The Nature of Cause and Effect

Philosophers approach the study of "causation" on two different levels.  There is the "Humean" or "Systemic" level, and there is the detailed "Physical" level.  Most modern philosophical discussions of causation take place at the Systemic level (see, for example, Hume, Mackie, Lewis).  But there are a few philosophers who approach the topic at the Physical level (see, for example, Salmon, Dowe, Fair).

Causes and effects are those things that are related by the relation of causation (if indeed it is a relation, there being some debate on the matter).  Causes and effects are variously called "objects", "events", "states of affairs", "situations", "facts", "facta", "properties", "tropes", "propositions", "statements", or "conditions".  For ease of exposition, I will employ the term "event" to mean any or all of these things.

According to Mautner's Dictionary of Philosophy(1), a philosophical analysis of causality would be an explanation of the concept of causality that "draws attention to its constituents, its presuppositions, its implications, etc." and shows how the concept can be "reduced to elements belonging to some basic category".   In other words, a satisfactory analysis of the concept of causation would be one that explained what causality was in terms that

(i) employs concepts (words) that are more ontologically fundamental, and therefore presumably simpler and more easily understood; and

(ii) does not draw upon concepts (words) that themselves could only be analyzed in terms of causality.

For an analysis of causality to be "better" than the concept of causality itself, it will have to explain just what causality is (and what are its presuppositions, implications, etc.) in terms of concepts whose meanings are more easily understood and explained than is causality itself.  Otherwise, there would be no gain, and we might just as well treat the concept of causality as sui generis.  An analysis of causality that draws upon concepts whose implications and presuppositions are more obscure than is causality itself would therefore not be a satisfactory analysis.  Also, obviously, a satisfactory analysis of causality cannot be circular  -  cannot employ concepts that themselves can only be analyzed in terms of causality.

"Systemic" versus "Physical" Causation

David Hume employed the concept of causation in two separate senses.  He employed the Physical concept of causation when he refered to the actual material, physical, scientific connection between an event A and an event B that exists quite independent of any conscious mind.  But he employed the Systemic concept of causation when he refered to the belief formed by some conscious mind about the necessary association of some event A and some event B.

"All reasonings concerning matter of fact seem to be founded on the relation of cause and effect.  By means of that relation alone we can go beyond the evidence of our memory and senses.  If you were to ask a man, why he believes any matter of fact, which is absent, (for instance, that his friend is in the country, or in France) he would give you a reason, and this reason would be some other fact, as a letter received from him, or the knowledge of his former resolutions and promises.  A man finding a watch or any other machine in a desert island, would conclude that there had once been men on that island.  All our reasonings concerning fact are of the same nature.  And here it is constantly supposed that there is a connection between the present fact and that which is inferred from it.  Were there nothing to bind them together, the inference would be entirely precarious.  The hearing of an articulate voice and rational discourse in the dark assures us of the presence of some person.  Why? Because these are the effects of the human make and fabric, and closely connected with it.  If we anatomise all the other reasonings of this nature, we shall find that they are founded on the relation of cause and effect, and that this relation is either near or remote, direct or collateral.  Heat and light are collateral effects of fire, and the one effect may justly be inferred from the other."
        David Hume, An Enquiry Concerning Human Understanding(2)

  "We have no other notion of cause and effect, but that of certain objects, which have been always conjoined together, and which in all past instances have been found inseparable.  We cannot penetrate into the reason of the conjunction.  We only observe the thing itself, and always find that from the constant conjunction the objects acquire an union in the imagination.  When the impression of one becomes present to us, we immediately form an idea of its usual attendant; and consequently we may establish this as one part of the definition of an opinion or belief, that it is an idea related to or associated with a present impression."
        Dave Hume, A Treatise of Human Nature(3)

In his exploration of the psychology of human beliefs, in his A Treatise of Human Nature, Hume explicitly proclaims that he does not deny the existence of Physical causation, but that it is the nature and origins of Systemic causation that is the focus of his attention.  On the one hand, Hume talks about "cause" as a relationship between "objects" that we observe in our experience, and connect in our minds.  On the other hand, Hume talks about "secret" and "concealed" causes that we are unable to discover.  "'[T]is commonly allow'd by philosophers, that what the vulgar call chance is nothing but a secret and conceal'd cause"[Treatise I, III, xii].  Hume does not deny that there are such "hidden" causes that underlie and explain the precedency and contiguity of observations in our experience.  But Hume clearly states that his

"intention never was to penetrate into the nature of bodies, or explain the secret causes of their operation.  . . .  For besides that this belongs not to my purpose, I am afraid that such an enterprise is beyond the reach of human understanding, and that we can never pretend to know body otherwise than by those external properties which discover themselves to the sense."

Hume's purpose in the Treatise was to "explain the nature and causes of our perceptions, or impressions, and ideas"[Treatise, I, II, v].  Hume, like Descartes and Locke before him, despaired of the ability of science to penetrate the "springs and principles, which are hid, by reason of their minuteness or remoteness"[Treatise, I, III, xii].

Systemic or Humeian causation, then, is the belief that human minds form about the nature of the causal relationship between two events - the cause and the effect.  At the Systemic level, the concern is not about how the cause causes the effect.  The concern is rather that the cause causes the effect.  Physical causation, by comparison, is the more detailed investigation of just how the cause causes the effect.  Physical causation approaches the discussion of causation from the perspective of the science of physics.  (And as it turns out, most articles from this perspective appear in journals focused on the Philosophy of Science.)

The Constant Conjunction Analysis of Causation

When Hume wrote these words in 1740 he was reasonably correct in his characterization of our common every day understanding of the relationship between cause and effect.  However, this was before the scientific revolution of the Age of Enlightenment.  In particular Newton's First Law of Motion "Objects in motion tend to stay in motion, and objects at rest tend to stay at rest unless an outside force acts upon them."  In other words, any event that we can observe constitutes a change in the previously existing status quo.   And by Newton's Law, any such change requires the application of force  -  a flow of energy.

Since the time of Newton then, our common understanding of the physics of energy flow has constrained our talk of cause and effect.  It is certainly true that we notice instances of cause and effect by the constant conjunction of events.  But contra Hume's suggestion above, for us to assert that one event causes another event is to assert that there is a suitable energy flow from the causing event that initiates the change that is the effect event.  Which is not, of course, to say that we are necessarily aware of what that flow of energy is, or of any details of the steps of the flow.  It is merely to say that there is such a flow.

cause - 1.  a.  The producer of an effect, result, or consequence.  b.  The one, such as a person, an event, or a condition, that is responsible for an action or a result.(4)

effect - 1.  Something brought about by a cause or an agent; a result.

The "higher level perspective" (what I like to refer to briefly as "causation-1") is a view of "cause and effect" consistent with Hume's analysis.  An observed repeated conjunction of two events - one labelled as the "cause", and the other labelled as the "effect".  Suppose at 8.21 PM, I make an experiment: I think "Sound of thunder".  At that exact same moment, you seem to "hear" the sound of thunder.  Only no-one else did.  Cause and effect?  How does one prove that?  The way Hume says (in his rules for judging causes and effects)?  If this happens just once, we mark it down as happenstance.  If it happens occasionally but not consistently, we mark it down as simple coincidence.  But if it happens consistently, repeatedly, and especially if we can make it happen at will, we can  -  à la Hume  -  recognise the concatenation of events as a candidate cause-effect pair.  This sort of thing happens all the time, and is the general way in which we identify cause-effect linkages. 

Combine this notion with the focus of science.  Science, in examining the Humeian cause-effect pair that is my thought and your hearing of thunder, will attempt to find out how your thought "caused" my heard thunder.  And it will do that by attempting to track the transfer of energy between your thought and my hearing.  While Newtonian Mechanics is not the most accurate available theory of physics, it has been more than adequately demonstrated as sufficient for all but relativistic or quantum events.  To propose, therefore, that your hearing thunder is the effect is to propose that the biochemical reactions in your head that is your hearing of thunder must be initiated by some application of external stimuli  -  an application of force  -  a transfer of energy originating in the cause  -  the biochemical reactions in my head that are my thinking "Sound of thunder". 

If scientific investigation cannot find such an energy flow (as would be likely in this case), then the hypothesis that my thought "caused" your hearing of thunder would be seriously questioned.  Other sources of the noticed linkage would be sought before scientists would be willing to throw out most of our understanding of physics.  Hence we have the "lower level perspective" of cause-effect relationships that is the flow of energy (application of force) between the event that is the "cause" and the event that is the "effect" (what I like to refer to briefly as "causation-2") that acts as a constraint on our "freedom" to notice pairs of Humeian cause-effect conjunctions of events. 

Understanding the relationship between "cause" and "effect" is critical to our understanding of reality, and critical to how we survive "The slings and arrows of outrageous fortune".  At the level of fundamental physics, the link between a cause and its effect can be determined by following the flow of energy.  The cause is always the creator of the energy that triggers the effect.  But at the level of practical day-to-day events, the link between cause and effect is often simply an observed correlation between the occurrence of two sets of circumstances.  Which set of circumstances is the cause and which is the effect is often not clear. 

The INUS Condition

In 1965, J.L. Mackie published a seminal article examining the causal relation from the Humeian Systemic perspective.  In this article he assumed only two generic events  -  a cause C and an effect E  -  that our native intuitions about causal relations stipulate are causally related.  From this he inquired whether and how the necessary and sufficient conditions might be applied in a manner consistent with our intuitions.

Mackie reasoned that for a cause to be sufficient for its effect, whenever the cause occurs, the effect must occur.  The cause can never occur without the effect occurring.  If C is a sufficient cause of E, then the presence of C necessarily implies the presence of E.  However, another cause Q may alternatively cause E.  Thus the presence of E does not imply the presence of C.  Mackie concludes that observation of day-to-day examples quickly reveals that this is much too strong a relation.  Our natural intuitions are not consistent with the suggestion that C is a sufficient cause of E.  An electrical short may have caused the fire.  But electrical shorts do not invariably cause fires.

Next he reasoned for a cause to be necessary for its effect, whenever the effect occurs, the cause must have occurred.  The effect can never occur without the cause occurring.  If C is a necessary cause of E, then the presence of E necessarily implies the presence of C.  The presence of C, however, does not imply that E will occur.  But again, observation of examples reveals that this relation is also much too strong.  Our natural intuitions are not consistent with the suggestion that C is a necessary cause of E.  The fire may have been caused by an electrical short.  But fires are not invariably caused by electrical shorts.

Mackie concluded that causes always have their effect in the context of a set of background circumstances.  Given different circumstances, the cause will not have the effect that it had in these particular circumstances.  Effects may have many possible causes under different sets of circumstances.  Causes may have many possible effects under different sets of circumstances.

Mackie proposed that a cause is an INUS condition for the effect.  And by that he means a cause is "an Insufficient but Necessary part of an Unnecessary but Sufficient condition" for the effect.  The sufficient condition is the entire suite of circumstances that existed at the time of the effect.  That entire suite of circumstances is also a necessary condition, since it includes all necessary conditions by definition.  Only one (possibly small) part of that entire complex set of circumstances is the part that we identify as the cause.

To say that the short circuit caused the house fire, therefore, is to say that this particular short circuit was an INUS condition for this particular house fire.  The short circuit was an insufficient part of the larger suite of circumstances because it could not cause the fire on its own (other conditions such as oxygen, inflammable material, etc. must have been present), but it was a necessary part of that larger suite of circumstances because (under those circumstances) the fire would not have started without the short circuit.  It is a necessary part because, without it, the rest of the conditions are not sufficient for the fire.  But this complex sufficient condition is not itelf necessary, since some other cluster of conditions, for example, an arsonist with gasoline, can produce the fire.

To quote Mackie -

"A is an INUS condition of a result P if and only if, for some X and for some Y, (AX or Y) is a necessary and sufficient condition of P, but A is not a sufficient condition of P and X is not a sufficient condition of P" [Mackie, 'Clauses and Conditions', American Philosophical QuarterlyVol 2, 1965, pp. 245-64).

There has been some debate over the details of Mackie's INUS analysis of causation, but his analysis has been largely accepted as the definitive analysis of deterministic causation at the Humeian Systemic level.  Given no other information other than the existence of two "events" that our native intuitions tell us are causally related, we can therefore conclude that -

(i) caues by themselves are not sufficient for their effects. The things that we identify as causes are but a (possibly small) part of a larger suite of conditions that together are sufficient for their effects; and

(ii) causes by themselves are not necessary for their effects. An effect may have many possible causes.

Probabilistic Causation

Of course, Mackie's analysis will not do for what is known as "probabilistic causation".  This is the sort of causation active in situations where a certain type of cause event is not always followed by the commonly expected effect event.  We identify some event as a "cause", because it is

"an [event] precedent and contiguous to another, and so united with it that the idea of the one determines the mind to form the idea of the other, and the impression of the one to form a more lively idea of the other." [Hume, Treatise, I, III, xiv]

But that psychological criterion for a "cause" and an "effect" does not necessitate that the cause is always followed by the effect.  Only that the two are associated sufficiently frequently as to couple the two in the mind.  And in obvious fact, we often employ the notions of cause and effect when the relationship is only vague  -  as in "smoking causes lung cancer".

To understand probabilistic causation, we will need to draw on someone like D.H.Mellor.  In his "The Facts of Causation", he presents a probabilistic understanding of causation that establishes an event as a cause if and only if it raises the chance of the effect event.  (Mellor goes into some extensive detail on just how he wants to understand "chance", but for this essay we can simply interpret it as "probability", and leave aside the philosophical difficulties inherent in understanding probabilities until an other essay.)  Based on his analysis, Mellor concludes that

(i) a cause is sufficient for its effect if and only if the cause entails the chances of the effect = 1. (Mellor has a particular "possible world" interpretation of "entails" in this statement, but we can ignore his refinements for the purpose of this essay, and take it to mean the standard logical entailment.)

(ii) a cause is necessary for its effect if and only if the absence of the cause entails the chances of the effect = 0.

Now obviously, for some cause C, the chances of its effect E might be something other than 1 (probability varying continuously between 0 and 1).  And if that is the case, if the cause only sometimes is followed by its effect, then the cause cannot be sufficient for its effect.  And if the absence of the cause is sometimes followed by the "effect" event, then the cause cannot be necessary for its effect.

The Counterfactual Dependence Analysis of Causality

The first attempt to provide a counterfactual explanation of causality was offered in 1748 by David Hume, who wrote -

"We may define a cause to be an object followed by another, and where all the objects, similar to the first, are followed by objects similar to the second. Or, in other words, where, if the first object had not been, the second never had existed."
    [Hume, An Enquiry Concerning Human Understanding, Section VII].

The core notion here is that the meaning of causal propositions can be explained in terms of counterfactual conditionals.   The proposition "C causes E" (or "E because C") is to be analyzed (explained) as -

(1) If C had not occurred, then E would not have occurred.

But Hume, after introducing the idea, never expanded on his counterfactual approach to understanding causality.   So it was left to his successors to explore the implications of this formulation.  The main difficulty facing his successors was the obscurity of counterfactual conditionals themselves.  Two problems remained to be resolved - understanding the truth conditions of counterfactual conditionals, and their apparent reference to unactualized possibilities.

In 1973, however, David Lewis presented what has become perhaps the best known and most thoroughly elaborated counterfactual theory of causation(5).  Lewis defines the notion of counterfactual dependence between events as  -

(2) Where C and E are two distinct possible events, E causally depends on C if and only if, if C were to occur E would occur; and if C were not to occur E would not occur.

Whether E occurs or not depends on whether C occurs or not.  This dependence is "counterfactual" because it holds whether or not C or E actually occur.  It holds even if C or E do not actually occur.  Strictly speaking, Lewis's definition differs slightly from what I have presented here, because he talks in terms of chains of causal dependence rather than direct causal dependence.  But for the purposes of this essay, we can ignore that refinement.

Lewis argues that the concept of causality is a concept of "Something that makes a difference", and that counterfactuals are the best way of representing that more fundamental notion.

"We think of a cause as something that makes a difference, and the difference it makes must be a difference from what would have happened without it. Had it been absent, its effects  -  some of them, at least, and usually all  -  would have been absent as well."
    [Lewis, "Causation", Journal of Philosophy, Vol 70: p.161]

It is worth noting, in passing, that this analysis of causality demands that C and E be distinct and independent events  -  C and E cannot be identical, overlap, nor imply each other.  Lewis argued that this restriction is necessary in order to reject "false positives"  -  pairs of events that our intuitions dictate are clearly non-causally related.  Lewis also argues that, for the same reason, backtracking counterfactuals must also be excluded.  Only counterfactuals that (typically) hold the past fixed up until the instant the counterfactual antecedent is supposed to obtain are acceptable analyses of causality.

So far so good.  But to this point Lewis is merely refining Hume.  The challenge remains of understanding the truth conditions of counterfactual conditionals, and their apparent reference to unactualized possibilities.  Here is where Lewis applies his "Possible World Semantics".

Possible Worlds Semantics specifies that the truth conditions for counterfactuals can be analyzed (explained) in terms of similarity relations between possible worlds.  A possible world W1 is said to be "closer" to the actual world (W0) than another possible world W2 if W1 resembles W0 more than W2 does.  This resemblance relation produces what Lewis calls a "weak ordering" of worlds  -  any two worlds Wi and Wj can be ordered with respect to their "closeness" to (the degree to which they "resemble") the actual world (ties permitted).

In terms of this similarity relation then, the truth condition for the counterfactual "If C were the case, E would be the case", is -

(3) "If C were the case, E would be the case" is true in W0 if and only if (i) there are no possible C-worlds; or (ii) some C-world where E holds is closer to W0 than is any C-world where E does not hold.

(I shall ignore the first case, wherein the counterfactual is vacuously true.)  Lewis' basic idea here is that the counterfactual is true just in case it takes less of a departure from actuality to make both the antecedent and the consequent true than it takes to make the antecedent true and the consequent false.

When Lewis first presented this analysis of causality in terms of counterfactual dependence, the generally accepted explanation of causality was in terms of lawful regularities of nature.  It was also commonly recognized that such regularity theories faced a number of problematic counterexamples where our intuitions conflicted with the theory.  Lewis' counterfactual analysis is not subject to the same counterexamples.  So when first introduced, Lewis's counterfactual analysis of causality offered considerable explanatory benefits.  Deeper analysis since that time, however, has revealed a number of difficulties.  Two of these problems I believe disqualify the Counterfactual Dependence theory as a satisfactory analysis of causality.

The first problem is that possible worlds are not inspectable.  Whether they are abstract concepts as many maintain, or real existents as Lewis maintains, they are not causally connected with this, the actual world.  We too easily forget that this means that we cannot really inspect any other possible world than our current world.  So the question of whether C or E holds in some possible world is not a question of empirical investigation.  What in fact holds in any other possible world can have no actual bearing on the answer, regardless of how we choose to express the results of our determination.  Given that all we have epistemic access to is the actual world, how could we know anything about these other possible worlds or what holds in them?  How, therefore, are we judge whether one world is "closer" than another to the actual world?  How could we even guess?  Obviously, we can't.  Although Lewis discusses the resemblance relation at considerable length in his Counterfactuals(6), what remains obscure is how we can determine the relative "closeness" of C-worlds wherein E holds and does not hold.  Whether C or E holds must be determined on the basis of factors that are known to us here in this actual world.  What we wish to assert about the relative "closeness" of possible worlds can be so only by stipulation.  Whatever the judgement, the grounding for our judgements of "closeness" has to be right before us in this actual world.  But how we make that judgement, remains unexplained.

Complicating this difficulty is the fact that the problem of trans-world identity has not been resolved.  Consider a proposition of counterfactual dependence like "If Ann were to throw the ball [at the window], the window would break."  Possible worlds semantics demands that we examine every possible world in which Ann throws the ball to see if any of those worlds in which the window does not break is "closer" to the actual world that worlds in which the window does break.  Obviously, from the above argument, we do not do this examination in anything like an empirical sense.  Rather we do it conceptually, on the basis of what we stipulate about these possible worlds.  But just what is it that (conceptually) picks out an instance of "Ann" or "the ball" or "the window" in any other possible world than this actual world.  Some philosophers (Kripke in particular) have suggested that trans-world identity is established only by identical origins.  So any existent in some possible world that had the same parents (manufacturing plant?) would be the "same" Ann, ball or window.  But this runs into infinite regresses.   The hypothesis leaves problematic the question of the identicality of the origins  -  and so forth with infinite circularity.  And if that is the case, then clearly our judgements of resemblance and closeness are prior to, and not dependent on the possible worlds semantics.

What this means is that Lewis' notion of "closeness" or "similarity" or "resemblance" between possible worlds is more obscure and less fundamental than is the notion of "causality" that he seeks to explain by their use.  This, I believe, disqualifies the counterfactual dependence analysis as a satisfactory analysis of causality.

The second problem is related to the first, in that it develops from Lewis' notion of the kind of "departure" from actuality that would be necessary to make either (or both) the antecedent and/or the consequent true.  Suppose we stipulate that W1 is identical to W0 at some time t1 and then there occurs a "departure" necessary to make W1 into a C-world (a possible world wherein C counterfactually holds  -  say one wherein Ann throws the ball).  How do we determine what this "departure" is, and how do we determine whether it takes less of a departure from actuality to make both the antecedent and the consequent true than to make the antecedent true and the consequent false.  Obviously, to judge whether any hypothetical departure might make either the antecedent or the consequent true, we must draw upon our understanding of how a possible world would evolve through time, given some change in the status quo.  But that understanding is itself an understanding of causality  -  an understanding of how the actual world reacts to stimulii.  In other words, Lewis' concept of how possible worlds can "differ" from this our actual world, and the relative "closeness" of different possible worlds, is itself dependent on our concept of causality.

What this means is that Lewis' notion of "closeness" or "similarity" or "resemblance" between possible worlds is fatally circular.  This, I believe, also disqualifies the counterfactual dependence analysis as a satisfactory analysis of causality.

The Conserved Quantity Analysis of Causation

So much for two different sorts of analyses from the Systemic perspective.  Now let's consider an analysis of causation from the Physical perspective.  For this we need to turn to the thinking of philosophers like Wesley Salmon and Phil Dowe.  Within the conserved quantity conception of causation, causation is intimately coupled with the conservation laws identified by physical science.  At this level of analysis, an event (in the generic sense established above) necessarily involves a change in the quantity of some conserved property of some specific entity  -  for example, a change in the momentum of a billiard ball, or in the kinetic energy of a molecule, or the spin of an electron.  The definitions of "cause" and "effect" are based on the source and drain of those changes.  If, for example, some amount of momentum is transferred from one billiard ball to another, the change that contributes the momentum is the "cause" and the change that absorbs the momentum is the "effect".

An analysis of causation at this detailed Physical level has the distinct advantage of being immune to the difficulties of "over-determination" and "pre-emption" that plague the Systemic level analysis.  On the other hand, being an analysis at the detailed level of particle interaction, it is not the appropriate analysis for such examples of causation as smoking causing cancer, or the raising of taxes causing higher unemployment.  Any more than it would be appropriate to discuss the dynamics of internet traffic in terms of electron flow through semi-conductors.  Although the former is indubitably based on the latter.

At the Systemic level of analysis, to say that some event "causes" some "effect" is to say that there is something inherent in the "cause" such that the "effect" would not have come about without the prior or coincident occurrence of the "cause".  In the realms of the physical sciences, where the Physical level of analysis is the norm, this relationship has been made much more specific.  In the physical sciences, some event "A" is identified as the "cause" if and only if it generates the energy flow which initiates the "effect" event "B".  In any cause-effect relationship there is always a transfer of some conserved quantity  -  usually abbreviated as "energy" but specifically to be understood as meaning any of the conserved quantities involved.  The physical sciences can be viewed as an effort to understand the transfer of "energy" involved in cause-event chains with greater and greater detail, over longer and longer chains.

Causation-2 is indisputably reductionist.  As such it is indisputably the improper level from which to understand such "cause-effect pairs" as the contribution of early childhood education on adult lifetime achievement, or from which to discuss the most significant potential "cause" of your favourite candidate winning or loosing the next election.  But it is equally indisputably the correct level from which to understand how cigarette smoking "causes" cancer, how the window got broken when Johnny threw the ball, or how I perceive fluctuations in air density in my vicinity as "The sound of thunder".

Thus, for example, "I threw the baseball and broke the window".  The cause is the baseball, and the effect is the broken window.  More precisely, the cause is the kinetic energy of the baseball impacting on the glass of the window.  The more detailed the scientific investigation of this cause-effect relationship, the finer the detail of the steps that are identified.  And the greater the resolution of detail in the flow of energy involved.

Once you have gained some basic level of knowledge of the cause-effect relationship, you can then predict with a fair degree of accuracy how reality is going to behave.  If I throw this baseball towards that window, I have a pretty good expectation that the window will break.  Here too, the more detailed the scientific knowledge gained of the flows and transfers of energy, the more accurate the predictions that can be made.

To understand a cause-effect relationship is to understand what circumstances in reality generate or result in other circumstances in reality.  To understand cause-effect relationships is key to the ability to predict how reality is going to behave.  If you know what effects result from what causes, you can predict how reality is likely to respond when you see or anticipate the causes.  Where understanding the cause-effect relationships really pays off, however, is when we attempt to change the effect by altering the cause.  If we don't want the window to break, and we know that a thrown baseball causes an effect of a broken window, we can avoid future broken windows by preventing the baseball from impacting the window.  Or, alternatively, because we understand the consequences of the flows of energy involved, if we cannot prevent the baseball from impacting the window, we might be able to strengthen the window to withstand the impinging kinetic energy of the baseball.  Or again, alternatively, if we see a broken window and a baseball on the floor, we can be confident that there is some connection, and seek out the source of the baseball.

The ability to predict how reality is going to behave in response to various possible courses of action is fundamental to survival.  To know that when I see this leaf there is an edible tuber beneath it, when I see this colour the fruit is ripe for eating, when I smell that odour there is a predator up wind, are all vitally important elements of survival.  The key to survival, in all walks of life and at all times past, present and future, is the ability to choose "causes" that are likely to result in desirable "effects".  Because of the vital importance of this ability to our continued survival, Homo sapiens has evolved over the aeons to be rather good at identifying the cause-effect relationships we see in reality around us.

But when we start to pay attention to this ability of ours, it is often not as simple as the above description makes it first appear.  On a day-to-day basis, it is almost never as straight forward as scientifically tracing the transfer of energy involved.  Most of the time, outside the realms of the physical sciences, all we can say with any assurance is that two kinds of circumstances often occur together.  The Humean notion of cause and effect.

Picking the Right Systemic Causal Relata

If we choose the wrong set of events as the "cause", we find ourselves pursuing theories of how reality works that become overly complex, and ultimately self-defeating.  By reversing field, and realizing that we have the cause-effect relationship backward, we discover that our theories become simpler, that they have broader application, and that they offer greater opportunities for deeper understanding.

Consider the following chain of reasoning, as a simple example.  At each step we have two sets of circumstances that we have observed are correlated.  At each step we have an assumed cause-effect relationship.  And at each step, we use this assumed cause-effect relationship to govern some behavioural choice:

This is a rather simplistic example, but it highlights how important it is for simple issues of survival that we get our understandings of the cause-effect relationships right more often than not.  When we get our understandings wrong, then we will wind up staying out in the rain in winter, and probably die of exposure.  We are descendants of a long line of hungry but fragile omnivores who have successfully managed to predict where and when to find edible fruits, which way the tiger will jump, and to stay out of the rain in winter.

History is littered with numerous examples of a correlation of events where we have mistaken the direction of the cause-effect relationships.  Often, our understanding of the causal relation is aided by the temporal differences involved.  But we do not always have that luxury.  Here are three different examples to highlight the difficulties we get ourselves into when we do not pay proper attention to picking the right event as the cause.

Education and IQ Scores

For populations of some minimum size, there is a well documented correlation between the scores that subjects achieve on various IQ tests, and the levels of education that they have attained.  Related evidence reveals that high IQ test scores in children are positively correlated with future school grades, future earnings potential, and future rise up the social hierarchy.  Similarly, for adults there is a positive correlation between high IQ test scores and past school grades, current income levels, and current status in the social hierarchy (socio-economic status).  The question is  -  is the "richness" (quality and quantity) of one's educational experience the cause of high IQ test scores, or is whatever IQ tests measure the cause of the richness of one's educational experience.  Some experts argue that whatever it is that IQ tests measure, it is the cause of the better quality and greater number of years of education attained by those who test with higher IQs.  Other experts argue that it is the richness of one's educational experience that results in the higher IQ test scores.  There is no undisputed evidence either way, and no general consensus as to which is the correct cause-effect relationship.

Lets assume, for the moment, that it is the richness of education that is the cause, and the high IQ test scores that is the effect.  This proposition would have some significant implications for public policy.  If the quality and extent of early childhood education is a strong causative factor in high IQ test scores, then it would make good policy sense to invest large sums of tax money in improving the educational system.  Especially for those who start out with disadvantages in early school grades, family income, or social position.  And especially for children, where presumably, a rich educational experience would have the greatest impact.  (This assumes, of course, that the existing observed correlation between high IQ test scores and future earnings potential and social position remains relatively constant.  And it assumes, again of course, that greater future earnings potentials and higher social positions are desirable things, a discussion I will leave for later.)

On the other hand, lets reverse the relationship and assume instead that it is the high IQ test scores that is the cause, and the richness of one's educational experience the effect.  This proposition also would have some significant implications for public policy.  It would suggest that investing large amounts of money to enhance the educational experience of low-IQ children would be wasted.  Money should instead be invested in enhancing the educational experience of high-IQ children, with perhaps only remedial assistance provided for those with lower IQ test scores.

Frequently, in situations with such dramatic differences in the social consequences, when there may be no clear indication which relationship is the correct one, people choose the cause-effect assumption that most appeals to them  -  most fits in with their preconceived prejudices.  But unfortunately, when society embraces one particular interpretation of the cause-effect relationship, it usually has the ancillary effect of stifling scientific investigation into the evidence.  And more often than not, people emotionally wedded to one particular interpretation will refuse to see any evidence that runs counter to their preferred view of reality. 

This example is a good case of social censureship.  The public (and especially the media) display a marked approval for the hypothesis that high IQ scores are the effect and not the cause of a richer educational experience.  As a result, there has been a significant amount of public money invested into programs to enhance the early childhood educational experience.  (The "Head Start" program in the United States, and similar smaller scale efforts in Canada and Britain have been marketed on this basis.)  When a book came out that challenged this hypothesis (The Bell Curve, Richard J. Herrnstein & Charles Murry, 1994), it was resoundingly criticized  -  not generally for the quality of their research, but for their temerity of challenging the "accepted wisdom".  But in the last couple of decades, possibly in response to the challenge presented by The BEll Curve, there has developed a growing body of evidence that suggests that these large public investments in early childhood education have not had the expected result(7)

While this evidence is neither sufficiently convincing, nor sufficiently without possible criticisms, it is suggestive that it is IQ test scores that is the cause of the higher levels of educational richness experienced by those who test with higher IQs, rather than the other way around.  But this is not an answer that most people will easily accept.  It flies in the face of the public espousal of equality. 

The way that the public has reacted to this conflict leads easily to the discussion of Animism.

Animism

animism - 1.  The attribution of conscious life to natural objects or to nature itself.

When Mankind first started to ponder the mysteries of the Universe, he naturally drew upon that portion of the Universe he knew the best - himself.  When I want to raise my hand, I simply want my hand to rise.  If I want that fruit over there, I simply want my hand to reach out and grab it.  Discussing this simple observation with you reveals to me that the same principle works for you as well.  But what about this rock that, every time I let go of it, falls to the ground.  Why does it do that?   Well, in drawing upon the parallel of why I or you do anything, it must be because the rock wants to get to the ground.

This sort of reasoning   -   by analogy with human action   -   leads directly to the hypothesis that everything that happens in nature, happens because some consciousness wants that it happen.  This belief is is founded on the analogy that non-human things do things for the same reasons that humans do things  -  there is a will to act.  Thus the cause of the rock falling is the will of the rock to reach the ground.  And the will of the rock is only apparent from the analogy with human action.  The effect is observed, the cause is assumed based on the analogy.  It is a simplistic belief that is a very natural extrapolation from our familiarity with our own actions.  I have a small step ladder in the kitchen that I swear just waits for me to try to fold it up so it can pinch my fingers.  And when I hit my thumb with the hammer, it is not me that I cuss, it is that cursed malevolent hammer.

But a serious (versus a facetious) belief in Animism results from the confusion of cause and effect.  Animism is based on the proposition that a cause (an apparent conscious will of the rock to get closer to the Earth) generates an effect (the rock gets closer to the Earth).  Whereas a non-Animist explanation of the relationship would have a cause (the rock gets closer to the Earth) generating an effect (an apparent conscious will of the rock to get closer to the Earth).  

As the internal logic of an Animist belief is explored, certain logical consequences are almost inevitable and are far reaching.  If the bounty of the harvest is the effect of some conscious will, then it would make more sense to invest time and effort in influencing or placating that conscious will, instead of investigating the biology and agronomy of plant growth.  Investigations into biology and agronomy might even be regarded as treading on the territory of the conscious will involved.  We are, after all, territorial animals.  So it would be in keeping with the reasoning by analogy with human behavior, to assume that the conscious will that governs nature is also territorial in some way.  The result of a wide spread belief in Animism is, therefore, a social focus of attention on the placation and appeasement of the conscious wills involved.  Prayer, supplication, and offerings of various sorts, accompanied by elaborate rituals, are the hallmarks of an Animist social culture.  This is not a description of ancient history.  All religions even today, are essentially Animist in origin and current nature.  The Judeo-Christian-Islamic religion is perhaps less Animist than is, say, Hinduism.  But the Catholic Church, as one simple example, still maintains that all events that occur are "God's Will".  Of course, there is considerable debate in certain circles as to how "God's Will" gets translated into the events that occur.  Opinions vary all the way from a direct intervention in every event (the basis of prayer after all), to an "Uncaused Cause" that set the Universe in motion and now simply watches. 

The last three millennia of history are replete with examples of how Animist belief structures have struggled against scientific investigation.  Galileo was severely punished, and almost executed, for daring to suggest that what the Church decreed was not in fact how reality behaved.  And even today, the teaching of evolution in the schools gets many parents into a serious snit.  With each new scientific foray into the physics of cause and effect, the Animist culture has retained its essential animistic proposition by "tweaking" its structure of theories on how reality works.  With each new scientific revelation that reality does not actually work the way that the Animist theories suggest, the Animist theory has retreated to accommodate, withdrawing the animating conscious will from those areas where science understands the physics involved.  And the Animist theory has become more complex, adding more and more special assumptions in order to deal with the reality that science reveals.  Animism has also become less and less willing to predict how reality will be and behave, and less and less open to being refuted by scientific investigation.

Animism does have one "saving grace", if you can call it that.  Its central hypothesis of a "conscious will" that animates some or all actions of Nature is sufficiently ill-defined that it is impossible to prove that it does not exist.  This feature was not available to the other great cause-effect mistake I would like to consider. 

Earth Centrism

"Earth Centrism" is the belief that the Earth is the centre of the Universe, and all of the heavenly bodies circle an Earth that stands still.  Like Animism, it is a belief easily arrived at through reasoning by analogy with human action.  Imagine you are sitting on a log floating peacefully in a lake, and suppose I come and swim around you.  I appear on one side of you, pass in front of you, disappear on the other side of you, only to reappear where I did the first time.  Just like the Sun and Moon do for someone watching their passages.  All the while, you have been sitting there quite unmoving.  What path did I swim to generate the effect you saw? -- a circle, with you as the centre.  Therefore, by analogy, what paths do the heavenly bodies follow to create the effects we see?   -- why a circle of course, with the Earth as the centre.  Earth Centrism is thus based on the proposition that the cause (the Earth is the centre of the Universe) generates an effect (the motions of the heavenly bodies).  If the Earth is the centre of the Heavens, and the heavens rise in the East and set in the West, then it is obvious to any observer that the Heavens must circle the Earth.

As astronomical observations accumulated, this simple theory became untenable.  It was obvious to any studious observer that simple circles would not suffice.  In order to maintain their essential proposition that the heavens circled the Earth, circles (called epicycles) were added to circles.  By the time of Tycho Brahe and Copernicus, the theory had become so complex that the orbit of the planets were described by epicycles on the epicycles on the circles.  Astronomical calculation was becoming such a complex endeavour that only mathematical wizards could predict any distance into the future.

An ancillary fall-out of the Earth Centrist theory was a complete inability of any related understanding to explain how the heavenly bodies stayed up there and what moved them.  The Earth-Centrist theory had no openings through which one might address this sort of problem.  For similar reasons, it was not even conceivable that what kept the heavenly bodies up there was the same thing that kept our feet on the ground.  Earth and the Heavens were necessarily two different realms, each governed by completely different principles.

Copernicus recognized that the Earth-Centrist astronomical theory was no longer acceptable.  So he reversed the cause-effect relationship, and proposed that the cause (the motions of the heavenly bodies) generated an effect (the Earth is the centre of the Universe).  Viewing the cause-effect relationship like this makes it obvious that the effect can be achieved by an "optical illusion".  Propose that the Sun is the centre of the Universe, instead of the Earth, and that the Earth rotates on its axis while orbiting around the Sun, and the "optical illusion" is complete.  The orbits of the heavenly bodies make it appear as if the Earth is the centre of the Universe.

Astronomy suddenly became much simpler.  With the recognition of the correct cause-effect relationship, the theory of how reality worked offered enormous opportunities for understanding heretofore incomprehensible aspects of reality.  And even though Copernicus' initial supposition for the orbits of the planets proved wrong, the Sun-Central theory was robust enough to accommodate the refinements of Kepler, Newton, Einstein, and Hubble (among others).  By correcting the understanding of the cause-effect relationship, subsequent additions to the new understanding would broaden the application of the theories.  The Heavens and the Earth were now one realm, governed by one set of principles.  Gravity explained both the motions of the heavenly bodies, and what kept our feet on the ground.

With the Animist example, we have seen how a confused understanding of a cause-effect relationship can result in an authoritative prohibition of any scientific investigation of the evidence.  And how the fundamental proposition underlying the belief retreats but never capitulates in the face of contrary evidence.  With the Earth-Centrist example, we have seen how a confused understanding of a cause-effect relationship can result in an overly complex adaptation to contrary evidence. 

Copernicus was not completely correct in his description of how the planets revolve around the Sun.  But he was a damn site more accurate than the theories he replaced!    

What is the Difference Between a Law of Nature and an Accidentally True Generalization?

The modern debate over this question appears to be taking place between two schools of thought.  There is the "Humean" school of the Mill-Ramsey-Lewis view of Laws of Nature as regularities in nature.  And there is the "anti-Humean" school of the Dretske-Tooley-Armstrong view of Laws of Nature as relations of necessity between Universals.  At the metaphysical level, the two sides to the debate have vastly different conceptions of the relation between Nature and the Laws.  The Humeans maintain that the Laws are descriptions of matters of fact -- the facts determine the Laws.  The anti-Humeans maintain that it is the Laws that determine matters of fact. 

What the Humean school undoubtedly has right is that most of the things we honour with the label "Law of Nature" are nothing more than recognized patterns in the mass of experience we have with Nature.  Scientists search for and discover larger patterns in our experience and generate sweeping generalizations, frequently applicable only in "ideal" circumstances, and often understood to hold only "approximately".  The more basic of these generalizations, the more of science that they support, the more likely they are to be graced with the honorific of "Law of Nature".  The patterns involved need not be clear and crisp patterns of unquestionable regularity.  Because we are such consummate pattern recognition devices, they can be rather muddy partial patterns, that hold only "for the most part".  Sometimes, of course, we are fallible and the patterns are not really there.  As Nancy Cartwright has pointed out these generalizations must be viewed through the noise and fog of "non-existent idealized circumstances", "ceteris paribus", "mutatis mutandis", and a multitude of similar caveats. 

So for the Humean, what differentiates an accidentally true generalization from a law of nature is, in the first place, that the pattern we have noticed must be expected to continue into the future.  We must anticipate that our future experiences of nature will reveal that the pattern continues unchanged.  If not, then the generalization is not the identification of a persisting regularity of nature, and is not a candidate for a law of nature.  In the second place, the generalization must play some role in underpinning the rest of our understanding of nature.  If the candidate generalization can be shown to be the foundation of enough of such other lesser laws and rules, then it is honoured with the "law of nature" label.  In other words, to a Humean, the Laws of Nature systematize our descriptions of our experiences of Nature.  The Laws of Nature are the basic theorems or axioms of a model/theory (or consistent collection of models/theories) that most simply accounts for the widest range of experiences. 

What the anti-Humean school undoubtedly has right, on the other hand, is that the Laws of Nature have an unmistakable element of necessity about them.  According to the anti-Humeans, the Humeans ignore this intuitive element.  The anti-Humeans therefore rely specifically upon it to mark the distinction between laws of nature and accidentally true generalizations.  But anti-Humeans face the serious, as yet unresolved, metaphysical difficulty of providing an explanation of just what this necessity amounts to.  Just how it is explained varies according to the anti-Humean philosopher.  But claiming the necessity to be brute is to ignore the problem, and labelling it as the relation of Necessitation is to merely label the problem. 

But consider the analysis of causation by Messrs. Fair, Dowe, and Salmon.  If their approach is correct, causation is best understood in terms of the conservation of some small number of key quantities (like energy, momentum, and so forth).  And if that is the case, then the conservation restrictions governing causation, would be laws of nature.  In fact, on this basis, they would be the only "fundamental" laws of nature.  All the rest of what we commonly refer to as laws of nature would be just higher level "common" laws of nature, deriving their stature from the causation defined in the "fundamental" laws, and subject to all the problems highlighted by Cartwright.  But the still unanswered question is, just what ensures that energy, say, is conserved across causal interactions?  How is the relation of necessitation cashed out?  While it is obvious that there is some kind of necessity at work here, it is entirely unclear just how to understand that necessity.  But consider that it is part of what it means to be the surface of a sphere that dictates that the surface is finite, unbounded and equal to 4πr2.  Possibly it is part of what it means to be a Universe that those conserved quantities are conserved. 

This is just one example of a description of the relation of necessitation that anti-Humeans rely upon to distinguish laws of nature from accidentally true generalizations.  If an inductive generalization has none of the required necessity about it (in the case of the causation example, has none of the required causal relations about it), then it is classed as an accidentally true generalization.  If it does have the required necessitation (or causal properties), then it qualifies as a "common" laws of nature.

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Notes and References

(1) Mautner, Thomas; The Penguin Dictionary of Philosophy, Penguin Putnam Inc., New York, New York. 1996. ISBN 0-14-051250-0. pg 18-19.

(2) Hume, David;  An Enquiry Concerning Human Understanding (Second Edition), Eric Steinberg, Ed., Hackett Publishing Company, Indianapolis, 1993.  ISBN 0-87220-229-1.  Chapter on Cause and Effect, Part I. 

(3) Hume, David;  A Treatise of Human Nature. Ernest Mossner, Ed., Penguin Books Inc., London, England.  1985.  ISBN 0-140-43244-2.  Chapter 19, Section iv. 

(4) Unless otherwise specified, all dictionary definitions are quoted from The American Heritage® Dictionary of the English Language, Third Edition copyright © 1992 by Houghton Mifflin Company.  Electronic version licensed from INSO Corporation; further reproduction and distribution restricted in accordance with the Copyright Law of the United States.  All rights reserved. 

(5)  Lewis, David; "Causation", Journal of Philosophy, 70: 556-67. reprinted in Causation, Ernest Sosa and Michael Tooley, eds. Oxford University Press, Oxford, England, 1993. ISBN 978-0-19-875094-9

(6)  Lewis, David; Counterfactuals, Blackwell Publishing, Oxford, England. 1973. ISBN 0-631-22425-4

(7)  Coulson, Andrew J.; "Head Start: A Tragic Waste of Money" in the New York Post, January 8, 2010.
        Currie, Janet & Thomas, Duncan;  "Does Head Start Make a Difference?" in The American Economic Review, Vol 85, No 3 (1995), Pgs 341-364.

 

Anscombe, G.E.M.; "Causality and Determination" in Causation, Ernest Sosa and Michael Tooley, eds. Oxford University Press, Oxford, England, 1993. ISBN 978-0-19-875094-9

Armstrong, D.M.; "Going Through the Open Door Again: Counterfactual versus Singularist Theories of Causation" in Causation and Counterfactuals, Collins, John & Hall, Ned & Paul L.A. (eds.). The MIT Press, Cambridge, Massachusetts, 2004.ISBN 0-262-53256-5.

Bennett, Jonathan: "Event Causation: The Counterfactual Analysis" in Causation, Ernest Sosa and Michael Tooley, eds. Oxford University Press, Oxford, England, 1993. ISBN 978-0-19-875094-9

Berofsky, Bernard; "The Counterfactual Analysis of Causation" in The Journal of Philosophy, Vol 70, No 17 (Oct 11, 1973, pp 568-569.

Crane, Tim: "All the Difference in the World" in The Philosophical Quarterly, Vol 41, No 162 (Jan 1991), pp 1-25.

Carroll, John W.; "Nailed to Hume's Cross" in Contemporary Debates in Metaphysics, Theodore Sider, John Hawthorne, Dean W. Zimmerman eds. Blackwell Publishing, Oxford England, 2008. ISBN 978-1-4051-1229-1

Cartwright, Nancy; How the Laws of Physics Lie, Oxford University Press, Oxford, England, 1983. ISBN 0-19-824704-4.

Cartwright, Nancy; "Models: The Blueprints for Laws" in Philosophy of Science, Vol 64, Supplement. (Dec 1997), pp S292-S303.

Choi, Sungho; "The Conserved Quantity Theory of Causation and Closed Systems" in Philosophy of Science, Vol. 70, No. 3 (Jul., 2003), pp. 510-530

Davidson, Donald; "Casual Relations" inCausation, Ernest Sosa and Michael Tooley, eds. Oxford University Press, Oxford, England, 1993. ISBN 978-0-19-875094-9

Dowe, Phil; "What's Right and What's Wrong with Transference Theories" in Erkenntnis,Vol. 42, No. 3 (May, 1995), pp. 363-374

Dowe, Phil: "Causality and Conserved Quantities: A Reply to Salmon" in Philosophy of Science, Vol. 62, No. 2 (Jun., 1995), pp. 321-333

Dowe, Phil; "The Conserved Quantity Theory of Causation and Chance Raising" in Philosophy of Science(Supplement: Proceedings of the 1998 Biennial Meetings of the Philosophy of Science Association. Part I: Contributed Papers), Vol 66, pp. S486-S501

Dowe, Phil; "Causal Processes" in The Stanford Encyclopedia of Philosophy(Fall 2008 Edition), Edward N. Zalta (ed.), URL=<http://plato.stanford.edu/archives/fall2008/entries/causation-process/>.

Ducase, C.J.; "On the Nature and the Observability of the Causal Relation" in Causation, Ernest Sosa and Michael Tooley, eds. Oxford University Press, Oxford, England, 1993. ISBN 978-0-19-875094-9

Ehring, Douglas; "The Transference Theory of Causation" in Synthese, Vol. 67, No. 2, Causation and Scientific Inference and Related Matters (May, 1986), pp. 249-258

Fair, David; "Causation and the Flow of Energy" in Erkenntnis, Vol. 14, No. 3 (Nov., 1979), pp. 219-250

Garrett, Don;   "The Representation of Causation and Hume's Two Definitions of Ã�â"��Ë�"Cause'" in Nous, Vol 27, No 2 (June, 1993), pp 167-190

Harrison, Jonathan;   "The Impossibility of 'Possible' Worlds" in Philosophy, Vol. 74, No. 287 (Jan., 1999), pp. 5-28

Hitchcock, Christopher; "What's Wrong with Neural Diagrams" in Causation and Explanation, Joseph Keim Campbell, Michael O'Rourke, Harry Silverstein eds. A Bradford Book MIT Press, Cambridge, Mass. 2007. ISBN 978-0-262-53290-7

Horwich, Paul: "Lewis's Programme" in Causation, Ernest Sosa and Michael Tooley, eds. Oxford University Press, Oxford, England, 1993. ISBN 978-0-19-875094-9

Hume, David;   A Treatise of Human Nature, 1739.Online Library of Liberty, URL = <http://oll.libertyfund.org/EBooks/Hume_0213.pdf>    
(Citations will be given in "Treatise, Book, Part, Section" format.)

Hume, David;   An Enquiry Concerning Human Understanding, 1748.Eighteenth-Century Studies, URL = < http://18th.eserver.org/hume-enquiry.html#5>   (Citations will be given in "EUH, Section, Part" format.)

Kim, Jaegwon; "Causes and Events: Mackie on Causation" inCausation, Ernest Sosa and Michael Tooley, eds. Oxford University Press, Oxford, England, 1993. ISBN 978-0-19-875094-9

Kim, Jaegwon; "Causes and Counterfactuals" in Causation, Ernest Sosa and Michael Tooley, eds. Oxford University Press, Oxford, England, 1993. ISBN 978-0-19-875094-9

Lewis, David; Counterfactuals, Blackwell Publishing, Oxford, England. 1973. ISBN 0-631-22425-4

Lewis, David; "Casuation" in Causation, Ernest Sosa and Michael Tooley, eds. Oxford University Press, Oxford, England, 1993. ISBN 978-0-19-875094-9

Lewis, David; "Causation as Influence" in Causation and Counterfactuals, Collins, John & Hall, Ned & Paul L.A. (eds.). The MIT Press, Cambridge, Massachusetts, 2004.ISBN 0-262-53256-5.

Lyon, Ardon; "Causality" in The British Journal for the Philosophy of Science, Vol 18, No 1 (May 1967), pp 1-20.

Mackie, J.L.; "Causes and Conditions" in American Philosophical Quarterly 2, 1965, pp. 245-64

Mackie, J.L., The Cement of the Universe: A Study of Causation, Oxford University Press, 1974, ISBN 0-19-824642-0.

Maudlin, Tim; "Causation, Counterfactuals, and the Third Factor" in Causation and Counterfactuals, Collins, John & Hall, Ned & Paul L.A. (eds.). The MIT Press, Cambridge, Massachusetts, 2004.   ISBN 0-262-53256-5.

Mellor, D.H.; The Facts of Causation, Routledge, New York, New York, 1995. ISBN 0-415-19756-2

Menzies, Peter, "Counterfactual Theories of Causation" in The Stanford Encyclopedia of Philosophy(Fall 2009 Edition), Edward N. Zalta (ed.), URL = <http://plato.stanford.edu/archives/fall2009/entries/causation-counterfactual/>.

Morgan, Stephen L. & Winship, Christopher: Counterfactuals and Causal Inference, Cambridge University Press, New York, New York, 2007. ISBN 978-0-521-67193-4

Otte, Richard; "Indeterminism, Counterfactuals and Causation" in Philosophy of Science, Vol 54, No 1 (Mar 1987), pp 45-62.

Pearl, Judea; Casuality: Models, Reasoning, and Inference, Cambridge University Press, New York, New York, 2000. ISBN 978-0-521-77362-1

Richards, Thomas J.;   "Hume's Two Definitions of 'Cause'" in The Philosophical Quarterly, Vol 15, No 60 (July, 1965), pp 247-253.

Salmon, Wesley C.: "Probabilistic Causality" in Causation, Ernest Sosa and Michael Tooley, eds. Oxford University Press, Oxford, England, 1993. ISBN 978-0-19-875094-9

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Salmon, Wesley C.; "Causality Without Counterfactuals" in Philosophy of Science, Vol 61, No 2 (June 1994), pp 297-312.

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