. J.J.C. Smart wrote,

And by “a necessary being” the cosmological argument means “a logically necessary being”, i.e., “a being whose non-existence is inconceivable in the sort of way that a triangle’s having four sides is inconceivable”.… Now since “necessary” is a word which applies primarily to propositions, we shall have to interpret “God is a necessary being” as “The proposition ‘God exists’ is logically necessary”. (in Flew and MacIntyre 1955: 38; in a later work Smart (Smart and Haldane 1996: 41–47) broadened his notion of necessity.)

Many recent discussions of the cosmological argument, both supporting and critiquing it, interpret the notion of a necessary being as a being that cannot not exist (O’Connor 2008: 78, 2013: 38). For example, Gale-Pruss contend that speaking about necessary beings does not differ from speaking of the necessity of propositions (see section 5). As such, as Plantinga notes, if a necessary being is possible, it exists (God, Freedom and Evil, 1967: 110). It is a being that exists in all possible worlds. The only question that remains is whether God’s existence is possible. This notion is similar to, if not a modernization of, Aquinas’s contention that God’s essence is to exist. Aquinas attempts to avoid the accusation that this invokes the ontological argument on the grounds that we do not have an adequate concept of God’s essence (ST I,q.2,a.1). However, if we understand “necessary being” in this sense, we can dispose of the cosmological argument as irrelevant; what is needed rather is an argument to establish that God’s existence is possible, for if it is possible that it is necessary that God exists, then God exists (by Axiom S5).

But this need not be the sense in which “necessary being” is understood in the cosmological argument. A more adequate notion of necessary being is that the necessity is metaphysical or factual. A necessary being is one that if it exists, it neither came into existence nor can cease to exist, and correspondingly, if it does not exist, it cannot come into existence (Reichenbach 1972: 117–20). If it exists, it eternally maintains its own existence; it is self-sufficient and self-sustaining. So understood, the cosmological argument does not rely on notions central to the ontological argument. Rather, instead of being superfluous, the cosmological argument, if sound, gives us reason to think that the necessary being exists rather than not.

Mackie replies that if God has metaphysical necessity, God’s existence is logically contingent, such that some reason is required for God’s own existence (Mackie 1982: 84). That is, if God necessarily exists in the sense that if he exists, he exists in all possible worlds, it remains logically possible that God does not exist in any (and all) possible worlds. Hence, God, as Swinburne notes (2004: 79, 148) is a logically contingent being, and so could have not-existed. Why, then, does God exist? The PSR can be applied to the necessary being.

The theist responds that the PSR does not address logical contingency but metaphysical contingency. One is not required to find a reason for what is not metaphysically contingent. It is not that the necessary being is self-explanatory; rather, a demand for explaining its existence is inappropriate. Hence, the theist concludes, Hawking’s question “Who created God?” (Hawking 1988: 174) is out of place (Davis 1997). We will return to this discussion in section 8.

5. Argument from the Weak Principle of Sufficient Reason

Recently Richard Gale and Alexander Pruss (1999) advanced a modal version of the cosmological argument. They reject the strong version of the PSR, according to which “for every proposition \(p\), if \(p\) is true, then there is a proposition, \(q\), that explains \(p\)”. In its place they favor using a weak version of the PSR—it is possible that for every true proposition, there is a proposition, \(q\), that explains \(p\)—that they believe is less question-begging and more initially acceptable to critics. They phrase the argument in terms of contingent and necessary propositions. A contingent proposition is one that is both possibly true and possibly false (i.e., true in some worlds and false in others); a necessarily true proposition is true in every possible world. In its simplest form, the argument is (1) if it is possible that it is necessary that a supernatural being of some sort exists, then it is necessary that a supernatural being of that sort exists. Since (2) it is possible that it is necessary that a supernatural being of some sort exists, (3) it is necessary that this being exists. The being that Gale has in mind is a very powerful and intelligent designer-creator, not the all perfect God of Anselm, for this perfect God who would exist in all possible worlds would be incompatible with the existence of gratuitous and horrendous evils to be found in some of those possible worlds.

If one grants modal Axiom S5 (if it is possible that it is necessary that \(p\), then it is necessary that \(p\)), the critical premise in the argument is the second, and Gale and Pruss proceed to defend it using their weak PSR. They begin with the notion of a Big Conjunctive Fact (BCF), which is the totality of propositions that would be true of any possible world were it actualized. Since all possible worlds would have the same necessary propositions, they are differentiated by their Big Conjunctive Contingent Fact (BCCF), which would contain different contingent propositions. Let \(p\) be the BCCF of the actual world \(W\). Suppose, further, that it is possible that \(p\) has an explanation, that is, that it is possible that there is some proposition \(q\) that explains \(p\). As such, there is a possible world \(W_{1}\) that contains \(p\), \(q\), and the proposition that \(q\) explains \(p\). The question now is whether \(W_{1}\) is the actual world, that is, whether there is a proposition \(q\) that explains \(p\) in the actual world. Gale argues that \(W_{1}\) (which contains \(q\) and the proposition that \(q\) explains \(p\)) is the actual world, for since \(W_{1}\) contains \(p\), there can be no property of \(p\) that is not found in \(W_{1}\). Every conjunct of \(p\) will be a conjunct of \(p_{1}\) (the BCCF of \(W_{1}\)) in \(W_{1}\). Suppose that \(r\) is a conjunct of \(p\) in \(W\), then not-\(r\) cannot be a conjunct of \(p_{1}\) in \(W_{1}\)\(.\) Since \(W\) and \(W_{1}\) have the same properties, \(W_{1}\) is the actual world. Therefore, since these worlds are identical, the actual world contains \(p\), \(q\), and the proposition that \(q\) explains \(p\). That is, there is something that explains the BCCF of the actual world. The explanation of the BCCF cannot be scientific, for such would be in terms of law-like propositions and statements about the actual world at a given time, which would be contingent and hence part of the BCCF. Since the only explanations we can conceive of are personal or scientific, \(q\) provides a personal explanation of the BCCF in terms of the intentional action of a necessary being who freely brings it about that the world exists. \(q\) cannot report the action of a contingent being, for then the being would be part of \(p\) and explained by \(q\). But something cannot explain itself. Hence, although contingent, \(q\) reports the action of a necessary being. Gale concludes that although this necessary being exists in every possible world, this tells little about its power, goodness, and other qualities. To make this being palatable to theists, he offers that the argument be supplemented by other arguments, such as the teleological arguments, to suggest that the necessary being is the kind of being that satisfies theistic requirements. Since

the actual world’s universe displays a wondrous complexity due to its law-like unity and simplicity, fine tuning of natural constants, and natural purpose and beauty,… there exists a necessary supernatural being who is very powerful, intelligent, and good and freely creates the actual world’s universe. (1999: 468–69)

(For the detailed 18 step deductive argument, see Gale and Pruss 1999: 462–69).

Several objections have been raised about the argument from the weak principle of sufficient reason. Almeida and Judisch construct their objection via two reductio arguments. They note that, according to Gale’s argument, \(q\) is a contingent proposition in the actual world that reports the free, intentional action of a necessary being. As such, since the actual world contains the contingent proposition \(q\), non-\(q\) is possible. That is, there is a possible world \(W_{2}\) that contains \(p\), non-\(q\), and that \(q\) does not explain \(p\). But by Gale’s own reasoning, \(W_{2}\) is identical to the actual world. But the actual world cannot contain both \(q\) and non-\(q\). Thus, \(q\) cannot be a contingent proposition.

On the other hand, assume that \(q\) is a contingently necessary proposition, that is, that it is possible that \(q\) is necessary and possible that \(q\) is not necessary. By S5, we get that it is necessary that \(q\) is necessary, making it impossible that \(q\) is not necessary. As a result, it is both possible and not-possible that \(q\) is not necessary, which likewise shows that \(q\) cannot be a contingently necessary proposition. The only other option is that \(q\) is a necessary truth, which would beg the question. Thus, the argument fails by being unable to characterize \(q\). For rebuttals, see Gale and Pruss (2002) and Rutten (2012, Other Internet Resources: 84–87).

Graham Oppy (2000) similarly argues that suppose \(p_1\) is the BCF of some possible world, and \(p_{1}\) has no explanation. Then, given \(r\) (namely, that \(p_{1}\) has no explanation) there is a conjunctive fact \(p_{1}\) and \(r\). Since by hypothesis the conjunctive fact \(p_{1}\) and \(r\) is true in some world, on Gale’s account it is true in the actual world. Then by the weak PSR there is a world in which this conjunction of \(p_{1}\) and \(r\) possibly has an explanation. If there is an explanation for the conjunction of \(p_{1}\) and \(r\), there is an explanation for \(p_{1}\). Thus, we have the contradiction that \(p_{1}\) both has and does not have an explanation, which is absurd. Hence, no world exists where the BCF lacks an explanation, which is the strong principle of sufficient reason that Gale allegedly circumvented. Since accepting the weak PSR would commit the nontheist to the strong PSR and ultimately to a necessary being, the nontheist has no motivation to accept the weak PSR.

Gale and Pruss (2002) subsequently concede that their weak PSR does entail the strong PSR, but they contend that there still is no reason not to proceed with the weak PSR, which they think the nontheist would accept. The only grounds for rejecting it, they claim, is that it leads to a theistic conclusion, which is not an independent reason for rejecting it. Oppy, however, maintains that appealing to some initial instincts of acceptance is irrelevant. Perhaps the nontheists did not see what granting the weak PSR entailed, that it contradicted other things they had independent reasons to believe, or they did not fully understand the principle. There is a modus tolens reason to reject it, since there are other grounds for thinking that theism is false.

Jerome Gellman has argued that the Gale/Pruss conclusion to a being that is not necessarily omnipotent also fails; this being is essentially omnipotent and, if omnipotence entails omniscience, is essentially omniscient. This too Gale and Pruss concede, which means that the necessary being they conclude to is not significantly different from that arrived at by the traditional cosmological argument that appeals to the moderate version of the PSR.

Finally, there is doubt that Gale’s rejection of the traditional cosmological argument on the grounds that the necessary being could not be necessarily good is well grounded. Gale argues that since there are possible worlds with gratuitous or horrendous evils, and since God as necessary would exist in these worlds, God cannot be necessarily good. The problem here is that if indeed there is this incompatibility between a perfectly good necessary being (God) and gratuitous evils or even absolutely horrendous evils, then it would follow that worlds with God and such evils would not be possible worlds, for they would contain a contradiction. In all possible worlds where a perfectly good God as a necessary being would exist, there would be a justificatory morally sufficient reason for the evils that would exist, or at least, given the existence of gratuitous evils, for the possibility of the existence of such evils (Reichenbach 1982: 38–39). Beyond this, however, the point stands that the weak PSR entails the strong PSR, and as we argued above, defenders of the cosmological argument do not need such a strong version of the PSR to construct their argument.

6. The Kalām Cosmological Argument

A second type of cosmological argument, contending for a first or beginning cause of the universe, has a venerable history, especially in the Islamic mutakalliman tradition. Although it had numerous defenders through the centuries, it received new life in the recent voluminous writings of William Lane Craig. Craig formulates the kalām cosmological argument this way (in Craig and Smith 1993: chap. 1):

  1. Everything that begins to exist has a cause of its existence.
  2. The universe began to exist.
  3. Therefore, the universe has a cause of its existence.
  4. Since no scientific explanation (in terms of physical laws) can provide a causal account of the origin (very beginning) of the universe, the cause must be personal (explanation is given in terms of a personal agent).

This argument has been the subject of much recent debate, only some of which we can summarize here. (For greater bibliographic detail, see Craig and Sinclair 2009.)

6.1 The Causal Principle and Quantum Physics

The basis for the argument’s first premise is the Causal Principle that undergirds many cosmological arguments. (Oderberg [2002: 308] is mistaken when he tries to establish the uniqueness of the kalām argument by denying that the Causal Principle plays a role in kalām argument. It only does not play a role in supporting a particular premise in the argument.) Defenders and critics alike suggest that basing the argument on the Principle of Causation rather than on the more general Principle of Sufficient Reason is advantageous to the argument (Morriston 2000: 149). Craig holds that the first premise is intuitively obvious; no one, he says, seriously denies it (Craig, in Craig and Smith 1993: 57). Although at times Craig suggests that one might treat the principle as an empirical generalization based on our ordinary and scientific experiences (which might not be strong enough for the argument to succeed in a strong sense, although it might be supplemented by an inference to the best explanation argument that what best explains the success of science is that reality operates according to the causal principle), ultimately, he argues, the truth of the Causal Principle rests “upon the metaphysical intuition that something cannot come out of nothing” (Craig, in Craig and Smith 1993: 147). “No one sincerely believes that things, say, a horse or an Eskimo village, can just pop into being without a cause” (Craig and Sinclair 2009: 182), and this includes the universe.

The Causal Principle has been the subject of extended criticism. (We addressed objections to the Causal Principle as subsumed under the PSR from a philosophical perspective earlier in 4.4.) Some critics deny that they share Craig’s intuitions about the Causal Principle (Oppy 2002). Morriston (2000) argues that, for one thing, it does not seem to be an a priori truth, for not only does it lack “a kind of ‘luminosity’ that makes it impossible not to believe it, but closer inspection does not make it clearer that it is true” (2000: 156–59). He points not only to the presence of serious doubters (which he thinks he should not be able to find if it were truly an a priori truth), but also to quantum phenomena, and thereby joins those who raise objections to the Causal Principle based on quantum physics (Davies 1984: 200). On the quantum level, the connection between cause and effect, if not entirely broken, is to some extent loosened. For example, it appears that electrons can pass out of existence at one point and come back into existence elsewhere. One can neither trace their intermediate existence nor determine what causes them to come into existence at one point rather than another. Neither can one precisely determine or predict where they will reappear; their subsequent location is only statistically probable given what we know about their antecedent states. Hence,

quantum-mechanical considerations show that the causal proposition is limited in its application, if applicable at all, and consequently that a probabilistic argument for a cause of the Big Bang cannot go through. (Smith, in Craig and Smith 1993: 121–23, 182)

Craig responds that appeals to quantum phenomena do not affect the kalām argument. For one thing, quantum events are not completely devoid of causal conditions. Even if one grants that the causal conditions are not jointly sufficient to determine the event, at least some necessary conditions are involved in the quantum event. But when one considers the beginning of the universe, he notes, there are no prior necessary causal conditions; simply nothing exists (Craig, in Craig and Smith 1993: 146; see Koons 1997: 203). Pruss (2006: 169) contends that in quantum phenomena causal indeterminacy is compatible with the causal principle in that the causes indeterministically bring about the effect. Morriston is rightly puzzled by this reply, for, he asks, what

makes a cause out of a bunch of merely necessary conditions. Apparently not that they are jointly sufficient to produce the effect. (2000: 158)

If conditions are not jointly sufficient, is there reason to think that premise 1 is true? More recently, Craig argues that

not all physicists agree that subatomic events are uncaused…. Indeed, most of the available interpretations of the mathematical formulation of [Quantum Mechanics] are fully deterministic. (Craig and Sinclair 2009: 183)

For another, a difference exists between predictability and causality. It is true that, given Heisenberg’s principle of uncertainty, we cannot precisely predict individual subatomic events. What is debated is whether this inability to predict is due to the absence of sufficient causal conditions, or whether it is merely a result of the fact that any attempt to precisely measure these events alters their status. The very introduction of the observer into the arena so affects what is observed that it gives the appearance that effects occur without sufficient or determinative causes. But we have no way of knowing what is happening without introducing observers into the situation and the changes they bring. In the above example, we simply are unable to discern the intermediate states of the electron’s existence apart from introducing conditions of observation. When Heisenberg’s indeterminacy is understood not as describing the events themselves but rather our knowledge of the events, the Causal Principle still holds and can still be applied to the initial singularity, although we cannot expect to achieve any kind of determinative predictability about what occurs on the sub-atomic level given the cause.

At the same time, it should be recognized that showing that indeterminacy is a real feature of the world at the quantum level would have significant negative implications for the more general Causal Principle that underlies the deductive cosmological argument. The more this indeterminacy has ontological significance, the weaker is the Causal Principle. If the indeterminacy has merely epistemic significance, it scarcely affects the Causal Principle. Quantum accounts allow for additional speculation regarding origins and structures of universes. In effect, whether Craig’s response to the quantum objection succeeds depends upon deeper issues, in particular, the epistemic and ontological status of quantum indeterminacy, the nature of the Big Bang as a quantum phenomenon, the nature and role of indeterminate causation, and whether realist theories about quantum phenomena have serious traction. Quantum physics is murky, as evidenced by Bell’s gedanken experiments, as described by Mermin.

6.2 Impossibility of an Actual Infinite

In defense of premise 2, Craig develops both a priori and a posteriori arguments. His primary a priori argument is

  1. An actual infinite cannot exist.
  2. A beginningless temporal series of events is an actual infinite.
  3. Therefore, a beginningless temporal series of events cannot exist.

Since (7) follows validly, if (5) and (6) are true the argument is sound. In defense of premise (5), he defines an actual infinite as a determinate totality that occurs when a part of a system can be put into a one-to-one correspondence with the entire system (Craig and Sinclair 2009: 104). Craig argues that if actual infinites that neither increase nor decrease in the number of members they contain were to exist in reality, we would have rather absurd consequences. For example, imagine a library with an actually infinite number of books. Suppose that the library also contains an infinite number of red and an infinite number of black books, so that for every red book there is a black book, and vice versa. It follows that the library contains as many red books as the total books in its collection, and as many red books as black books, and as many red books as red and black books combined. But this is absurd; in reality the subset cannot be equivalent to the entire set. Likewise, in a real library by removing a certain number of books we reduce the overall collection. But if infinites are actual, a library with an infinite number of books would not be reduced in size at all by removal of a specific number of books (short of all of them), for example, all the red books or those with even catalogue numbers (Craig and Smith 1993: 11–16). The absurdities resulting from attempting to apply basic arithmetical operations, functional in the real world, to infinities suggest that although actual infinites can have an ideal existence, they cannot exist in reality.

Craig’s point is this. Two sets \(A\) and \(B\) are the same size just in case they can be put into one-to-one correspondence, that is, if and only if every member of \(A\) can be correlated with exactly one member of \(B\) in such a way that no member of \(B\) is left out. In the case of infinite sets, this notion of “same size” yields results like the following: the set of all natural numbers (let this be \(A\)) is the same size as the set of squares of natural numbers (\(B\)), since every member of \(A\) can be correlated with exactly one member of \(B\) in a way that leaves out no member of \(B\) (correlate \(0\leftrightarrow 0\), \(1\leftrightarrow1\), \(2\leftrightarrow4\), \(3\leftrightarrow9\), \(4\leftrightarrow 16\),…). So this is a case—recognized in fact as early as Galileo (Dialogues Concerning Two New Sciences)—where two infinite sets have the same size but, intuitively, one of them, as a subset, appears to be smaller than the other; one set consists of only some of the members of another, but you nonetheless never run out of either when you pair off their members.

Craig uses a similar, intuitive notion of “smaller than” in his argument concerning the library. It appears that the set \(B\) of red books in the library is smaller than the set \(A\) of all the books in the library, even though both have the same (infinite) size. Craig concludes that it is absurd to suppose that such a library is possible in actuality, since the set of red books would simultaneously have to be smaller than the set of all books and yet equal in size.

Critics fail to be convinced by these paradoxes of infinity. For example, Rundle (2004: 170) agrees with Craig that the concept of an actual infinite is paradoxical, but this, he argues, provides no grounds for thinking it is incoherent. The logical problems with the actual infinite are not problems of incoherence, but arise from the features that are characteristic of infinite sets. When the intuitive notion of “smaller than” is replaced by a precise definition, finite sets and infinite sets just behave somewhat differently, that is all. Cantor, and all subsequent set theorists, define a set \(B\) to be smaller than set \(A\) (i.e., has fewer members) just in case \(B\) is the same size as a subset of \(A\), but \(A\) is not the same size as any subset of \(B\). The application of this definition to finite and infinite sets yields results that Craig finds counter-intuitive but which mathematicians see as our best understanding for comparing the size of sets. They see the fact that an infinite set can be put into one-to-one correspondence with one of its own proper subsets as one of the defining characteristics of an infinite set, not an absurdity. Say that set \(C\) is a proper subset of \(A\) just in case every element of \(C\) is an element of \(A\) while \(A\) has some element that is not an element of \(C\). In finite sets, but not necessarily in infinite sets, when set \(B\) is a proper subset of \(A\), \(B\) is smaller than \(A\). But this doesn’t hold for infinite sets—as above where \(B\) is the set of squares of natural numbers and \(A\) is the set of all natural numbers.

Cantorian mathematicians argue that these results apply to any infinite set, whether in pure mathematics, imaginary libraries, or the real world series of concrete events. Thus, Smith argues that Craig begs the question by wrongly presuming that an intuitive relationship holds between finite sets and their proper subsets, namely, that a set has more members than its proper subsets must hold even in the case of infinite sets (Smith, in Craig and Smith 1993: 85). So while Craig thinks that Cantor’s set theoretic definitions yield absurdities when applied to the world of concrete objects, which entails that infinites cannot be actual, set theorists see no problem so long as the definitions are maintained. Further discussion is in Oppy 2006: 137–54.

Why should one think premise (6) is true—that a beginningless series, such as the universe up to this point, is an actual rather than a potential infinite? For Craig, an actual infinite is a determinate totality or a completed unity, whereas the potential infinite is not. Since the past events of a beginningless series can be conceptually collected together and numbered, the series is a determinate totality (1979: 96–97). And since the past is beginningless, it has no starting point and is infinite. If the universe had a starting point, so that events were added to or subtracted from this point, we would have a potential infinite that increased through time by adding new members. The fact that the events do not occur simultaneously is irrelevant.

Bede Rundle rejects an actual infinite, but his grounds for doing so—the symmetry of the past and the future—, if sustained, make premise 6 false. He argues that the reasons often advanced for asymmetry, such as those given by Craig, are faulty. It is true that the past is not actual, but neither is the future. Likewise, that the past, having occurred, is unalterable is irrelevant, for neither is the future alterable. The only time that is real is the present. Likewise, the argument that if the past were infinite, there would be no reason why we arrive at t0 now rather than earlier, fails.

For Rundle, the past and the future are symmetrical; it is only our knowledge of them that is asymmetrical. Any future event lies at a finite temporal distance from the present. Similarly, any past event lies at a finite temporal distance from the present. For each past or future series of events, beginning from the present, there can always be a subsequent event. Hence, for both series an infinity of events is possible, and, as symmetrical, the infinity of both series is the same. Since the series of future events is not an actual but a potential infinite (or, better, an “indefinitely extendible” series, 2004: 168), the series of past events is also indefinitely extendible. It follows that although the future is actually finite, it does not require an end to the universe, for there is always a possible subsequent event (2004: 180). Similarly, although any given past event of the universe is finitely distant in time from now, a beginning or initial event can be ruled out; for any given event there is a possible earlier event. But then, since there is a possible prior or possible posterior event in any past or future series respectively, the universe, although finite in time, is temporally unbounded (indefinitely extendible); both beginning and cessation are ruled out. (How Rundle [2004: 176–78] gets from the possibility of a subsequent event to actually ruling out cessation and beginning is less than clear.) Since there is no time when the material universe might not have existed, it is not contingent but necessary. Hence, although the principle of sufficient reason is still true, it applies only to the components of the material universe and not to the universe itself. No explanation of the universe is possible. The universe, as matter-energy, is neither caused nor destructible; not in the sense that it could have been caused or could cease, but in the sense that “the notions of beginning and ceasing to exist are inapplicable to the universe” (2004: 178).

But, one might wonder, are the past series and future series of events really symmetrical? It is true that one can start from the present and count either forward and backward in time. Rundle thinks that …\(x5\), \(x4\), \(x3\), \(x2\), \(x1\), \(t0\), \(y1\), \(y2\), \(y3\), \(y4\), \(y5\) are all on the same continuum, so that we cannot distinguish ontologically the time dimension of the future and past series. The two series, going into the past and into the future, would be the same in that however far we count from the present (\(t0\)) remains finite although indefinitely extendible. But is it true that, as he claims, with regard to the past, “any movement currently terminating can be redescribed as extending back”, that counting backward from the present is the same as counting from the past to the present (2004: 176)?

Craig says no, for in the actual world we do not start from now to arrive at the past; we move from the past to the present. To count backwards, we would start from a particular point in time, the present. From where would we start to count were the past indefinitely extendible? Both to count and to move from the past to the present, we cannot start from the indefinitely extendible. Indeed, if the past is indefinitely extendible, no matter where we started, we would have arrived at \(t0\) long before now.

Before the present event could occur the event immediately prior to it would have to occur; and before that event could occur, the event immediately prior to it would have to occur; and so on ad infinitum. One gets driven back and back into the infinite past, making it impossible for any event to occur. Thus, if the series of past events were beginningless, the present event could not have occurred, which is absurd. (Craig and Sinclair 2009: 118)

One cannot just reverse the temporal sequence of the past, for we don’t ontologically engage the sequence from the present to the past. Rundle’s two movements are quite disparate, such that the two sequences—of the past and of the future—are not symmetrical, which leaves intact Craig’s claim that a beginningless past would result in an actual and not a potential infinite.

Craig is well aware of the fact that he is using actual and potential infinite in a way that differs from the traditional usage in Aristotle and Aquinas. For Aristotle all the elements in an actual infinite exist simultaneously, whereas a potential infinite is realized over time by addition or division. Hence, the temporal series of events, as formed by successively adding new events, was a potential, not an actual, infinite (Aristotle, Physics, III, 6). For Craig, however, an actual infinite is a timeless totality that cannot be added to or reduced. “Since past events, as determinate parts of reality, are definite and distinct and can be numbered, they can be conceptually collected into a totality” (Craig, in Craig and Smith 1993: 25). The future, but not the past, is a potential infinite, for its events have not yet happened.

6.3 Successive Addition Cannot Form an Actual Infinite

Craig’s second argument addresses this very point.

  1. The temporal series of events is a collection formed by successive addition.
  2. A collection formed by successive synthesis is not an actual infinite.
  3. Therefore, the temporal series of events cannot be an actual infinite (Craig 1979: 103).

The collection of historical events is formed by successively adding events, one following another. The events are not temporally simultaneous but occur over a period of time as the series continues to acquire new members. Even if an actual infinite were possible, it could not be realized by successive addition; in adding to the series, no matter how much this is done, even to infinity, the series remains finite and only potentially infinite. One can neither count to nor traverse the infinite (Craig and Sinclair 2009: 118).

It might be objected that this sounds very much like Zeno’s paradoxes that prohibit Achilles or anyone from either beginning to cross an area or succeeding in doing so. But, notes Craig, significant disanalogies disallow this conclusion. For one, Zeno’s argument rests on progressively-narrowing, unequal distances that sum to a finite distance, whereas in traversing the past the equal distances continue to the infinity of the future. Second, Zeno’s distances are potential because of divisibility, whereas the distances from the past are actual distances or times to be traversed.

Morriston (2003: 290) critiques Craig’s thesis that forming the infinite series of events by successive addition presupposes a beginning point. He asks,

Why couldn’t there have been an infinite series of years in which there was no first year? It’s true that in such a series we never “arrive” at infinity, but surely that is only because infinity is, so to speak, “always already there”. At every point in such a series, infinitely many years have already passed by.

Why do we need to “arrive at infinity?” But Craig’s point is not that we cannot arrive at infinity in the past, but that we could not traverse the infinite to arrive at the present moment. Why this moment rather than another? But maybe, Morriston replies, that is just the way it is; “the past just is the series of events that have already happened”. To require a reason for the series of past events arriving at now is to appeal to the principle of sufficient reason, which he deems both suspect and inappropriate for Craig to invoke (Morriston 2003: 293). Furthermore, he argues, Craig’s argument mistakenly presupposes two independent series—a series of events and a series of segments of time they occupy—such that one can ask about how the former is mapped onto the latter, whereas in fact the two series are not independent. Craig (2010) replies that it is not a matter of sufficient reason, but that Morriston simply has not paid sufficient attention to the distinction between past and present tenses, on which potential and actual infinites are founded. A finite series that has the potential for further members, as with future events beginning with now, is actually finite and only potentially infinite. But a beginningless series of past events cannot add new members; it is actually, not potentially, infinite. There is a relevant distinction between the two series.

To illustrate his conclusion, Craig presents Bertrand Russell’s example of Tristram Shandy, who writes his autobiography. It takes him a year to write about one day of his life, so that as his life progresses so does his autobiography in which he gets progressively farther behind. Russell concludes that

if (Shandy) had lived forever, and had not wearied of his task, then, even if his life had continued as eventfully as it began, no part of his biography would have remained unwritten. ([1903] 1937: 358)

But, Oderberg (2002: 310) claims, Russell seems to have fallaciously moved from (1) For every day, there is a year such that, by the end of that year, Shandy has recorded that day, which is true, to (2) There is a year such that, for every day, by the end of that year Shandy has recorded that day. (2) is needed for Russell’s conclusion but fails to follow from (1). Shandy’s writing never catches up with his life; indeed, the longer he lives, even if for infinity, his writing would never catch up to his life but progressively would get farther behind. Indeed, if he has been living and writing from infinity, his autobiography is infinitely behind his life. Contrary to Russell, there will be days—an infinite number—about which he will be unable to write. As can be imagined, this example has been greatly contested, modified, and has generated a literature of its own. For samples, see Eells (1988), Oderberg (2002), and Oppy 2003.

Finally, it is objected that Craig’s argument presupposes an \(A\) view of time, where time flows from past to present to future and not all events tenselessly coexist. But can Craig’s argument be sustained if time is understood in the \(B\) sense, where all members of the series tenselessly coexist, being equally real (Grünbaum 1994)? On a \(B\) view of time there is no beginning, and it would seem that on this view the argument would collapse. Andrew Loke responds that even on a \(B\) view of time, one cannot realize the infinite by successive addition. It is impossible to count an actual infinite at any time because “an actual infinite has a greater number of elements than what could be counted by the process of counting”. This feature

is due to (i) the nature of the number of elements of an actual infinite set, which is an essential property of such a set, and (ii) the process of counting one element after another. (Loke 2014a: 76)

This response depends crucially on the distinction between an actual and a potential infinite.

6.4 The Big Bang Theory of Cosmic Origins

Craig and Sinclair’s a posteriori argument for premise 2 invokes recent cosmology and the Big Bang theory of cosmic origins. Since the universe is expanding as the galaxies recede from each other, if we reverse the direction of our view and look back in time, the farther we look, the denser the universe becomes. If we push backwards far enough, we find that the universe reaches a state of compression where the density and gravitational force are infinite. This unique singularity constitutes the beginning of the universe—of matter, energy, space, time, and all physical laws. It is not that the universe arose out of some prior state, for there was no prior state. Since time too comes to be, one cannot ask what happened before the initial event. Neither should one think that the universe expanded from some state of infinite density into space; space too came to be in that event. Since the Big Bang initiates the very laws of physics, one cannot expect any scientific or physical explanation of this singularity.

One picture, then, is of the universe beginning in a singular, non-temporal event roughly 13–14 billion years ago. Something, perhaps a quantum vacuum, came into existence. Its tremendous energy caused it, in the first fractions of a second, to expand and explode, creating the four-dimensional space-time universe that we experience today. How this all happened in the first \(10^{-35}\) seconds and subsequently is a matter of serious speculation and debate; what advocates of premise 2 maintain is that since the universe and all its material elements originate in the Big Bang, the universe is temporally finite and thus had a beginning. (For a detailed consideration of cosmogonic theories from the kalām

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