Monday, April 12, 2010

What is a Cause? (Part 2) Crossing the Desert

This post is part of my series on Steve Sloman's book Causal Models. For an index, see here.

I am currently working my way through Chapter 3 of Sloman's book which offers a basic introduction to the concept of causation. At the close of Part 1, causation was defined in terms of counterfactual dependence. In this part we will cover some of the problems with this definition.

1. Crossing the Desert
The problems facing the counterfactual definition are well illustrated by a famous thought experiment. I have encountered many versions of this but here I will stick with Sloman's version.

A Sheik, with a well-stocked harem, is setting out on a journey across the desert. Obviously, deserts are not always the most congenial of environments, so he needs to take some precautions. In particular, he needs to ensure he has plenty of fresh water in his water canteen.

Unbeknownst to him, all is not well in the harem. His wife and one of his mistresses are independently plotting his demise. The wife poisons the water in his canteen, while the mistress punctures the canteen so that the water slowly leaks out.

The Sheik sets out on the journey. After a few miles he feels parched. He unscrews the cap on his canteen and finds, much to his displeasure, that it is empty. He soon dies of dehydration.

Question: who caused the Sheik's death, the wife or the mistress?

2. The Mistress...Duh
The answer seems obvious to most: the mistress clearly caused the death of the Sheik. After all, he dies from dehydration not poisoning.

But this answer poses certain problems for our counterfactual definition of causation. The counterfactual definition envisages a "but for" relationship between cause and effect. Applying this to the case at hand, this entails that we must be able to say "but for the actions of the mistress the Sheik would not have died".

This statement is clearly untrue when applied to the scenario above. If the mistress had not punctured the canteen, the Sheik would still have died.

Our definition must be expanded to cover scenarios of this sort. The expansion must allow our definition to be sensitive to what actually happens while at the same time retaining the "possible worlds" aspect of causation.

This is a difficult task. Are there any solutions?

3. Mackie and the INUS
As a matter of fact there are. Perhaps the most famous attempt to deal with problem cases of this sort is that of JL Mackie. Sloman gives a quick summary of Mackie's definition, although he recommends reading the original.

It should also be noted that Sloman's book is not really about these philosophical puzzles so his discussion of Mackie is an aside.

Mackie argued that a "cause" is really only one element in a larger entity, namely a "sufficient set". The sufficient set consists of all the conditions that led to an effect. In the case of the Sheik's dehydration, the sufficient set would include: the biological needs of the human body; the physical environment of the desert; the Sheik's intention to cross the desert and the mistress's actions.

The sufficient set is not, by itself, necessary for producing an effect. This is obvious in the example given: we know that the sufficient set just described was not necessary for bringing about the Sheik's death; he could also have died from poisoning.

Mackie argued that a "cause" is actually an INUS, which is "An Insufficient but Necessary element of an Unnecessary but Sufficient set". Quite a tongue-twister, I'm sure you'll agree.

What singles out the mistress's actions as the true cause of the Sheik's death is that they are an INUS: the puncturing of the canteen is one (I) of the critical elements (N) in one (U) of the large set of conditions that led to the Sheik's death (S).

The poisoned water was not an INUS because the sufficient set that would have involved the Sheik drinking the water did not obtain.

4. Causal Graphs
Sloman's approach to causation involves the use of causal graphs. These are simple "box-and-arrow" diagrams where the boxes represent events and the arrows represent causal relations. He defines a cause as anything that can be represented as an arrow in a causal graph.

If that sounds philosophically suspicious (defining cause in terms of causal arrows?) that's because it is. Sloman acknowledges this but argues it is okay because the framework can explain how human beings use causal knowledge.

The causal graph approach actually suggests a simple answer to the Crossing the Desert thought experiment. There is a potential causal pathway leading from the wife's actions to the sheik's death; there is also a potential causal pathway leading from the mistress's actions to the sheik's death. However, the mistress's causal pathway interrupts or displaces the wife's causal pathway. This is illustrated below.

This approach to causation is developed to a much higher degree of sophistication in Chapter 4 of Sloman's book. We will be looking at that in due course.

5. Other Types of Invariant
Sloman closes chapter 3 by looking at how broad our theory of causation should be. He notes that a theory that explains everything explains nothing. There is then a fear that the theory of causal modeling outlined in his book could be explanatorily empty.

Sloman tries to head-off this criticism by looking at the concept of invariance. In chapter 2, Sloman had argued that causation is a type of invariance. In this chapter 3 he notes that it is not the only type of invariance. And since the theory he develops does not cover all types of invariance it is not, prima facie, explanatorily empty.

Other types of invariance would include part-whole relations, class-subclass relationships. These types of invariance are covered by set theory. This theory deals with a variety of logical relationships but it does not deal with the logic of causal intervention (as we shall see).

Likewise, probability theory covers other types of invariance (frequencies etc.) and overlaps considerably with causation theory. However, they are not equivalent. This is because probabilities can be applied to correlations and, as we saw in Part 1, correlation is not causation.

In the next entry in this series I will look at Chapter 4 of Sloman's book.


  1. Creationists often try and link Darwin to Hitler:

    Wiekart in his book claims "“Darwinism was not a sufficient condition for Hitler’s atrocities, but it was a necessary condition.” Without Darwinism, I believe, Germany would have resisted Hitler. It was not the only necessary link leading up to Nazism, but it was one of them."

    I disagree with that claim, but it suggests a chain or tree of causes all of which were required but none in isolation would be sufficient.

  2. Historical causation is almost impossible to work out since you can't perform the manipulations required to make a counterfactual claim.

    Peter Turchin tries to deal with some of these issues in his work as far as I know, but I can't comment meaningfully since I haven't studied it in sufficient depth.

    I haven't looked into Wiekart much. He seems to be suggesting that Darwinism was an INUS but I'd say that's a somewhat meaningless claim if - as I suspect - it is meant to have some contemporary relevance. Why? Because if the worry is that Darwinism will lead to a recrudescence of Nazism, then it would need to be shown that the exact same sufficient set as obtained in 1920s Germany is currently in existence. I doubt that could be sustained.

    I presume you are familiar with R.G Price and Hector Avalos's responses?

  3. Sadly I am not familiar with them, John, but point me in the right direction and I'll a look.

    With regard to causation (or lack thereof), you might want to touch on correlation, lurking variables and multicollinearity as well.

  4. And Weikart seems to be 'arguing to consequences' - he's a fellow of the discovery institute, the right wing organization behind 'intelligent design'.

  5. Yeah I knew about Weikart's association.

    R.G. Price's response is available here (focuses mainly on criticisms of Darwin himself):

    Avalos's here (focusing mainly on the role of Protestant anti-semitism):

    He also has some version of this response in The Christian Delusion (edited by John Loftus).

  6. Do you mind expanding a bit on how causation is a type of invariance? Do you mean that the past-future correlations are invariant to changes in unrelated experimental variables?

  7. Well Sloman goes into this a bit in Chapter 2 of his book. I skipped over it. He's refer to features of our conceptual universe (like causal relations, or taxonomic and part-whole relations) that remain constant in the face of changes to other variables.

    He brings it up when discussing perception. He says animals have selective attention and that they mainly attend to invariants. He has a few examples of this. The one that struck me the most concerned collision detection, i.e. the ability to tell how soon an object will collide with you.

    If an object is traveling at a constant velocity (a big assumption, perhaps) then there is an invariant relationship between the size of the image of the object on your retina and the time to collision. (Divide image size by rate of expansion to get time to collision).

    He claims research on locusts suggests they have neurons dedicated to this task. Alas he doesn't give a specific reference.

  8. Hilary Putnam makes a very interesting argument in The Many Faces of Realism that underscores the notion that "every effect has its cause" isn't as simple a notion as it appears.

    Putnam invites us to imagine a pressure cooker on which the safety valve has jammed, causing the cooker to explode. Why did the cooker explode? We say that the cooker exploded because the valve failed to open. We don't say that the cooker exploded because an arbitrary section of the wall of the cooker, say one centimeter square, was in place and hence retained the steam, even though, from the perspective of physics, the stuck valve and this arbitrary section of cooker wall play identical roles: the absence of either would have allowed the steam to escape and averted the explosion.

    Why do we insist that the faulty valve caused the explosion, and not an arbitrary area of the wall? Because we know that the valve "should" have let the steam escape - that is its function, what it was designed to do. On the other hand, the arbitrary bit of surface was not doing anything wrong in preventing the steam from escaping; containing the steam is the function of that patch of cooker surface. Hence, in the instance of this human artifact, there is an inescapably normative element to what superficially appears to be a simple physical relationship of "cause and effect."

    Putnam concludes that, in asking "Why did the explosion take place?" - and knowing what we know and knowing what interests we have - our explanation space consists of the alternatives:

    (1) Explosion taking place.
    (2) Everything functioning as it should.

    What we want to know is why (1) is what happened, as opposed to (2). We are simply not interested in why (1) is what happened as opposed to an infinite collection of alternatives such as,

    3) An arbitrary patch of surface is missing, and no explosion takes place.

    In short, our interests dictate that the presence of a given area of the wall of the cooker, and countless other facts about the physics of the explosion, take their places as background conditions rather than causes of the explosion. This discrimination between causes and background conditions cannot be provided by an account of the explosion supplied by mathematical physics, because the normative, designed aspects of the cooker cannot be deduced or described at the level of physics. Consideration of causation in this sense requires knowledge of the history of the mechanism - the story of its origins and purpose - in addition to its present physical state. Hence an irreducible explanatory relativity must be introduced if we are to understand the cause of this explosion.

    This is not, however, to say that there is no objective adjudication to be had regarding the truth of the assertion that the stuck valve caused the explosion. Quite the contrary. Once we have specified our interests, given the nature of our language, and, indeed, given our scientific practices (all of which help us discriminate foreground and background), it would be simply false to say that the wall of the pressure cooker caused the explosion - even though the physics of the explosion dictate that had that area of wall not been present the explosion would not have occurred. Indeed, it is only once we have identified our conceptual commitments and interests that the determination of the cause of the explosion at the level of our interests becomes an adjudicable, objective fact.

    (Recycling one's own stuff is not really plagiarism.)