What is a cause? Trying to distil clarity from a very muddy conceptPosted: 8 June 2013 | |
Scene 1: So! – shrieked the evil monocled Gestapo officer. Eef you do not tell me ze name off ze leader off your resistance group, I vill shoot zis prisoner. Make your choice keffully! Do you vish to be ze cause off ze death off zis poor eenocent civilian?
Fade to scene 2: And now m’lud, intoned the imposing barrister, as you have just heard, if the defendant had correctly diagnosed the plaintiff’s stomach pain as a torsion of the testicle rather than prescribing antacid tablets, the testicle could have been saved by a simple operation that would have enabled the plaintiff to live the happy, fulfilled sexual life that he so richly deserves. I ask the court to award damages of five million dollars against the defendant for causing this poor man’s loss of sexual function.
Fade to scene 3: Have you found out why my car won’t start asked Jedediah. Well, I’m not sure, mister, said the mechanic, with a sarcastic look on her face, but it might have something to do with this snake that’s gotten its tail wedged in your starter motor. Mind your hands there, it looks a bit annoyed. Well golly, said Jedediah, who’d’ve thought that a little ol’ critter like that could cause so much trouble?
Three stories, three problems, three causes. Or are they?
If our heroine refuses to name the resistance leader to the Gestapo, will she have caused the civilian’s death? Or will the Gestapo officer have caused it? Or both? Or something else?
Did the doctor really cause the loss of the plaintiff’s testicle, or was it the fact that it managed to twist so as to strangulate the blood supply, or perhaps it was the plaintiff’s genes that gave them a particular anatomy that made them vulnerable to such an occurrence? If the latter then were the plaintiff’s parents the cause of the loss, or should we perhaps blame the person that introduced the parents to one another?
And was the snake really the cause of Jedediah’s car problems, or was it that he’d parked his car in the bush while camping overnight, providing an enticing warm place for any passing snakes to nestle in the warm engine?
The idea of cause and effect is an ingrained part of our language. We all feel that we know what the terms mean. But do we really? The above examples show how it’s not usually possible to point to one thing and say that is the cause of this. We might feel however that, with more care and thought, we will be able to precisely describe what really caused any given event.
The amazing answer is that No, actually we can’t. There is no such thing as a single cause of an event in the way it is traditionally thought of. The purpose of this essay is to examine the idea of cause (and effect) and work out what, if any, meaning we can give to this vague and rubbery, yet ubiquitous concept.
A natural place to start looking for a meaning seems to be to ask whether a cause is a necessary or sufficient condition, or both, for its effect to occur.
None of the suggested causes in the preface are necessary conditions. There are plenty of other ways the civilian could have died, the testicle been lost or the car failed to start. So we can dismiss necessity as a feature of causes straight away.
What about sufficiency? Neither of the suggested causes in the first two stories in the preface are sufficient conditions. The prisoner could have refused to snitch but the Gestapo officer relented and didn’t shoot the civilian. The undiagnosed twisted testicle could have untwisted by itself, or another doctor passing five minutes after the defendant misdiagnosed it could have had a look and diagnosed it correctly. The snake is another story though. Having a snake’s tail wedged in your starter motor effectively guarantees that your car will not start. So perhaps some causes are sufficient conditions for their claimed effects. We’ll come back to that later.
If I go to the dentist and ask why my lower right incisor aches, she may find decay in it and say “the cause of your ache is decay in the tooth”. The decay is neither a necessary nor a sufficient condition for the ache. The ache could be psychosomatic with no decay, or there could be decay but a dead nerve, in which case I’d feel no ache.
Yet I know what she means. So what is it that I, and any other dental patient, understands from the dentist’s statement?
I think it is that the situation I am experiencing while sitting in the dentist’s chair, call it situation S1, may be compared with another situation S2, that is identical to S1 in every respect except that there is no decay in the tooth. In neither case do I suffer psychosomatic hallucinations, nor is the tooth’s nerve dead. The only physical differences between the two situations is the decay. If a message takes a nanosecond to travel along a nerve from the tooth to my brain then in the situations one nanosecond later than S1 and S2, call them S1a and S2a, S1a will have me experiencing toothache and S2a will not.
Now the dentist has not explicitly mentioned an alternative situation, but that’s because it’s implied. I naturally interpret her statement as meaning “According to my observations and the biology they taught me at dental school, the key difference, in the toothy-brainy part of your body, between you and somebody very like you that does not have a toothache is that you have decay and they do not”.
We can formalise this idea of a cause with a precise definition:
- S1 and S2 are descriptions of alternative possible states of a system at time t, and
- the difference between S1 and S2 is C, and
- theory T requires that event E occurs at time t+dt if the system state at time t is S1, and
- theory T requires that event E does not occur at time t+dt if the system state at time t is S2,
then C is the cause of E in system state S1 with respect to system state S2, according to theory T.’
Note that lines 3 and 4 use the concept of sufficiency, raised in the previous section. S1 is sufficient reason for E to occur and S2 is sufficient reason for E to not occur.
People rarely, if ever, refer to two alternative system states when saying something is a cause. Usually, as with the dentist, the natural choice for S2 is evident and need not be stated. But it is useful to remember that there is nearly always an implied comparison state S2 when we talk about causes. Whenever controversial or confusing claims are made about causality, as happens so often in litigation, politics and philosophy in particular, it can help enormously if we analyse the claim by trying to identify what the implied comparison state is.
The appendage to the definition – ‘according to theory T’ – might seem superfluous and annoying to some. After all, people don’t usually quote a theory when they say that pricking the balloon with a needle caused it to burst. Nevertheless, just like the comparison state, a theory is always there. In the case of the balloon, the theory is Physics, as taught at modern universities. Training in Physics up to third-year university would provide all the understanding needed to explain the pop of the balloon.
Looking at the dentist example, we see that our interpretation of her diagnosis does include reference to a theory, viz: ‘according to … the biology they taught me at dental school’.
Now we might imagine that both Physics and Biology are just parts of a Grand Theory of Everything, of which science has so far only discovered a portion. If that were so, then we could leave off the appendage to our description of a cause, and just imply that the theory we mean is the Grand Theory of Everything.
But although some might find the Grand Theory of Everything a nice idea, and wish there really were one out there, we have no reason to suppose there is. I discuss this further in my essay ‘Some random thoughts on whether the world is random’. The conclusion is that, unless we are prepared to regard an enormous list of everything that ever happens in the universe as a theory of everything (which most people wouldn’t) there is no way to decide what sort of a collection of statements could qualify as such a theory. Is there a word limit? Does the collection have to be finite? Does it have to be expressible in English? Does it have to be comprehensible by an intelligent human?
In addition, as I argue in my essay ‘Replacing Truth with Reason’, there may not even be any ultimate description of the universe. Our scientific advances may lead to increasingly more complicated theories that, while intriguing, exciting and pragmatically useful, never converge to a final, stable, ultimate theory. Perhaps the universe is too complicated to be described by any theory.
So we will have to put up with the appendage for the time being. Devout Platonists may wish to assume that there is a Grand Theory of Everything, and omit the appendage, implying that T is that Grand Theory. But that is an act of faith that I do not feel inclined to emulate.
It does however seem reasonable to omit the appendage when conversing in the vernacular, if our implication is understood to be not that T is the Grand Theory of Everything, but that it is “Science as taught at universities, in the year in which we are speaking”. I will call this Science 2013, as that is the year in which I am writing. This ties the use of ‘cause’ to a sense of what the best scientists in the world currently understand about how the world works, and that seems to me to pretty accurately reflect how the person in the street would understand the term ‘cause’.
When discoursing philosophically though, as in this essay, it will be wise to retain the appendage specifying the reference theory, in order to be clear.
Some scenarios in which we might like to talk of causes do not naturally suggest comparison states. We might for instance consider the Cosmic Microwave Background Radiation (CMBR) that suffuses the sky, which is left over from the ‘last scattering surface’ of the Big Bang. We want to say that the Big Bang caused the CMBR. But we are stymied by the fact that we cannot think of an alternative situation with no CMBR. That situation would have to have no Big Bang, and hence possibly no spacetime, and hence no place in which to observe the lack of CMBR.
Here is an alternative definition of ‘cause’ that solves that problem.
‘If S is a description of a physical system at time t and theory T requires that event E occurs at time t+dt if the system was in state S at time t, then we say that S is the cause of E in system state S, according to theory T.’
In most situations this definition will be useless, because it requires a full description of the system state at the prior time. In order for E to be inevitable, that will have to be something like the location, momentum, type and spin of every particle within radius c.dt of the location of E (c is the speed of light) at time t. That is way too much information for everyday use. It’s a bit like saying ‘everything’ is the cause of E. But it may be useful to have this definition available as an alternative if we want to talk about causality in relation to situations that don’t have natural comparison scenarios.
In order to distinguish our two definitions of cause we’ll call the first one the Comparative Definition and the second one the Singular Definition. If we don’t specify, we’ll mean the Comparative definition because that’s likely to be most often the one we mean.
Looking back at the snake’s tail story, we can see that that meets the definition of a Singular cause of the engine not starting, if the tail is still wedged in the starter motor when the electric current unleashed by the ignition key hits the coils in the motor. If the time the current hits the coils is t, then we can say that the configuration of a spherical region of space with radius 10cm centred at the middle of the starter motor is the cause of the engine not commencing to fire at t+3.3×10-10 seconds, and that region includes the wedged snake’s tail.
A Singular cause is always sufficient for its effect, but the price we pay for that sufficiency is that the cause either has to be a complete description of the state of an enormous volume or, as is the case with the snake’s tail, the effect must occur a very tiny interval of time after the cause (a third of a nanosecond here).
The two definitions I have suggested require a cause to be earlier than its effect, which we call being ‘temporally prior’. Sometimes people talk of causes that are not temporally prior, so we should consider whether that can make sense. There are two common ways people do this.
Some people give examples of what they think are physical causes that are simultaneous to their physical effects. They all turn out however, to be based on a misunderstanding of physics. There is a very simple reason why one physical event cannot cause another that happens at the same time, and that is the principle of relativity, which states that physical influences cannot travel faster than the speed of light. For event E1 at time t to affect event E2, also at time t, would require the influence of E1 to travel the distance between the two locations in no time at all, that is, at an infinite speed, which would break the speed limit and irritate the Great Cosmic Traffic Cop.
Examples offered of putative simultaneous causes are
- a ball (cause) sitting on a pillow and causing a depression (effect), or
- pushing one end of a lever down (cause) so the other end goes up (effect).
It is not the ball’s presence at time t that causes the depression in the pillow at time t, but the ball’s presence at earlier times. We can see this by imagining the ball suddenly magically pouffing out of existence. The pillow would not instantly regain shape. Rather it would start to spring back to its original, undepressed shape. If the ball were present on the pillow up to time t and instantly then disappeared, the shape of the pillow at time t would be exactly the same as if the ball were still there. The depression would gradually disappear as the pillow started to regain its usual shape after time t. In the real, non-Harry Potter world, change takes time.
Similarly, the footpath of a bridge does not stay up because its supporting beams are there, but because those beams were there an instant earlier.
When we push down one end of a lever, the other end does not instantly lift. Rather, a shock wave travels through the lever, deforming it in such a way that, a tiny instant of time later, the other end lifts. The shock wave travels at the speed of sound in the lever, which will be very fast indeed if it is made of a stiff substance like steel, but still much slower than light. Because the wave is so fast, we cannot perceive it without specialised equipment, so the effect seems instantaneous. If we had a fast enough camera, we might even be able to film the deformation of the lever as the shock-wave passes through. But we’d need an enormous enlargement of the frames to see the lever’s deformation in the film, because the shockwave of the initial push has probably reached the other end before the end we are pushing has moved a millimetre.
Readers who are familiar with the Quantum Mechanical phenomenon of entangled particles might hope for a loophole in the cosmic speed limit via the fact that, when one member of a pair of entangled particles is measured, the wave function collapses and the other member attains a definite value of the measured quantity.
This ‘spooky action at a distance’ as Einstein called it, does not however break the speed limit, because no physical influence is being transmitted. The wave function is simply a mathematical abstraction we use in Quantum Mechanics to make predictions and its collapse has no physical significance. In particular, there is no experiment we can do to find out whether the wave function of a particle has already collapsed. It will collapse when we make the measurement in the experiment, but that cannot tell us whether it had already collapsed before that.
So in summary, there is no escape from the cosmic speed limit, and hence there is no such thing as a simultaneous physical cause.
Another way people try to escape the need for temporal priority is to talk of a cause as something ‘non-physical’ that entails its effect via the laws of logic rather than of science. They could for instance say that the rules of arithmetic are the cause of 2+2 equalling 4, or that the fact that all men are mortal and Socrates is a man is the cause of Socrates being mortal.
This could be formalised by saying that if A→B where A and B are propositions and → denotes logical entailment (if the proposition before the arrow is true then the proposition after the arrow must be true) then A is the cause of B. Let’s call it a Logical Cause to distinguish it from the Comparative and Singular definitions of causes that we discussed above. In this context only, we will refer to causes meeting those definitions as ‘physical’ causes. Defining ‘physical’ is usually a controversial mess. But here all we mean by ‘physical cause’ is a cause that satisfies our Comparative or Singular Definitions.
There’s nothing incoherent about defining logical causes this way. No contradictions or ambiguities arise. The trouble is just that it’s a completely different use of the term cause from how it is used in relation to everyday physical things, so one cannot apply any conclusions drawn about physical causes to logical causes, or vice versa.
Further, there is already a perfectly good word in use within the field of symbolic logic for a logical cause. It’s called an antecedent. And the thing coming after the arrow is called a consequent.
So all we achieve by using ‘cause’ in this context is confusion, by applying a word that has a meaning in a different, completely unrelated field (the physical) to a concept that already has a perfectly clear label in this field.
Readers should beware of arguments that try to use logical causes. Such arguments might use words like ‘now consider causes that are logically prior rather than temporally prior to their effects’. The only reason I can think of to use the word ‘cause’ for a logical antecedent is to try to smuggle in some of the properties of physical causes and apply them to logical causes, without the validity of doing that being challenged. As logical and physical causes have no relation to one another, other than in a vague, touchy-feely sort of way, it is invalid to apply any properties of physical causes to logical causes.
Another problem of not requiring causes to be temporally prior is that it creates ambiguity as to which of the two events is the cause and which is the effect. In the physical case, this is clearly resolved by requiring a cause to be earlier than its effect. We lose that capacity if we don’t require temporal priority.
In the logical case, if we have A→B but not B→A then we can say, if we wish, that A is a Logical Cause and B is its logical effect. But if we have both A→B and B→A then there is no basis for saying one of A and B is the cause and the other is the effect. We will see in the next section how this can lead to grief.
Causation in philosophy
More than 2000 years ago Aristotle thought and wrote about causation, in a way that has been adopted by many philosophers since then. He listed four types of cause, of which only one, the Efficient Cause, is close to the way the term is typically used now. Unfortunately, even the notion of an Efficient Cause is bound up with Aristotle’s ideas about physics which, being pre-Newtonian, are incompatible with the way we now understand the world to work.
Nevertheless, philosophers still blithely make arguments using the word ‘cause’, only rarely pausing to consider what if anything the word actually means, and whether it really belongs in their arguments. A notable exception is Bertrand Russell in his marvellous 1912 essay ‘On the notion of cause’.
Here are a couple of examples of how ‘cause’ is used in philosophical arguments, and how we can use the considerations above to understand them better.
There is a very old and venerable argument that there must be a being (God) that is the cause of the universe’s existence. There are a number of versions, including a popular one that has been revived recently, based on a medieval Islamic argument from the Kalam school. All versions of the argument rely on God being a Cause for the universe. An obstacle to all these arguments is that there can be no ‘before’ the universe, as time is itself a feature of the universe, not something that applies outside it. So there cannot be a cause that temporally precedes the universe. Devotees of the First Cause argument sometimes respond that God is logically prior, rather than temporally prior to the universe. That is, God→Universe.
There are two problems with this argument.
Firstly it relies on a premise that every object of a certain type must have a cause. It tries to generate support for that premise by appealing to our experience, and all the examples used are of physical causes. Hence the premise is restricted to physical causes and tells us nothing about non-physical causes, which is what the argument wishes to argue God is. This is a smuggling attempt, of the kind discussed above.
Secondly, what the argument actually does is to reason from the existence of the universe to the existence of God. That is, Universe→God.
But now we have a situation that is logically symmetrical between God and the Universe, which a logician would denote as God↔Universe. Each implies the other, so we cannot say that one is logically prior. One might be tempted to say that there was a time, before the creation of the universe, when there was only God and no Universe, which makes God prior, and hence the cause. But that route is forbidden because it relies on the existence of time, which is part of the Universe.
So the philosopher that pursues this route is committed to saying that, if there is a God, then it is caused by the Universe as much as it causes the Universe.
Such a conclusion is likely to satisfy neither theist nor atheist, and demonstrates quite nicely the futility of trying to reason about causes that do not temporally precede their effects.
Epiphenomenalism is a hypothesis that says mental events (consciousness) are caused by physical events in the brain, but have no effects upon any physical events. In other words, brain activity causes consciousness, but consciousness does not cause any brain activity.
For this to be the case, given our definition of cause, a mental event must occur after the physical (presumably brain) event to which it relates. Hence the brain event can be a cause of the mental event, but not vice versa.
Importantly, if the mental event occurs simultaneously with the related brain event then we cannot say that either causes the other, because neither precedes the other. This is a crucial observation because sometimes people talk about Epiphenomenalism as if it is a simultaneous occurrence caused by the contemporary brain activity. However, as we have seen above, for simultaneous events there is no way to identify which is cause and which is effect. So a mind-body model that involves simultaneous processes is not Epiphenomenalism.
Does all science rest on the assumption that everything has a cause? It might seem so, and this claim is often made, but it’s wrong. Science doesn’t need everything to have a cause, to be useful. Science rests on the observation that there are patterns in nature, such that systems appear to evolve in regular, repeatable ways that can be described by natural laws. If we can discover such a law, by inventing theories based on experimentation, and then testing the theory’s predictions using further experiments, then we may be able to predict future events, and shape the course of those events.
So science is best described not as a search for causes, but as a search for laws that describe how physical systems evolve.
We don’t even need to believe that everything is governed by natural laws. For instance, some interpretations of Quantum Mechanics hold that there is no law determining the precise time at which a radioactive particle will decay. The apparent absence of a cause for that particular aspect of reality does not however prevent us from making very precise predictions about the behaviour of physical systems using Quantum Mechanics.
In science we don’t need to have causes for everything, or even to believe they exist. At most we need causes for the important features of the system we are evaluating.
An important concept in physics is that of the light cone. For a given point P in spacetime, the past light cone is the set of all spacetime points from which a particle could have travelled prior to passing through P. There is also a future light cone, which is the set of all spacetime points that can be reached by a particle that first passes through P. The particles in question may be photons, which travel at the speed of light, or slower particles with mass, like electrons or cricket balls.
Physicists talk about two spacetime points as being ‘causally connected’ if one is in the other’s past light cone. This means that the later point can be affected by something that happens at the earlier point. Events at points that are not causally connected cannot affect one another. That is, changing what happens at one point will have no impact on the other. Such points are called space-like separated points.
For point P, the future light cone marks out the limits of the points P can causally influence, and the past light cone marks out the limits of what points can causally influence P. Hence the light cones are regarding as showing the limits of causality.
This usage harmonises with both our Comparative and Singular definitions. In the Singular definition, the cause (according to Science 2013) of an event E at spacetime point P, with time coordinate t, is the state of the set R of all points in P’s past light cone that have time coordinate t-h for some positive h. In the Comparative definition, if S1 and S2 are alternative possible states of R, such that E happens at P if R has state S1 but not if R has state S2, then the difference C between S1 and S2 is the cause of E in S1 with respect to S2, according to Science 2013.
It might seem that the light cone perspective adds an additional constraint to causality above the constraint in our definitions that causes must precede effects. For not only must the cause precede the effect, but it must also lie in the effect’s past light cone.
It turns out that, because of the theory of relativity, this is not an additional constraint at all. We can only say unambiguously that C precedes E if C is in E’s past light cone, because then the time of C will be earlier than that of E in every possible reference frame. If C is in E’s future light cone we can say unambiguously that E precedes C, so C cannot be a cause of E. That much is obvious. But if C is in neither the future nor the past light cone of E, it will be later than E in some reference frames and earlier than E in others. Einstein’s theory of relativity tells us that no reference frame is any more valid than any other, so C cannot be a cause of E if there is even just one reference frame in which it occurs after E (in fact if there is one such frame then there will be infinitely many).
This last consideration tells us that, if we ever discovered particles or other influences that could travel faster than light, it would destroy our notion of causality entirely. Because then we would have pairs of events that we thought were cause and effect, for instance the beginning and end of a path followed by one of these particles, but for which in some perfectly valid reference frames the effect preceded the cause. We would have to either jettison the notion of causality entirely, or develop a completely new one, that may only have very slight similarities to the existing one.
It is fortunate for us then that the superluminal neutrino speeds observed in experiments in 2011-12 turned out to be experimental errors.
In both our definitions of Cause we say theory T ‘requires that’ the effect occurs after the cause. However quantum mechanics tells us that nothing is certain to happen. Things we think of as inevitable are really only very, very likely. How then can we meaningfully talk of an effect being required to occur after its cause?
One solution is to replace statements of certainty by probability statements. We could replace ‘theory T requires that’ by ‘under theory T there is a greater than 99.9% probability that’. Here T is of course Quantum Mechanics. If we make this substitution in the Comparative Definition (twice, for the two instances of ‘theory T requires’) and the Singular Definition (once) then these definitions are ship-shape and ready to be used in the Quantum Mechanical world.
We might wish to go further and call C a cause if the probability of E occurring after S1 is lower than 99.9%, say 50%, and the probability of E not occurring after S2 is still 99.9%. In that case C is a sort of enabling condition for E to occur, but it does not guarantee it. If we wanted to go down that route it would be better to give this type of relationship a slightly different name like ‘probabilistic cause’, to avoid confusion with the cases where C makes E almost certain to occur.
A famous dictum that is often used in both science and social studies is ‘correlation does not imply causation’. Let’s put our Comparative Definition to the test to see if it supports this uncontroversial dictum. But because medical and social sciences are quite complex, we’ll use an example involving something simple instead – bowling alleys.
Imagine that a bowling alley has an easily depressed light switch placed in the middle of the alley, 20cm away from the central lead skittle. When depressed, the switch closes an electric circuit that illuminates a light above the skittles. After watching a few matches we notice that the light goes on for a fraction of a second and then off, immediately prior to every strike (knocking down all ten skittles). We have observed a correlation between illumination and strikes, and we wonder whether the light causes a strike.
First we compare two situations, describing the region R around the bowling alley, at the time a ball that has been bowled passes the switch. The situations S1 and S2 are identical except that in S1 the ball is on the switch and illuminating the light, while in S2 the ball is to the left of the switch, too far left for a strike to occur, and the light is not illuminated. The region R is large enough that nothing that is outside R when the ball passes the switch can change whether a strike occurs.
In S1, Science 2013 requires that a strike will shortly occur and in S2 it requires that a strike will not occur. So our definition of cause is satisfied. We can say that the difference between S1 and S2 caused the strike after S1. But what is the cause we have identified? It is everything in S1 that is different from S2.
That includes the light being on but it also includes the ball being in the middle of the lane. We could if we wish say that B caused the strike where B is ‘the light being on and the ball being in the middle of the lane’. The latter is consistent with what a lay person would think of as being the cause, so that’s a good start. It is reasonable to describe B as the cause. The bit about the light seems superfluous though. Can we get rid of it?
Yes we can, as follows. We add a new situation, S3, which is the same as S2 except that someone stands on the lane, avoiding the ball, and briefly depresses the light switch as the ball passes, if the ball does not itself roll over the switch. Now let’s compare S2 and S3. In both cases there is no strike. They are identical except for the man standing on the lane and the light being on. So it appears that the light being on is not a cause of a strike. The light illumination is correlated with, but not causative of, strikes.
This confirms that the Comparative Definition can, at least in this case, reproduce results that accord with our intuitions about causation.
We have developed a definition of cause – the Comparative Definition – that captures the everyday meaning of the term while removing ambiguity. The price of the additional accuracy was having to specify a comparison scenario S2 and a reference theory T.
For cases where a comparison scenario is not readily imaginable, we have an alternative definition – the Singular Definition – that still captures the commonly understood meaning. The price of this additional power is having to specify the prior scenario – the ‘cause’ – either over an enormous volume of space or a tiny period of time prior to the effect.
We have seen that an essential feature of any useful, unambiguous notion of cause is that it requires causes to precede effects in time. We observe that invocation of simultaneous causes or logical causes is usually a symptom of a flawed argument.
We have identified a way to generalise the notion of cause to handle the uncertainty that comes from Quantum Mechanics, by including probabilities in the description of a cause.
We have observed how these definitions of cause can be used in practice in a variety of fields of inquiry.
Finally, if we can take any ‘moral’ from this rather prolonged meditation, it is that in any argument that relies on notions of cause we should examine closely how the term ‘cause’ is used and what properties are ascribed to it in the argument. If this is not clearly set out, the argument may well have hidden flaws or, in some cases, be incoherent, no matter how plausible it may sound.
Andrew Kirk. Bondi Junction, 8 June 2013