The Kalam Cosmological Argument

The Kalam Cosmological Argument Abstract We show that the Kalam Cosmological Argument as proposed by William Lane Craig is not capable of being analysed without further re-interpretation because his terms are largely undefined in a structural sense. Even with minimal re-interpretation of his terms, we show that the argument may support at least four different conclusions. In one reading, the Kalam argument implies that the cause of the Universe must itself have a cause while in another, it implies the existence of a type of physically-unrealizable multiverse. It is possible to make the Kalam argument meaningful if it is assumed that the cause is composed of two independent parts. In general, when it is valid, the Kalam argument appears to imply that the cause of the Universe is deist and therefore at odds with the idea of an uncaused creator possessing personal characteristics (the theist position). The Kalam argument can also be shown to be sound for two independent co-creators. 1. preliminaries When a Muslim refers to god, he or she means Allah, the god of Muhammad. What does a follower of Judaism or Christianity mean when he or she uses the same term? It is rather more difficult to decide. The first five books of the Bible (the Pentateuch), when read as documents, give us several concepts of god, most notably, El, the god of Abraham and YHWH, the god of Moses. These are translated into English as god and lord respectively (quite specifically in small capitals). The consort of El and, later of YHWH, was Asherah. At some point in Jewish history, these two main gods appear to have been merged to create a single god (Exodus 6 : 2 3) and Asherah was eliminated. Thus it may be the case that when a Christian speaks of god, he or she means a composite god (comprising the gods of Abraham and Moses) but bearing the single name YHWH. Further, whichever deity they have in mind, Muslims, Christians and Jews always use the term God as a proper noun when referring to it. What do atheists mean when they speak of god (in the singular) or when they use the word God as a proper noun? It is by any means not easy to determine the meaning unambiguously. If such atheists once belonged to the Jewish- 1

Christian tradition then it is probable that their idea of god is the composite YHWH of Jews and Christians. Otherwise, it is possible that god of the atheists is a synecdoche or more general figure of speech. It is probable that neither theists nor atheists of the Western tradition have any clear idea of god. That is, it is likely that theists have a vague feeling that a god should have certain loosely-defined attributes and that the atheists simply disagree. 2. introduction David Wood, a Christian apologist, in a YouTube video entitled The Problem of Evil and the Skeptic s Dilemma, lists over 20 arguments which he believes support the position of theists. Amongst these are William L. Craig s Kalam Cosmological Argument and Leibniz s Cosmological Argument. The latter is essentially the question: Why is there something rather than nothing? This has long known to be an unsatisfactory argument (based on the notion of contingency). Closer examination shows that Leibniz s question is actually quite meaningless because we do not know the salient characteristics of nothing in this context. Further, the concept of nothing is notoriously difficult define, let alone understand, requiring (apparently) the existence of a state of non-existence. Such a notion takes us into the Buddhist realm and is not normally associated with the Jewish-Christian view. In fact, all the arguments listed by David Wood are burdened by (perhaps insurmountable) difficulties. One of the problems with arguments with proceed from seemingly fundamental truths is that they have a tendency to throw up paradoxes. The researches of Gottlob Frege and Bertrand Russell, for instance, ought to convince us that it is often impossible to express an idea, even if it were true, in natural language. This was also appears to be the view of Kurt Gödel. Thus naïve set theory (which is an approximation to natural language) cannot be used as a foundation for logic because of Russell s Paradox. It so happens that the construction of a logically-consistent set theory is itself a major undertaking which has demanded the exertions of an army of mathematicians. 2

This lack of rigour (and it appears, effort) in the formulation of cosmological arguments makes them little more than a sequence of aphorisms disguised as syllogisms. In the light of the foregoing, we should expect the Kalam Cosmological Argument to fail. In this paper, we will not attempt a refutation of the Kalam Cosmological Argument because Craig s god may indeed have created the Universe, perhaps at the point of the Big Bang. Our aim, rather, is to demonstrate that the Kalam argument is highly ambiguous and implies, among other possibilities, the existence of a bipartite creator or a multiverse. 3. The Kalam Cosmological Argument A cosmological argument for the existence of a god was most recently advanced by the theologian and philosopher, William Lane Craig, and (according to Wikipedia) runs thus:- a. Whatever begins to exist has a cause; b. The universe began to exist; Therefore: c. The universe has a cause. Further, the cause is identified with a personal god which in the case of Craig is most probably the composite YHWH. We now show that this argument is ambiguous. In one interpretation, it implies that the cause cannot remain unaffected by the major premise (a). In another, if the cause is unaffected by (a) then a certain type of multiverse, rather than a universe, results. Such a multiverse is shown to be incompatible with that postulated by physicists. In order to rescue the argument, it appears necessary to postulate a bipartite YHWH, made up of two independent parts: an invariable brain and a variable body. The argument can also be meaningful if YHWH is treated as a Turing Machine. Two significant assumptions underlying the argument appear to be: 3

(i) actual infinities do not exist (to permit explicitly the existence of a finite past); (ii) past and future can be unambiguously defined with respect to the present (unlike in the General Theory of Relativity). Assumption (i) is at odds with modern mathematics in which transfinite numbers (actual infinities) are constructible objects. Moreover, a tacit assumption running through the argument and (the commentary it has necessitated) is that (iii) the cause is unconstrained; (iv) the cause does not have definable, quantifiable or realizable attributes. To illustrate Assumption (iv), we consider Craig s conclusion, which is: If the universe has a cause, then an uncaused, personal Creator of the universe exists, who sans the universe is beginningless, changeless, immaterial, timeless, spaceless and enormously powerful. This is a very troublesome assertion because we do not know the meanings of the terms beginningless, changeless, immaterial, timeless and spaceless. For instance, the supposed definition: beginningless is without a beginning is a tautology and serves no useful purpose without some sort of frame of reference. In other words, we require some conceptual structure in which beginning is well-defined or at least declared as an undefined term which, under certain rules, may be permitted to appear in propositions. Needless to say, the meaning of powerful is far too vague and woolly to analyse in the given context. We may distinguish two types of definitions: constructive and non-constructive. By a constructive definition we mean a procedure which will allow us to construct the definition from simpler elements. Further, we must be able to demonstrate that a realizable notion can be so constructed, that is, the defined object can have some sort of existence. On the other hand, a non-constructive definition in our present context means that the the notion is defined by induction and no example of it is specified. So, for instance, in order to define unbounded, we may choose concepts or 4

things which have progressively larger and larger volumes (equivalently, areas or lengths). Then, if this process were continued indefinitely, we could declare that the infinite would (for practical purposes, at least) be reached, although we might have no means of providing any actual example of the infinite. Thus we see that Craig s terms, beginningless, changeless, timeless and spaceless are difficult or impossible to define, either constructively or nonconstructively. Note that it is possible to define immaterial in a non-constructive manner but since there is an equivalence between energy and matter, we have to extend the meaning of the term to include energy as well. So Craig s personal creator must be devoid of both matter and energy. Finally, it is not clear if changeless and timeless are entirely distinct concepts. For valid definitions, therefore, whether constructive or non-constructive, we need a structure which is complex enough to sustain them. Since Craig does not supply a context for the terms he uses, we have choose a structure which will carry them. Since the terms space, time, etc. have geometrical interpretations, we now attempt to interpret the Craig s assertion geometrically. Then we see that in any of the commonly studied geometries, Euclidean, Riemannian, Bolyai-Lobachevskian, etc., an object which is beginningless, changeless, immaterial, timeless and spaceless may be taken to be an ideal point. Thus, taken collectively, these properties could serve as the definition of functional non-existence, that is, a form which exists but which is incapable of performing any function. Thus Craig, in failing to supply constructive (or non-constructive) meanings for the terms he uses, could be saying that his personal creator is enormously powerful but possesses no capacity to function. Perhaps contrary to majority opinion, the last statement is not necessarily meaningless; a consistent theory can be constructed along these lines but this very likely will not the considered satisfactory by Craig. For, any such theology is probably more consistent with deist ideas rather that theist ones. It is possible to remedy Craig s concept of a personal creator if its attributes were changed to encompass the beginning and the end and everything in between (instead of beginningless ); 5

comprehend all change (instead of changeless ); be all matter (instead of immaterial ); be all time (instead of timeless ); be all space (instead of spaceless ). Such a definition (which has its own difficulties) would take Craig towards the Hindu notion of Brahman (note: not Brahmin, a Hindu priestly caste or Brahma, a god in Hindu mythology). Thus, to sustain his own interpretation of the Christian position, Craig is forced to leave undefined the terms beginningless, changeless, immaterial, timeless and spaceless in respect of his personal creator. In summary, therefore, it is not possible to provide an analysis of the Kalam Cosmological Argument as it stands. Notwithstanding, it is still possible to examine its implications by re-interpreting one of Craig s non-existence criteria and we do this in the next section. 4. analysis of the argument For convenience, we identify Craig s personal creator with the composite god YHWH. By the foregoing, we re-interpret one of his criteria, namely, timeless, to (v) YHWH is capable of measuring time (coordinate time) in his own frame of reference and this time may or may not be related (by a single-valued transformation) to time measured in the Universe; (vi) the coordinate time measured by YHWH can be partitioned into intervals and is well-ordered (the concepts of past, present and future are uniquely defined). With this modification, consider the diagram below which is a graphical representation of the Kalam Cosmological Argument. 6

past B 0 time measured by YHWH future expansion envelope Big Bang time measured by a physical clock expansion envelope The Kalam Argument: YHWH begins measuring time, denoted by B, in his own frame of reference from B α < B 0 onwards using any reliably accurate analogue of a physical clock. At the point B 0 of YHWH s time, he causes the Big Bang. This is also the beginning of physical time and if we denote the nominal physical time of the Big Bang by T 0, then we may set B 0 T 0. By the symbol, we mean that the two instants are linked in some unknown manner. YHWH then continues to keep a record of his coordinate time. First we accept the attributes Craig ascribes to the composite YHWH as a small subset of the total number and call this S, the state of YHWH. That is, The State of YHWH: The state of YHWH, denoted by S, is labelled by undefined attributes including, amongst very many others, beginningless, changeless, immaterial, timeless, spaceless and enormously powerful. In order for the Kalam argument to be consistent, any interpretation of YHWH (as the uncaused cause of the Universe) must avoid being affected by Craig s premise (a). There are at least four possible interpretations of the Kalam Cosmological Argument. First Interpretation: The state of YHWH at time B α is S (by virtue of the 7

fundamental hypothesis). In the time interval B α B < B 0, YHWH s persists in the state S and he does not create any Universes. At time B 0, YHWH creates the Universe. We ask: what is YHWH s state at B 0? If YHWH s state at B 0 is S then why were no Universes created in the interval B α B < B 0 when his state was also S? Therefore, we may reasonably conclude that there was a change in YHWH s state. In other words, we may say that S S or that the state S has been transformed into the state S. The state S began to exist precisely at time B 0. By the major premise (a), it must have a cause. What was that cause? Thus by premise (a), either there exists another cause (perhaps another god) or YHWH caused the change in his own state. In the first possibility, YHWH is no longer uncaused and hence, other objections, such as infinite regress, also arise. We deal with the second possibility in the Fourth Interpretation below. That is, we will construct a mechanism by which YHWH might himself have achieved the transformation S S. For now, we are concerned with the cause of the change in YHWH s from S to S. We assume that it has its origin at a point B 1 = B 0 1 and is of such a small magnitude that it is insensible to YHWH. We wish to show that a second god need not be postulated. So let the magnitude of this cause be x. We assume that at time B 0, x = x 0 = 1 so that the cause acts with unit force on YHWH to initiate the Big Bang. At the point B 0 (1 1/2 n ), let x = x n = 1/2 n. Thus in the vicinity of the point B 1, n is of such a magnitude that YHWH would be unable to detect it. Further, if the origin of the cause is undetectable, we, along with YHWH, may reasonably claim that the cause is uncaused. Hence there is no need to stipulate another creator or god. Therefore, to rescue the Kalam argument in this interpretation, we have to place a limit on YHWH s capacity to detect or measure vanishingly small magnitudes. Finally, what is the state of YHWH in the time B > B 0? Our question is: does he return to the state S, remain in the state S or enter another state S? In 8

particular, if he remains in state S, he may be caused (or compelled in some way) to create other Universes. Contrariwise, if he returns to state S, a change at a particular instant of YHWH s proper time has taken place and, by Craig s premise (a), it must have a cause. What could be that cause? Second Interpretation: In this interpretation, we may assume that creation of the Universe is a function integral to the very constitution of YHWH. That is to say, if we accept that YHWH s state is S, then S includes the attribute: creator of the Universe at time B 0. So, in order to avoid the application of premise (a), we accept that the creation of the Universe is pre-determined by its inclusion in S. Therefore, when the Universe is created at B 0, no cause can be ascribed to YHWH as creator because S does not change. This in turn implies that the existence of the Universe is a necessary, not contingent, fact depending solely on the existence of YHWH in the state S. For if the Universe had not been created at time B 0 then the definition of S is defective and so the existence of YHWH then becomes uncertain. More generally, every action performed, being performed or to be performed by YHWH must be represented in S and must be part of his definition so as to avoid the application of the major premise (a). Since YHWH and the Universe (as well as the results of all his actions) are bound together, he is absolutely constrained and cannot be regarded as a free agent. It is obvious that an incompatibility arises by virtue of Assumption (iii). Third Interpretation: In this third interpretation, the state S of YHWH is absolutely constant. Thus, since he created the Universe at time B 0, he must have created and continues to create Universes at every instant of his coordinate time B. Therefore the number of Universes created and being created by YHWH is ℶ 1, the transfinite number representing the cardinality (size) of the continuum (assuming the continuum hypothesis). This implies that the number of Universes is not denumerable, that is, it cannot be counted using integer or rational numbers. If ℵ 0 represents the cardinality of the set of integer numbers, then by the continuum hypothesis, ℶ 1 = 2 ℵ 0 9

So the number of Universes created by YHWH is of a different order of infinity (so to speak) from that postulated by physicists, for whom the number of universes (comprising the multiverse) is denumerable. Fourth Interpretation: We revisit the first interpretation and consider the second possibility we noted there: that YHWH caused himself to create the Universe while being subject to Craig s premise (a). We now assume that YHWH is composed of two parts. The first part is an intelligence or brain, defined by the set of properties, S 1, which we postulate to be absolutely invariable. The second part of YHWH is a body which is defined by the set of properties S 2 and we allow this to vary and therefore be subject to premise (a). Finally, we assume that the YHWH s body carries out the instructions which are pre-programmed to be transmitted to it from the brain. We set S = S 1 + S 2 to be consistent with the definition of the state of YHWH in the First Interpretation. We now posit that S 1, the set of properties defining the brain of YHWH, contains an absolutely constant but very large number of instructions which it transmits to his body during the passage of his coordinate time, B. Thus the god YHWH has no control over the contents of his brain and his body is constrained unconditionally to follow any instruction it receives. Let there be M instructions in S 1 of which M c (with M c M) may be considered elementary. An example of the latter may be the instruction: initiate the Big Bang. By Craig s condition (i), M cannot be a transfinite (infinite) number. The elementary instructions stored in the brain of YHWH can then be used in more complex instructions which it then transmits to his brain. In particular, we are interested in conditional instructions, the simplest of these having the form: if T then execute X; otherwise execute Y. In this, Y may be the instruction: do nothing. We further stipulate that T varies with the proper time of YHWH and X, Y are elementary instructions (numbered among the M). Since there are M c elementary instructions, the number of simple condition instructions (of the aforementioned type) is M c (M c 1). For each valid condition, T, the total number of possible conditional instructions, c, to which YHWH s 10

body will be subject is M c M c (M c 1) Let I be the set of simple conditional instructions, containing c elements. Then I is a subset of S 1. We assume, in particular, that the instruction to create the Universe at a precise time, B 0, is an element of I. A general problem now presents itself: if S 1 contains a very large but finite number of instructions then it is reasonably certain that there will exist problems that YHWH s brain could not solve. This is the reason why we have not taken the simpler route and modelled it on a Turing machine. Recall that theoretical limitations are a fundamental feature of the Turing machine (such a limitation is Hilbert s Decision Problem). We will now outline the means by which YHWH may avoid such a problem. With the foregoing in mind, we examine the state of YHWH at time B 0, the point in his proper time at which the Big Bang is initiated. As we stipulated earlier, it is only YHWH s body which acts and is thus affected by Craig s premise (a). So, since S 1 is held absolutely constant, we allow S 2 change to the state S 2 at B 0. By the application of premise (a), the transformation S 2 S 2 has a cause but this cause is just one of the elements of I, perhaps in combination with other elements of S 1, but no other. That is to say, since the set of simple conditional instructions, I, and the general set of instructions, S 1, are both fixed, they are immune to premise (a); in particular, no other god need be involved. We see that YHWH s actions (through his body ) are controlled absolutely by his programming via the invariable set conditional instructions, I, and the state of his brain, S 1. This contradicts Assumption (iii) but the effect of this contradiction can be minimized by making M and M c very large. Then c, the number of elements in I, will also be very large and YHWH will, for practical purposes, have effective free will. Of course, in the limit, YHWH will inevitably encounter a problem which the program contained his brain cannot solve, but the probability of this eventuality is vanishingly small. 5. Conclusion We have shown that the Kalam Cosmological Argument is ambiguous by showing that it can be interpreted in at least four different ways. The chief difficulty 11

with the argument is the lack of a sufficiently complex structure through which the terms used in the argument may be adequately defined. In its native form, with undefined terms, the argument can only be analysed if at one of the terms (namely, time) is re-interpreted. Even with this re-interpretation, it is not possible to reach an unambiguous conclusion. It is possible to remove some of this ambiguity if we postulate a bipartite cause of the Universe. Such a resolution is likely to run counter to the theist view of the cause of the Universe and instead support deism. If, on the other hand, we go a step further and postulate a pair of co-creators, the Kalam argument can be made sound. In doing this, we are essentially using a structure complex enough to sustain the idea that a change must have a cause. For, with at least two co-creators, we may define a means of exchange between them which will make causation a self-contained process shared by the pair. Further, such a pair of co-creators can have free-will, unlike a single creator. The actions of a pair of co-creators may most simply be represented as a coupled system of linear ordinary differential equations. The nature of the interaction between them can then be identified and studied methodically. 12