LECTURE #10: Metaphysics and Epistemology of Causation


A Revised Version of My Argument

Do Effects Necessitate Their Causes?

Do Causes Necessitate Their Effects?

Can Timeless Facts Cause Time-Bound Effects?

How do We Know the Principle of Causation?

A Revised Version of My Argument

As I argued last week, the sort of argument from contingency that I have tried to carry out depends in the end on a particular view of the asymmetry of causation, namely, that effects necessitate their causes (where both effects and causes are considered as tokens rather than as types). If we add such a principle to our set of assumptions, it is possible to construct an argument for the existence of a necessary first cause that is different in several respects from the one I gave in my 1997 paper. Here's a revised version of the argument:

  1. Assume that there is at least one contingent fact.
  2. This fact must have a wholly contingent part (see my paper). Let's call this part x.
  3. Normally, a fact has a cause (the defeasible causal principle).
  4. So, x has a cause. (from 3). If this cause is not wholly contingent, then it has a part that is a necessary cause of x. So, assume that this cause of x is wholly contingent.
  5. Since x has at least one wholly contingent cause, there is such a thing as the sum or aggregate of all the wholly contingent parts of causes of x. Call this BC(x), for the "backward cone of x".
  6. We may presume that BC(x) has a cause (by pinciple 3). Call this cause F.
  7. Since F is a cause of BC(x), and BC(x) includes at least one cause of x, F is a cause of x.
  8. If F were contingent, then it would overlap with BC(x), since it would have a wholly contingent part that is part of a cause of x.
  9. Causes and effects do not overlap.
  10. Therefore, F is a necessary fact.
  11. If F had a cause, G, then G would not necessitate F. But, since F is necessary, every fact necessitates it. So, F is uncaused.
This version has two advantages over the original:

Here's how we can show that BC(x) is minimally contingent. Let's say that a fact y is minimally contingent just in case it is wholly contingent, and it necessitates only necessary facts (that is, it does not necessitate any separate, contingent facts). Suppose BC(x) were not minimally contingent. Then there would be a wholly contingent fact, z, such that BC(x) and z do not overlap and BC(x) necessitates z. If asymmetric necessitation and causal order are exactly the same thing, this would mean that z was part of some cause of part of BC(x). But then z would be part of some cause of x itself, and so z would have to be part of BC(x), which is impossible. Hence, there is no contingent fact that is strictly more necessary than BC(x). Therefore, we should expect, if BC(x) fits the general pattern, that BC(x) would have a cause that is absolutely necessary.

This model of causal asymmetry breaks the stalemate that would otherwise stymie the cosmological argument. When we reach BC(x), we have reached a fact that cannot have a contingent cause. We are thus pulled in two directions: we might think that since it cannot have a contingent cause, and facts typically do have contingent causes, that there is reason to think that BC(x) has no fact at all. Simultaneously, since most facts do have causes of some kind, and BC(x) cannot have a contingent cause, there is reason to think that BC(x) must have a necessary cause. The principle of causal asymmetry breaks the stalemate. If BC(x) is going to fit the general pattern (being caused by something more necessary), then it must have a cause that is more necessary than it, which must be a necessary cause. The fact that BC(x) does not have a contingent cause is no longer surprising: it is just what we would expect. What would be surprising would be for something minimally contingent like BC(x) to have a contingent cause.

This means that the question of the nature of causal asymmetry is a crucial one for the cosmological argument. In the next two sections, I will consider some reasons for adopting asymmetric necessitation as the correct model of causal asymmetry.

Do Effects Necessitate Their Causes?

In suggesting that effects necessitate their causes, I am talking about necessitation at the level of tokens, not types. For example, the particular event-token that was Caesar's death necessitates the existence of all of its token-causes, including the particular event of Brutus's knife-thrust. This does not mean that the type death-of-Caesar necessitates the type stabbing-by-Brutus. Caesar could have died in many different ways, only a few of which include a knife thrust on the part of Brutus. Nonetheless, the particular token-event that is Caesar's actual death could not have been had the particular token that was Brutus's knife-thrust had not preceded it.

I will mention here three reasons for thinking that effects do necessitate their causes. First, there is the phenomenon of the fixity of the past. We do not deliberate about the past, or consider how we may influence it. We do not do so even when we are ignorant about the past. Even if I do not know who won yesterday's sea battle, I know that it is too late now for me to do anything about it. This suggests that the particular token that is my present situation necessitates all of its causal antecedents, even those that are unknown to me. There are not two different possible worlds containing this present situation, in one of which the battle is won, and in the other the battle is lost. Hence, any action I take in the present situation cannot possibly affect which outcome yesterday's battle has.

The past is not absolutely necessary. If yesterday's battle was won, this does not mean that it could not have been lost. It simply means that there is no way to combine our present situation with a situation in which yesterday's battle was lost. The outcome of yesterday's battle is relatively necessary: given the existence of the present situation, the existence of the outcome is necessary.

A second reason for believing that effects necessitate their causes is that this provides us with an account of what causal asymmetry is. We can distinguish between the cause-effect and the effect-cause relations: effects necessitate their causes, not vice versa. We could instead treat causal asymmetry as a brute, unexplained primitive, but this should be avoided, if possible. Alternatively, we could use the asymmetry of time to determine the direction of causation: causes always precede their effects in time. There are two problems with this temporal model. First, temporal asymmetry is no less mysterious than causal asymmetry, so we will have made little progress. I would argue that it is causal asymmetry that explains temporal asymmetry, and not vice versa. In fact, I would argue for a causal theory of both space and time, which is possible only if we do not use temporal relations in the specification of causation. Second, it would be rash to assume that all causes precede their effects in time. As I will argue later, there seem to be such things as timeless causes, that are not located in time at all. Moreoever, simultaneous causation does not seem to be impossible. Finally, the idea that in some special cases, the cause might actually be later than its effect, does not seem to be absurd. We can imagine cases of time travel, or of faster-than-light signals, that would break the usual relationship between time and causation, and these imagined situations do not seem to be intrinsically impossible.

A third reason for accepting the postulate that effects necessitate their causes concerns the identity-conditions for event-tokens. If tokens necessitate their causes, then we can specify the individual essences of tokens. That is, we can give a set of conditions that enables us to decide when one token is identical to another, and when we have two, numerically distinct tokens. The conditions would involve the following: first, we would specify the type (the intrinsic qualities) of the token. Then, we would do the same for all of the parts of the token. Finally, we specify the network of causes of the token and its parts The identity of each of these cause-tokens is specified in exactly the same way, until we reach, in the end, the uncaused first cause. This enables us to decide when two tokens are identical. If they have the same types, the same parts, and the same causes, then they are identical; otherwise, they are not the same, no matter how similar they may be.

Do Causes Necessitate Their Effects?

This issue we have confronted many times before, in considering the cosmological argument from Plato through Aquinas. I have labelled this issue "modality". Some, including al-Farabi and ibn Sina, have clearly endorsed the thesis that causes necessitate their effects. This thesis also seems to be implicit in the principle of sufficient reason. If a cause does not necessitate its effect, then it does not provide a truly suficient reason for it, since we could still ask why, in this case, the cause was followed by its effect.

Nonetheless, I will argue that causes do not typically necessitate their effects. In fact, I am inclined to think that they never do. There are four reasons for this conviction. First, if causes necessitate their effects, and effects likewise necessitate their causes, then we no longer have an account of the asymmetry of causation. In addition, it is difficult to see how we could maintain the idea that causes and effects are separate existences, if they mutually imply each other.

Second, if we supposed that causes necessitated their effects, then we would be led to an inflation of causes. For example, suppose there is an explosion in Welch hall that is caused by the presence of flammable gas, oxygen and a spark. These three conditions do not necessitate the explosion: in addition, there are infinitely many negative conditions that must be specified. For example, the explosion would not have happened had there been fire extinguisher foam in the lab. Similarly, if the hall had been full of water, the explosion would have been prevented. If causes necessitate their effects, then the cause of the explosion must include the absence of fire extinguishing foam, the absence of water, and the absence of infinitely many other conditions. This point does not depend on rejecting determinism. Even if the world were deterministic, so that there was a sufficient condition for every event, we could still say that causes do not necessitate their effects. We could include only the positive facts within the cause, omitting all of the mererly negative conditions that would have to be added to construct a sufficient condition.

Third, there are a number of thought experiments that suggest that causation is possible without necessitation. For example, J. L. Mackie, in The Cement of the Universe, describes a vending machine that indeterministically produces a candy bar when a quarter is inserted. A candy bar is never produced except when a coin is inserted. However, when a coin is inserted, a candy bar is not always produced. Nonetheless, Mackie argues that we would accept that, when a bar is actually produced, the production of the bar is caused by the insertion of the quarter. This fact does not by itself settle the question at hand, since we are interested in whether token-causes necessitate their token-effects, and Mackie's thought experiments concerns types (bar-production, coin-insertion), not tokens. However, if the relationship between types can be indeterministic, there seems little reason to deny that the same thing is possible between tokens. Even if individual tokens of coin-insertion did not necessitate individual tokens of bar-production, we would still be inclined to think that some tokens of coin-insertion caused corresponding tokens of bar-production, when the insertion is in fact followed by the production of a bar.

Fourth, there is some evidence that our world is indeterministic. If the world is indeterministic (at the level of tokens as well as types), and yet there are cause and effect relations, then causes cannot necessitate their effects. There are two reasons for thinking that the world is indeterministic. First, if the world were deterministic, then all deliberation would illusory. Deliberation is always between real options, real possibilities. In making a decision, I must assume that the options I am considering are real possibilities, given the actual state of the world, including my own state (psychological and physiological). If determinism is true, then in every case, there is only one possibility for action. All other options are excluded by the present state of the universe, including my own state of mind and character.

Determinists would argue that deliberation is still significant, since deliberation and decision can themselves be part of the process that causally determines our actions. However, the issue is not that of the efficacy of deliberation, but of its veridicality (its correspondence with reality). If determinism is true, then a key distinction, without which all deliberation would be impossible, namely, the distinction between what is already fixed and settled, and what is still "up for grabs", is an illusory and empty distinction. Everything is already fixed -- the future every bit as much as the past. We do not know everything about the future, but we do not know everything about the past either. The determinist has great difficulty explaining why it is reasonable to deliberate about the future but irrational to deliberate about the past. The determinist could reply that it is impossible to influence the past, since the causal order always agrees with the temporal order. However, this only moves the problem back a step. The determinist also has great difficulty explaining the asymmetry of time, since a deterministic universe is typically time-reversible. If anything, determinism would seem to imply that it would make more sense to try to change the past than the future, since the future is determined, given the present, but the determinist can leave open the possibility that the present does not determine a unique past.

A second reason for rejecting determinism concerns moral responsibility. Peter van Inwagen and Ted Warfield have fashioned a strong argument for the incompatibility of moral responsibility and determinism. This argument involves just two premises. First, I cannot be responsible for the initial state of the universe, nor for the laws of the universe. Second, if I am not responsible for A, and A necessitates B, then I am not responsible for B. If determinism is true, then all of my actions are necessitated by the initial state of the universe. Hence, if determinism were true, then I would not be responsible for any of my actions.

In this case, there are a number of well-known responses by the compatibilist (one who believes that determinism and responsibility are compatible). For reasons of time, we will have to leave this debate to one side.

If we reject the thesis that causes necessitate their effects, what can we say about the relationship between causes and effects? We could insist that causes make their effects very probable. In fact, we can come very close to the necessitation thesis, by requiring that the conditional probability of an effect, given its cause, is equal to 1. A probability equal to 1 is not the same thing as necessity, since events of probability zero can and do happen. For example, if we had a wheel, and we let each point on the wheel's perimeter correspond to some unique real number between 0 and 1, and we spun a perfectly precise pointer in the center, the probability that the pointer will end up pointing at an irrational number is 1, while the probability that it will point at a rational number is 0, despite the fact that there are infinitely many rational numbers at which the pointer could stop.

Let us say that an event is weakly explainable if it has a cause such that the probability of the event, conditional on this cause, is equal to 1. We could then consider the thesis of almost-determinism. Almost-determinism is the thesis that almost all events are weakly explainable. This would give us a very predictable world, practically indistinguishable from a deterministic world. It seems that the thesis of almost-determinist gives the determinist all he or she can and should want.

On a related point, it is important to realize that indeterminism is not incompatible with the thesis that everything that happens is directly and meticulously under God's control. From my perspective, it is a mistake to think that God's decrees cause the corresponding created fact. The relationship between decree and fact is too intimate to count as a causal connection. It would be better to say that the decree and the created fact are two aspects of the same underlying reality. If the world is indeterministic, and God's control is complete, then it is God's decrees that are contingent, not necessitated by God's nature and previous decrees.

As we shall see, contingency can enter the world in two ways. First, the divine decrees may themselves be contingent, undetermined by God's nature and prior decrees. Second, some of the divine decrees may stipulate that there be non-necessitating, "secondary" causation between created facts. When we look at van Inwagen's paper, "Chance in a World Sustained by God", we will look more closely at this possibility.


It might be helpful, before moving on to the next major question, to summarize some of the important theses that have come up in the preceding discussion and to consider the logical relationships between these theses.

Necessitation Thesis: causes necessitate their effects.

Principle of Sufficient Reason: except for self-explanatory facts, every fact has a causally prior, necessitating condition.

Determinism (type level): every temporally bound situation-token is such that the occurrence of a token of its type was necessitated by the earlier occurrence of a token of some specific type.

Determinism (token level): every temporally bound situation-token is such that that its occurrence was necessitated by the occurrence of some earlier token.

Fatalism: every fact is absolutely necessary (there are no contingent facts). Defeasible Principle of Causality: normally, facts have causes.

Strong Principle of Causality: all wholly contingent facts have causes.

One could embrace either determinism or the principle of sufficient reason without accepting the necessitation thesis, by distinguishing between the cause of a thing (which does not necessitate it) and the sum total of causally prior conditions (which does necessitate it). For example, one might want to include only positive facts in the cause, while the necessitating condition might include infinitely many negative conditions (as in the case of the Welch hall explosion). Nonetheless, most people who accept PSR or determinism also work with a necessitarian conception of causation.

One can be a determinist without accepting the PSR. For example, one might believe that the past is infinitely long, and nothing causes or determines the entire series to be as it is. In contrast, the PSR entails determinism, both at the type and the token level. Determinism does not entail fatalism, since the whole infinite regress of causally determined events might be thoroughly contingent. If we accept the PSR and also assume that any self-explanatory fact is absolutely necessary, then fatalism follows.

Can timeless facts cause timebound facts?

There are in fact two issue here: (i) does causation depend on a temporal relation, broadly conceived? and (ii) does causation depend on physical or measurable time, time along the privileged axis in our local universe? Some philosophers, such as Swinburne and Hugh Ross, clearly distinguish between time in the broad sense and physical time. For them, it is a matter of the definition of causation that the answer to the first question is, Yes. However, it is really the second question that is the crucial one in connection with the cosmological argument. If th answer to the second question is Yes, then there is no way that a first cause could be the cause of the entire physical universe, including its space-time framework, since the first cause would have to be a part of that framework in order to cause anything.

However, there are several reasons for thinking that the answer to the second question is No. First, we must admit that logical and mathematical realities, although they are certainly outside physical spacetime, can be causally efficacious. Otherwise, it would be impossible for us to have knowledge in logic and mathematics, and impossible for us to think about and refer to particular mathematical objects, like specific numbers or numerical relations.

Second, it seems plausible to suppose that space and time are themselves definable or constructible in terms of causal relations. One event is earlier than another, just in case the first is causally prior to the second, or if the first is spatially related to an event causally prior to the second. Two events are in the same spatiotemporal neighborhood just in case there are direct causal relations between the two. What we call physical or measurable time is a simple and systematic system of measurement that can be imposed on the whole network of causal relations. It is reasonable to expect that some of the causal network will lie outside of the system of measurable space-time. At least, it would be a remarkable coincidence if all of the causal network could be included in a single simple and systematic measurement system. Therefore, from this perspective, it seems reasonable to think that there might be exceptions to the general rule of causation occurring within physical spacetime.

Third, scientific realism depends on the possibility of timeless causation. Scientific realism is the thesis that we sometimes know that our scientific theories are approximately true. Philosophers and historians of science are generally agreed that the acquisition of empirical data alone does not determine which scientific theories we accept. This is known as the "indeterminacy of theory by data". In addition to data, we use considerations of simplicity, symmetry, and elegance to guide our theory choice. For example, scientists accepted Copernicus' theory despite the fact that, for over 200 years, it did not fit the astronomical data as well as Ptolemy's theory. The fit with data was less important than the fact that Copernicus's model was vastly simpler than the ramshackle, epicyle-laden Ptolemaic model.

However, if our choice of theories is guided by considerations of simplicity and elegance, then our scientific beliefs constitute knowledge only if these aesthetic preferences are a reliable guide to the truth. In order for these to be truly reliable, there must be some causal mechanism that ensures that the deep structure of the world (as describable by our theories) is, by and large, very simple, symmetrical, elegant, etc. Any such causal mechanism must be a timeless fact, since it causes the history of the world to take a certain form or shape. This is especially so in light of general relativity, which takes the form of space and time to be themselves an essential part of the structure of the world. Hence, there must be a cause that determines the spacetime structure of the universe, introducing a bias toward simplicity. Thus, there must be at least one cause that lies outside of time.

How do We Know that the Causal Principle is True?

Traditionally, there have been three answers to this question:

  1. Empirical support -- we know the principle by induction upon observed instances of caused facts.
  2. Indispensable presupposition of all empirical enquiry -- if we do not assume the causal principle, we cannot know anything on the basis of observation or induction.
  3. Natural light of reason -- we know the principle naturally and directly, without need for any further reason or evidence.
These three answers are not mutually exclusive. The strongest case for the principle of causality makes use of all three. We could take the combination of (2) and (3) to give some slight or weak support for the principle. These two considerations alone might not put us in a position to know that the causal principle is true, but they might make it reasonable for us to believe and use the principle. Once we have given the principle some positive status, however weak, we can use the existence of empirical support (answer 1) to pull ourselves up by our bootstraps. That is, once we can justify some reliance on causation, we can start a "virtuous spiral" to boost the status of the principle to higher and higher levels, finally reaching full-blown knowledge.

The main objection to making use of empirical evidence in support of the causal principle comes from Hume. In both his Treatise concerning Human Nature and his Enquiry into Human Understanding, Hume argues that any appeal to empirical evidence in support of the causal principle is viciously circular or question-begging, given (2) above, namely, the fact that all empirical enquiry presupposes and relies upon the causal principle. As I have argued above, the most promising reply to Hume is to attempt to turn this vicious circle into a virtuous spiral. If we can argue that the natural light of reason, or the requirements of engaging in empirical inquiry, are sufficient to give some warrant or support to the causal principle, then we can use our actual success in finding causes as a reason for repeatedly upgrading the warrant, until we reach a state of rational certainty.

This virtuous-spiral move depends on the fact that we can break the causal principle up into a variety of sub-principles, narrow or restricted versions of the principle. For example, we could use the principle that all of our memories have causes in one instance, and in another instance use the principle that all historical records have causes. In this way, we can, without circularity, use one sub-principle in gathering empirical support for other sub-principles. So long as all the sub-principles can begin with some positive status, and so long as the actual results of empirical investigation cooperate, we can gradually raise the status of each of the constituent sub-principles, without ever reasoning in a circle.