The argument in my article on the cosmological argument follows the usual pattern. Hence, we can discuss it by considering the usual four headings: focus, rationale, temporality, modality and closure. Finally, I will discuss my responses to several objections.
The focus of my argument is broader than any that we have seen. I assume that every fact of a certain kind has a cause. By "fact", I mean a concrete part of the world, like an event, process, condition or state of affairs. Facts are the kinds of things that make declarative sentences, like "Caesar has died", true. Facts enter into cause and effect relations with other facts.
We can distinguish between "types" and "tokens", to use terms introduced into philosophy by C. S. Peirce. Each individual penny is a token, and the property or kind of penny-hood is a type. Each penny is a token of one and the same type, which is multiply realized in different places at different times. My argument concerns fact-tokens, not fact-types. For example, we can use the phrases "that Caesar died", "Caesar's dying" or "Caesar's death" to refer either to a fact-token, the particular, actual occurrence that constituted the ending of Caesar's life, or to a fact-type, the kind of occurence in which the individual Caesar dies. Thus, the token of Caesar's death includes the actual thrust of Brutus's blade, and that very token would not have existed had Caesar died in some other way, of old age, for example. In contrast, the type, Caesar's dying, could have been realized in many different ways, including the actual assassination and the non-actual dying in old age. My argument focusses on the actual token I call the cosmos. This token includes all of the wholly contingent fact-tokens in the world as parts -- had the slightest detail been different anywhere at any time, the particular token I am calling 'the cosmos'would not have existed. It would instead be replaced by a different token. The fact-type, the existing of a universe, could have been realized by many different possible tokens. My argument focusses on the particular token that actually realized this type.
If we assume that every fact has a cause, then there could exist no uncaused fact. Instead, I assume that every wholly contingent fact has a cause. Facts that are partly or wholly necessary need not, and indeed cannot, be caused. Since facts are concrete, actual things, we can talk meaningfully about the parts of a fact. Consequently, I use the principles of the mathematical theory of mereology, the theory of the part-whole relation. The most important principle of mereology is the aggregation axiom. This axiom states that, if there are any things of kind K, then there is such a thing as the aggregate of all the K's. For example, there is such a thing as water, so we can talk meaningfully about the aggregate or "mereological sum" of all the world's water.
I assume that an aggregate cannot exist unless all of its parts exist. This means that a necessary aggregate must have only necessary parts, since if an aggregate has a contingent part, then that part might not exist, which would mean that the aggregate would not exist either. Aggregates are not like bodies or institutions, which can go on existing without the same parts. However, a contingent aggregate can have necessary parts. If we glue together some contingent and necessary facts, the resulting aggregate is contingent as a whole.
I assume that an absolutely necessary fact cannot be caused. If a fact is caused, then all of its parts are caused. So, any fact that contains a necessary fact cannot be caused. Therefore, it is only wholly contingent facts that can be caused. A wholly contingent fact is a fact that has only contingent parts.
I argue that the causal principle should be thought of as empirically supported. We find that a wide variety of facts are caused. This includes conditions both small and large (from atomic physics to astronomy and cosmology), both recent and ancient, both transient and long-lasting. We even discover that many everlasting conditions have causes. For example, the fact that the physical world is approximately Newtonian is caused by certain features of general relativity. Similarly, the ideal gas laws are caused by the underlying dynamics of the gas molecules, and Brownian motion is caused by atomic collisions. In these cases, the effects are not limited to a particular region of space or time. Thus, we have good empirical reason to believe that every fact that can be caused, that is, every wholly contingent fact, has a cause.
In my article, I use the rationale for a first cause that was first developed by ibn Sina and also created, independently, I think, by Leibniz. This is the aggregative rationale that we discussed last week. We use the aggregation axiom to construct the aggregate of all wholly contingent, actual facts, which I call C. I prove that C is itself wholly contingent, since there is no way that any necessary parts could be included in it. Consequently, my causal principle entails that C itself must have a cause. I assume that causes and effects are always separate things, with no overlap or common parts. Therefore, the cause of C must have no wholly contingent parts, or else it would overlap with C. But every contingent thing has a wholly contingent part (whatever is left over after all the necessary parts have been deleted), so the cause of C must be a necessary fact.
I try to build into my argument no assumption whatsoever about the relationship between causation and time. There are several reasons for this. The main reason is that I want to avoid introducing superfluous assumptions. In addition, there is a good reason for wanting to avoid the synchronic conception of causation. As we saw in analyzing Adler, the synchronic versions of the cosmological arguments assume that there is no such thing as inertia, and this assumption seems implausible. The fact that the universe has existed in the past does seem to provide some kind of causal explanation of its present existence.
We also have some reason for resisting a commitment to the diachronic conception. As we have seen, if time itself had a beginning, and the beginning of the universe is simultaneous with the beginning of time, then it is difficult to find a moment at which God could cause the universe to begin. I don't think this is an insuperable problem, but it does cause some awkwardness. If we assume a diachronic model of causation, we must either assume that there was some sort of "time before time", or we must assume that God's act of creating was instantaneous, even though all physical states have a positive duration (take up some interval of time). In contrast, if we reject the diachronic model, we can leave open the possibility that the temporal universe had a timeless. atemporal cause.
The diachronic model includes a requirement that causes always be earlier in time than their effects. This requirement seems less compelling if we entertain the possibility that causation is the fundamental reality, and that space and time are derivative relations, depending on the underlying network of causal connections. Instead of saying that causes must precede their effects, we can say that the relation of "earlier-than", where it is appropriate, must correspond with the "cause-effect" relation. Similarly, instead of saying that there can be no action (causation) at a distance, we can instead define distance as that at which there is no action. In other words, what makes two events close in space is the existence of direct causal links between their parts.
If we take such an approach toward explaining the existence of space and time,we can explain why causes are typically earlier than their effects (at least, in our experience, which is limited to things locatable in space and time). This explanation, however, does not rule out the possibility of cause-efffect connections that have no temporal dimension whatsoever, as in timeless causes of temporal reality.
If we conclude that the first cause is a necessary fact and that every other fact is caused by the first cause, and we assume that causes always necessitate their effects, we must conclude that every fact is necessary, that there are no contingent facts in the world. This seems clearly wrong. Consequently, I will argue that causes do not typically necessitate their effects. Instead, the relation between causes and effects is much weaker: causes make their effects probable, not necessary.
Our actual practices, both in everyday life and in the sciences, confirm this position. We rarely if ever discover a condition that is followed invariably by some other specific condition. We are content if we can find some condition that makes its effect very likely. For example, it was determined that the fragility in cold temperatures of the O-ring was part of the cause of the Challenger accident. This does not depend on our being able to reproduce conditions that would, in every case, lead to an identical explosion. It is enough that it is very probable that a O-ring would crack under the sort of conditions experienced by the Challenger.
Similarly, in the social and biological sciences, causal connections are almost always statistical in nature. We know that tobacco causes lung cancer, even if we cannot predict which smokers will get cancer at which times. The strong probabilistic relation is enough.
In the theory of quantum mechanics, we have good reason to believe that the causes of quantum events do not necessitate their effects. Standard quantum mechanics is indeterministic in its formulation: the results of interactions with quantum systems are assigned probabilities between 0 and 1. We know that if there are any deterministic, necessitating "hidden variables" that are omitted from the standard QM model, these hidden variables must be very wierd, capable of very strong effects instantaneously at great distances. (Bell's theorem states that any deterministic hidden variable must be "non-local".)
Consequently, I assume that the connection between the first cause and the cosmos is an indeterministic one. The first cause need not have caused this universe, nor perhaps any universe at all. There is no explanation of why it caused this one rather than another, if by "explanation" we mean a cause that necessitated that this universe rather than another should exist. Hence, I am rejecting the Principle of Sufficient Reason, in its strictest version, where 'sufficient reason' means 'necessitating reason'. It may be that each of the immediate effects of the first cause were highly probable, and in that sense we can give an adequate reason for them, but none were strictly necessary.
To begin with, I must move from a necessary fact to a necessary being. My first cause is not God, but rather a fact. Every fact that we are familiar with involves both one or more beings, and one or more properties or relations that characterize those beings. Thus, the fact that Socrates was snub-nosed involves both Socrates and the property of being snub-nosed, and the fact that Plato was the teacher of Aristotle involves the beings Plato and Aristotle and the relation of being-the-teacher-of. We may presume that the First Cause also involves one or more beings as well. Since this fact is necessary, and whenever any fact is actual, the beings involved in that fact must actually exist, it follows that the being or beings involved in the first cause must exist necessarily.
If there are several necessary beings, they are strongly inseparable. None can exist without the others' existing. Consequently, they form a closeknit system. Call this necessarily existing system 'God'. God one or more properties in that primordial fact. These properties are causally fundamental -- any other properties that God or any other beings may have are caused by God's having these properties in the first cause. I call the causally fundamental properties of a thing its attributes. Hence, God has attributes, and God has these attributes of necessity.
Next, I argue that all of God's attributes are immeasurable. This argument is based on the feeling that measurability entails contingency. If a property is measurable, then its value falls somewhere on a continuous spectrum. This means that it makes sense to consider arbitarily small variations in this value. Where arbitrarily small variations are conceivable, it seems reasonable to conclude that some such variations are really possible. Hence, a measurable attribute could be slightly more or less, for some sufficiently small increment. This means that no measurable attribute could be necessary. Since God's attributes are necessary, they must all be immeasurable.
If God's attributes are immeasurable, then God cannot be located in space and time, nor can God be any kind of physical object. Anything located in space or time has measurable attributes, since spatiotemporal location is always a causally fundamental property, and spatiotemporal location is always measurable. This means that the first cause cannot be a fact about matter, since some of the attributes of matter are measurable.
Hume argues that we can reasonably infer that the world has a cause only if we observe a large number of worlds and find causes in each case. I argue, in response, that all we need to do is find one category of things, in this case, wholly contingent facts, to which the world belongs and for which we have good empirical confirmation of the fact that things in this category have causes. In applying the general causal principle to the world, we are applying it to a novel situation, but we do this all the time. The skeptic owes us a special reason for doubting that the world has a cause.
William Rowe has argued that the principle of sufficient reason can be shown to be false. Rowe argues that the existence of positive contingent facts is itself a contingent fact. No causal explanation of this fact is possible, since the explanation would have to be either necessary or contingent. If it were necessary, then it would be a necessary and not a contingent fact that there are contingent facts. If it were contingent, then it would be part of what needs to be explained, namely, that there are contingent facts.
My response to Rowe's objection involves two elements. First, I use a principle of causation, and not the Principle of Sufficient Reason. In my view, causes do not necessitate their effects. Thus, it is possible for a necessary fact to cause a contingent fact. Second, it is fact-tokens and not truths that are caused. The truth, that there are contingent facts, is not itself a fact. Instead, it is a proposition that is made true by any one of a large number of contingent facts. It is these facts, and not the true proposition, that are caused.
Another interesting problem was raised by James Ross. Ross points to the difficulty of causally explaining the contingent fact that God caused the world. If we say that God caused that God caused the world, we begin a slide down an infinite regress, since this new fact is also contingent and hence in need of explanation. My response here turns on the fact that it is only wholly contingent facts that need to be caused. The fact that God caused the world is a mixed fact, in part necessary (since it includes God's existence) and in part wholly contingent (since it includes the existence of the world). The mixed fact is not caused. Its wholly contingent part is simply the world, which is indeed caused (by God).
The most serious objection to my version of the cosmological argument points to one anomalous feature of the world. In general, contingent facts have contingent causes. The world cannot have a contingent cause, since every contingent fact overlaps it. Since the world is an exception to one rule, that wholly contingent facts have contingent causes, there seems to be some reason to believe that it may be an exception to a very similar rule, namely, that wholly contingent facts have causes of some kind.
This objection involves thinking of the causal principle as a defeasible rule. A defeasible rule is one that generates a presumption in favor of a conclusion, but a presumption that is rebuttable in light of additional information. For example, the law includes a defeasible rule that every witness is truthful. Unless some positive evidence can be provided to impeach the veracity of witness, there is a presumption that everything the witness testifies to having seen is truthful. Similarly, we might take the success of finding causes in so many domains as providing a basis for a defeasible rule that entitles us to assume that any given fact has a cause.
I think that an adequate answer to this objection is not easy to give. It involves digging deeper in the the very nature of causation. In particular, to answer the objection, we must acquire a fuller understanding of the asymmetry of the causal relation: what makes the relation of cause to effect different from the relation of effect to cause. In light of my own work on the nature of causation, I have a proposal for explaining the asymmetry of causation that is relevant to the present objection. I propose that, at the level of tokens, an effect necessitates its cause, but a cause does not necessitate its effect. Thus, the effect-to-cause relation is one of asymmetric necessitation.
I have several independent grounds for advancing this proposal. I will mention just two of them. First, it seems to correspond to an intuitively plausible account of the identity-conditions for fact-tokens. If the causes that led to Caesar's death had varied in any way from their actual course, then Caesar would undoubtedly have died in the course of time, but the particular fact-token that is the death of Caesar would not have existed. Instead, Caesar's dying would have been realized by some other, numerically distinct token. In contrast, the very same token could have existed even if the subsequent course of events had taken a different turn. The causes of a token are essential to its identity -- its effects are not. One and the same token fact cannot have had different causes than those it actually had, but it could very well have had different effects.
Second, this proposal corresponds closely to our view of the fixity of the past and the openness of the future. In our present situation, it does not make sense to deliberate about how to influence the past (even parts of the past of which we are ignorant), since our present situation-token necessitates all of the situation-tokens in its own causal past. In contrast, it does make sense to deliberate about the future, since there a number of distinct futures whose existence is compatible with the existence of our present situation.
If we accept this proposal, we can adopt as a defeasible rule the very simple principle that, normally, facts have causes. We can then infer two further things. First, no necessary or mixed fact can be caused, since a necessary fact is necessitated by any other fact, and so it cannot asymmetrically necessitate another fact. Any fact that is not wholly contingent must be an exception to the causal principle. Second, any fact that is minimally contingent must have a cause that is necessary. (A minimally contingent fact is a wholly contingent fact that necessitates only necessary facts.) Consequently, we can explain why the world does not have a contingent cause. The world is no longer anomalous, an exception to the general principle. Instead, it fits the general pattern exactly: every wholly contingent fact has a cause that is more necessary than it. If the world did not have a cause that is necessary, this would constitute a breaking of the fundamental pattern. The inference to a first cause is simply the result of pushing our ordinary practice of causal inference to the ultimate limit.