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The Pragmatic Roots of Context - Bruce Edmonds

2. Causal Structure

In any but the simplest (e.g. linear) systems, effects can have a great many causes (when modelled in absolute terms). In most systems, the web of causation is so dense that the number of factors that could be included in a model of an event is limited only by the resources we put into it. This is what has been called "causal spread" by Wheeler and Clarke in
[19]. It has led some philosophers to argue that many (i.e. non-statistical) notions of causality are only meaningful for simple systems (e.g. [18]). This causal spread makes the complete modelling of an event impractical - we are forced to concentrate only on a small subset of possible factors. Of course, this omission of factors in our models is only effective if either they are so reliable that their omission is unimportant for practical purposes or if we are able to recognise when our restricted model is likely to be applicable. In either case we will not attempt to use the model when it is inapplicable.

Formalisations of causality always involve assumptions about the set of possible factors. Usually they merely present a test which can be used to reject the hypothesis that a given factor or variable is causally irrelevant. The strongest formulation I have found is that of Pearl [15]. He presents an algorithm for finding all the factors that are causes, but under the assumption that no causally relevant factor has been omitted from the initial set of possible factors.

I will illustrate this "causal spread" with two examples, which will be used to motivate the approach that follows. The first is the causation involved in a man breaking a leg and the second the inference involved in interpreting an utterance.

Example 1. A man is distracted and falls off a small ledge onto a pavement. When he lands his leg breaks. What caused his leg to break? It could be attributed to many things: the hardness of the pavement; the weakness of his femur; the way he landed on the leg; gravity; the mass of his body; him falling off the ledge; the ledge itself; the height of the ledge; the distraction; or even the man's distractability. There seems to be no end to the number of factors one could include as causes of the fracture. Whether one does count each of these as causes is arbitrary from an absolute external viewpoint. It can depend on the extent to which we judge each of them as unusual. For example, if the ledge was there due to a freak subsidence we might say that this subsidence was the cause - if the ledge was normal (the side of some steps) but the distraction was exceptional (there was a couple making love in the middle of the street) we would say the distraction was the cause.

Example 2. Two people, Joan and Jill, are talking: Joan says "We'll go and have a friendly chat in a bar."; Jill replies "Yeah, right!" which is (correctly) taken to mean by Joan that Jill thinks that this is a bad idea and does not want to go. In what way was the negative message conveyed? In other words, what allowed Jill to infer the meaning of Joan's utterance? There could be many such factors: the tone of Jill's voice; that the peer group to which Jill and Joan belong always say "Yeah, right!" when they disagree; that Jill is pointing a gun at Joan; that they are both are locked away in jail and so the suggestion was impossible to carry out; that Jill had been neurotically repeating "Yeah, right!" over and over for the past two years since her sister died etc. The answer could have been any one of these or any combination of them. Even if many of these factors were present Joan may have only used one or two of them in her inference, the rest being redundant.

Our models of the world (physical or social) are distinctly limited constructs. We could not possible learn useful models of our world if we had to include all the possible causes. In practice, we have to restrict ourselves to but a few causes that we judge to be the significant. The means by which we reach such judgements can vary greatly depending on the circumstances (including our knowledge etc.).

In general (as developing human beings) we start by learning simple models of our world, i.e. those with only a few explicated causes and only introduce more causes as we need to. The more causes we include in our model the more generally applicable, but also the more unwieldy, it becomes. If we are lucky, the natural world is so structured as to allow us to abstract away some of this detail and find a more generally applicable model for certain aspects that are relevant to us. Sometimes we can construct models that have sufficiently wide conditions of application that it is convenient for us to consider them as general truths. However, such cases, are exceptional - they tend to be highly abstract and so to apply them one typically has to bring the cluttering detail back in to the model in the process of applying it to a particular situation. In many models in the field of physics, this detail is frequently bought in as either initial conditions or auxiliary hypotheses.

In this paper I want to consider aspects of the more usual models we learn and apply, not the exceptional ones that are we consider as generally applicable. There is a view that somehow more general models are better, because they are not restricted to particular domains of applicability, and hence should be the focus of our study. According to this view more specialised knowledge should be represented as specialisations of these `general' models. I dispute this - I contend that although there is great theoretical economy of representation in the more abstract and generally applicable models, the huge difficulties of applying them to common situations often precludes them as a sensible way to proceed. It would be incredible indeed if it just so happened that the world was constructed so that it was always sensible to work via the most general structures possible!

The Pragmatic Roots of Context - Bruce Edmonds - 31 MAR 99
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