Abstract
The Kalam Cosmological Argument is perhaps the most widely discussed of the theistic arguments. With the revival brought about by William Lane Craig and its popularization brought about by the Internet in general and YouTube in particular, there is no shortage of objections. What seems most fascinating is the degree to which objectors to the argument, even in the professional philosophical literature, misunderstand the assumptions about the ontology of time upon which the argument is built. Specifically, Craig’s version of the Kalam argument assumes a relational or reductionist view of time, and yet so often the objectors assume (without argument) a Platonist view of time. One might try to repair these objections by giving an argument for a Platonist view. The problem is that the Kalam argument is robust enough that it can be adapted to almost any view of time’s ontology. In short, Platonism regarding time serves as no threat to the Kalam Cosmological Argument.
A Brief Overview of Kalam
The Kalam Cosmological Argument can be stated quite simply with two premises and a conclusion.
(1) If something begins to exist, it has a cause
(2) Material reality began to exist
(3) Therefore, material reality had an immaterial cause
This paper will focus on the properties of the first cause. According to their article in Blackwell, Craig and Sinclair state that the cause of material reality must be uncaused and beginningless. Given the impossibility of an infinite number of past events, this cause must be changeless and immaterial, since material things change incessantly at the microscopic level.[i]Craig and Sinclair also note that on a technical level, the Kalam argument only demonstrates that metric time had a beginning. If there were an undifferentiated time before creation, God would be temporally prior to creation, but there would be no moment one second, one hour, or one year before creation.
Discussions surrounding this argument often involve what it means for something to begin to exist, and whether the arguments against the sufficiency of the material world apply equally to God. If the past has to be finite, then how is it that God is not also finite in the past? A better way to rephrase the question is: “If the past is finite, how can God be eternal in the past? How can God be from everlasting to everlasting?”
Craig answers this through a careful definition of what it means to begin to exist. The definition goes something like: “A being b begins to exist at time t if and only if b exists at t, there is no time interval immediately prior to t at which b exists, and there is no state of affairs in which b exists timelessly.”[ii]This is to say that a being can be both eternal and finite in the past as long as there is a state of affairs when (or where) the being exists timelessly. When talking about the finitude or infinitude of the past, we need a definition that allows us to state coherently “time began to exist” and “time did not begin to exist.” Otherwise, the beginning of time becomes a matter of arbitrary stipulation rather than a matter of thorough philosophical investigation.
Morriston objects to this idea, yet does not state his assumptions explicitly. He argues that it is not possible for God to be apart from time “prior” to creation.[iii]He takes the view of Grunbaum and Swinburne stating that something does not begin to exist unless there is a prior time in which that thing does not exist.
A Brief Excursion Regarding Premise 2
It is puzzling the way that some objectors are so quick to dismiss the philosophical arguments against the infinitude of the past. Take the argument that an actually infinite number of things cannot exist. Morriston, Oppy, and others suggest that if transfinite arithmetic violates intuition, then one should say “so much the worse for intuition.” This seriously underestimates the problem presented by Hilbert and others. The real problem is not that the existence of actual infinites would allow people to build weird and spooky hotels that defy intuition, but that it would allow us to perform, in reality, mathematically invalid operations. Inverse operations with infinite cardinals are every bit as invalid as division by zero or taking a base 1 logarithm. If one’s ontology allows for such operations, then that should serve as a reductioagainst any such ontology.
Worse, the transfinite cardinals such as ℵ0 seem far more problematic than set theorists are generally willing to admit. Consider Cantor’s formula for dealing with infinite cardinals. He stipulated that two sets A and B have the same cardinality if they can be put into a bijection. Think of a philosophy class where every student is sitting in a chair and every chair has exactly one student sitting on it. Cantor would say that the set of students and the set of chairs has the same cardinality. This comports without our intuitions about the size of groups, but it is not a complete description. In order to fit with our intuitions about size, we need to state that in order for the number of students and chairs to be equal, not only do we need to be able to pair one student to one chair so that there are no chairs or students left over, but we also need to be unable to pair our students and chairs so that each student is sitting in one chair apiece, and yet there are chairs left over. Transfinite sets fail this criterion, and hence the set of all natural numbers (for example) is not equal in size to anything, not even to itself. Set theorists might be able to ignore these problems and proceed anyway for utility’s sake. David Hilbert was a non-realist regarding mathematical objects, which may be why he allowed for mathematical discussion of these objects. The ontologist does not have such a luxury. Ontology has no place for such useful fictions, since the subject of ontology deals with what literally is the case.[iv]
Christ Rescued Us from Platonic Hell
The argument against actual infinites also serves as both an argument against a realist view of abstract objects, the B-theory of time on Christianity, and a formalized propositional view of omniscience. As a bonus, it can help us understand Christ’s ability to be both ignorant and omniscient. The issue of abstract objects has already been addressed at length by Craig, Azzouni, and others. The short answer to those who would object based on abstract objects is that it does not seem at all obvious that mathematical objects literally exist, or that our idea of truth be based on a view that forces us to believe that every noun in our vocabulary corresponds to an object in our ontology. Likewise, the existential quantifier seems more like a linguistic device than a symbol of ontological commitment.
On the B-theory of time, all moments in time are actualized. There is no objective passage of time, which means that there can be no such thing as a potentially infinite future. If one holds to a robust doctrine of immortality, one is committed to the view that humans will live with God in a temporal state for eternity. On presentism, this doctrine can be believed without commitment to actual infinites, since the number of events will be always finite and always growing. On the B-theory, one is committed to an actually infinite number of events.
Similarly, the argument against actual infinites requires us to think of divine omniscience in qualitative rather than quantitative terms. God’s omniscience is not an actually infinite collection of propositions. Instead, it can be thought of as a type of superthought, or super conscious state from which he can derive any true proposition. This may provide a helpful solution to the problem raised in Matthew 24, where Jesus says “But concerning that day and hour no one knows, not even the angels of heaven, nor the Son, but the Father only.” How can an omniscient being say such a thing? If we think of omniscience as a non-propositional thought, then we can suggest that in his incarnate state, Jesus used his human brain to think. If his human brain had access to that thought, but was not able to derive propositions from it, Jesus would possess both omniscience in a qualitative sense and yet simultaneously not know about that day or hour.[v]
Stopping Infinite Hammertime
Objections that an infinite future has the same problems as an infinite past also seem inadequate. Let’s use an illustration that Thomas Aquinas used to hammer out the details. Imagine an immortal smithy who uses a hammer for his work. Over time, the hammer wears out, and he throws it into a pile and then obtains a new hammer. Such a smithy who begins his work at and never stops would never have an actually infinite number of hammers in the pile. The number of worn out hammers will always be finite but growing without limit. A smithy who has been hammering for an eternal amount of time would in fact have an actually infinite pile of hammers. A thought experiment like this shows that the concept of an infinite future, given the A-theory of time (or presentism, for that matter) does not have the same potential difficulties as the concept of an infinite past. Even under presentism, the possibility of an infinite past at least presents the potential of an infinite accumulation effect. Such a difficulty cannot even in principle exist with an infinite future alone.
Platonism vs. Reductionism
Imagine a world containing nothing but a void filled with a dark aether. The world undergoes no change – it is completely static. Can we say that such a world can have a passage of time? In other words, can there be such a thing as time without events? If not, that is the reductionist view, also known as the relational view. If so, that is the Platonist view, also known as substantivalism or absolutism with respect to time. Another way to ask this question is: “Which has logical precedence, time or events?” On the reductionist view, events are logically prior to the passage of time. Time is not an independently existing entity or structure. Given the impossibility of an infinite number of past events, and that an event requires a change in the state of affairs, a reductionist is committed to the fact that some state of affairs exists prior to the first event. Since time comes into existence at the first event, we cannot say that the initial state of affairs is temporally prior to the first event, but that it is logically prior to it. Since, on this view, time comes into existence, no reductionist can coherently state that a being b does not come into existence unless there is a prior time when bdoes not exist. Any argument against the coherence of the previous view is not an argument against Craig’s view per sebut an objection to the reductionist view of time.
Many objections to the Kalam argument implicitly do just that, yet fail to state it explicitly when they argue against Craig’s view of time.[vi] Wes Morriston holds this unstated assumption in his critiques of Craig’s argument. He writes “You might wonder how long he thinks God has existed. Since God does not begin to exist, mustn’t he have existed forever? And wouldn’t that be an actual infinite of the very sort that Craig says is impossible?” Morriston also objects that God’s choice to create a finite temporal world cannot be an eternal choice, since an eternal sufficient choice entails an eternal effect. Such arguments misunderstand the concept of “eternal” on a reductionist view of time. Instead, the word “eternal” in regards to the past should be defined as “an object o is past eternal if and only if o exists and o did not begin to exist.” Therefore, the word can mean either “temporal and infinite” or “timeless.” God is eternal in that he exists changelessly in that initial state of affairs. God is needed for creation because no deterministic being can turn a changeless state of affairs into a temporal state of affairs. An eternal sufficient cause can indeed produce a non-eternal effect if the cause can act arbitrarily. Any argument against this will either collapse into an argument against libertarian free will or into an argument against the reductionist view of time.
It is easy to imagine a divine consciousness bringing time into existence on the reductionist view. In the initial state of affairs, God exists changelessly, holding one single, static state of consciousness. God acts, changing the state of affairs, and bringing time into being as an emergent phenomenon. In such a world, God exists timelessly apart from or “before” (in a highly metaphorical sense) time, since time supervenes on events, or on changes in the state of affairs. This is how “God’s life in time, so to speak, begins with creation. Subsequent to creation, God has a past and that past has a beginning, since it began with the creation of time and the universe.”
Two Ships Passing in the Night
Suppose that the objector is not bothered by any of this. The objector holds to a Platonist view of time and argues that Craig’s view of God and time is therefore incoherent. How might the defender of Kalam respond to such an accusation?
It does seem that the idea of bringing time into existence is, or at least might be, incoherent on the Platonist view. Indeed, it is difficult for the temporal Platonist to think of any event or act as logically prior to time. All acts require time, and on the Platonist view, time is the container within which events occur. The creation of time, if it is anything, is an event. On reductionism, the creation of time is unproblematic, since time is a byproduct of events. On Platonism, the creation of time is still an event, yet time is logically prior to all events. In order to create time, time has to already exist, and so the creation of time on temporal Platonism seems incoherent. Worse, the beginning of time would itself be an event, meaning that on temporal Platonism, time has to precede time, giving us an insoluble bootstrapping problem. It seems that this is the real objection coming from the likes of Morriston and others. Objectors who take this line of argumentation fail to state that they are rejecting a reductionist view of time, and hence, their discussions with defenders such as Craig involve both sides talking past one another.
The Kalam Argument on a Platonist View
The Platonist view of time has numerous problems on its own, which themselves might shut down any temporal Platonist objections to this argument. One of them concerns the ordinary view of time. Physical time is generally defined in terms of events. One second, for example is currently defined by the International System of Units as 9,192,631,770 transitions within a cesium atom, a reductionist definition if I ever heard one. One who objects to Kalam from a temporal Platonist view must deny that this is what time really is, or at least accept that time’s metric is reductionist, even if time is not. There are still potential problems with an actually infinite past, such as an infinite regress of nested temporal intervals, even if they do not have a metric. However, this is more of a problem for temporal Platonism than it is for the temporal Platonist view of the Kalam argument.
Can a temporal Platonist use the Kalam argument? It seems so, as long as the argument is modified slightly. The premises and conclusion are fine, but we need to modify the definition of beginning to exist. We can say that on temporal Platonism, an object o begins to exist at time t if and only if o exists at t and there is no time immediately prior to tthat t exists. The idea of being timeless apart from time does not seem coherent on temporal Platonism unless one wants to abandon presentism and fall right into the jaws either of the problems with the B-theory or McTaggert’s Paradox if one wants to adopt something like the growing block view. Because of the bootstrapping problem, temporal Platonism will require time that is eternal in both directions, meaning that an argument for the finitude of the past will not establish that the past is finite, but only that the number of past events is finite. One can argue, as Richard Swinburne does, that time is undifferentiated without a metric. Without events, an infinite past does not entail an infinite number of minutes or hours. Like divine omniscience, time is qualitatively infinite without being composed of an infinite number of parts, or containing an infinite number of events.
On a temporal Platonist view, one can say that God exists temporally prior to the material world. Since there cannot be an infinite number of past events, this means that there is some first event. If all causes are temporally prior to their effects, this does no damage to the Kalam argument. One can just say that God’s cause of the universe coming into existence is the first event, and the origin of the universe is perhaps the second event. One might object that on this view, why is it that God did not create the universe sooner? This argument does not help the objector because it applies to any view which contains a Platonist view of time and a finite number of past events. Why did the first event not happen sooner? This is not an objection to the Kalam argument, but an objection to temporal Platonism, and I will leave it to the temporal Platonist to answer it. One might wonder why we need to posit God on such a view, and the answer is that without a being who possesses libertarian free will, it seems impossible to connect an infinite past that lacks events with a future that contains events. No impersonal set of conditions can do this, since no deterministic entity can be entirely quiescent and then begin to change. Simple indeterminism will also not work, since the only candidates we have for random events are decaying particles and fluctuations in the quantum vacuum. Both of them are constantly in a state of flux, and governed by probability relative to metric-based time.
Conclusion
The reductionist-Platonist distinction is one of the most essential issues to understanding Craig’s version of the Kalam Cosmological Argument. If one wants to object to this first cause argument, the objector will need to be more explicit as to whether the Platonist or reductionist view of time is being assumed in the objection. Furthermore, the objector should be giving an objection that is not simply reducible to a criticism of the other position. Most Calvinist criticisms of Molinism are not really attacks on the specific doctrine of Molinism, but are instead arguments against libertarian free will. If the Calvinist wants to give such arguments, that is fine, but let us be upfront in what the Calvinist is critiquing.
Hopefully, the preceding article was able to shine some light on issues surrounding the Kalam Cosmological Argument. The key is that those who object to Craig’s model of the Kalam argument need to state that either his view fails even under a reductionist view of time and definition of coming into being, or show that both the Platonist view of time is correct and that the temporal Platonist version of the Kalam argument also fails. Unless and until the objector does that, I think that Craig’s view is the more plausible one.
[i]William Lane Craig and J. P. Moreland, eds., The Blackwell Companion to Natural Theology (West Sussex: Wiley-Blackwell, 2012), 192.
[ii]Paraphrased, but it gets the idea.
[iii]Wes Morriston, “Must the Beginning of the Universe Have a Personal Cause?: A Critical Examination of the Kalam Cosmological Argument,” Faith and Philosophy (vol. 17, No. 2, April 2000) 151.
[iv]A similar problem arises regarding the Riemann Zeta Function. This function is supposed to give us a solution to converging sequences of fractions such as ((1/2)+(1/4)+(1/9)+(1/16). . .) Riemann then used complex analysis to extend this function even to divergent sequences. This leads to odd results, implying that (1 + 2 + 3 + 4. . . = -1/12) and also that (1 + 4 + 9 + 16. . .= 0) The Riemann Zeta Function is a very useful tool in mathematics, but it is absurd to think that these divergent sequences literally have these sums.
[v]This view of divine omniscience also might help us escape from problems that plagued Kurt Gödel and Alan Turing. Consider the proposition B: God does not believe B. One can rework the proposition to remove all direct self-reference and all indexicals, as Gödel did in his incompleteness theorem, and still wind up with a paradox. If God believes the statement, he believes a falsehood. If he does not believe the statement, he lacks a belief in a true proposition. A non-propositional account of omniscience may be of help here.
[vi]Kant himself may have failed to appreciate this distinction. In his Critique of Pure Reason, the first antinomy assumes that time is a series of differing conditions. This assumes a reductionist view of time, since temporal Platonism can contain different times with the same conditions. Kant’s antithesis that “a beginning is an existence which is preceded by a time in which the thing does not exist” itself assumes a Platonist view of time, since a reductionist account of time can make perfect sense of time beginning to exist.
