Induction, novelty and possibilistic causality

The concept of induction normally bundles together a number of stages, of which the key ones are modelling and extrapolating. Here I speculatively consider causality through the ‘lens’ of induction.

If I perform induction and what is subsequently observed fits the extrapolation then, in a sense, there is no novelty. If what happened was part of an epoch where things fit the model, then the epoch has not ended. I only need to adjust some parameter within the model that is supposed to vary with time.  In this case I can say that conformance to the model (with the value of its variables) could have caused the observed behaviour. That is, any notion of causality is entailed by the model. If we consider modelling and extrapolation as flow, then what happens seems to be flowing within the epoch. The general model (with some ‘slack’ in its variables) describes a tendency for change, that can be described as a field (as Smuts does).

As with the interpretation of induction, we have to be careful. There may be multiple inconsistent models and hence multiple inconsistent possible causes. For example, an aircraft plot may fit both civil and military aircraft, which may heading for different airports. Similarly, we often need to make assumptions to make the data fit the model, so different assumptions can lead to different models. For example, if an aircraft suddenly loses height we may assume that it had received an instruction, or that it is in trouble. These would lead to different extrapolations. As with induction, we neglect the caveats at our peril.

We can distinguish the following types of ‘surprise’:

  1. Where sometimes rare events happen within an epoch, without affecting the epoch. (Like an aircraft being struck by lightning, harmlessly.)
  2. Where the induction was only possibilistic, one of which predictions actually occurred. (Where one predicts that at least one aircraft will manoeuvre to avoid a collision, or there will be a crash.) 
  3. Where induction shows that the epoch has become self-defeating. (As when a period aircraft flying straight and level has to be ended to avoid a crash – which would end the epoch anyway).
  4. Where the epoch is ended by external events. (As when air traffic control fails.)

These all distinguish between different types of ’cause’. Sometimes two or more types may act together. (For example, when two airplanes crash together, the ’cause’ usually involves both planes and air traffic control. Similarly, if a radar is tracking an aircraft flying straight and level, we can say that the current location of the aircraft is ’caused by’ the laws of physics, the steady hand of the pilot, and the continued availability of fuel etc. But in a sense it also ’caused by’ not having been shot down.)

If the epoch appears to have continued then a part of the cause is the lack of all those things that could have ended it.  If the epoch appears to have ended then we may have no model or only a very partial model for what happens. If we have a fuller model we can use that to explain what happened and hence to describe ‘the cause’. But with a partial model we may only be able to put constraints on what happened in a very vague way. (For example, if we launch a rocket we may say what caused it to reach its intended target, but if it misbehaves we could only say that it will end up somewhere in quite a large zone, and we may be able to say what caused it to fail but not what caused it to land where it did. Rockets are designed to operate within the bounds of what is understood: if they fail ‘interesting’ things can happen.) Thus we may not always be able to give a possible cause for the event of interest, but would hope to be able to say something helpful.

In so far as we can talk about causes, we are talking about the result of applying a theory / model / hypothesis that fits the data. The use of the word ’cause’ is thus a short-hand for the situation where the relevant theory is understood.

Any attempt to draw conclusions from data involves modelling, and the effectiveness of induction feeds back into the modelling process, fitting some hypotheses while violating others. The term ’cause’ is suggestive that this process is mature and reliable. Its use thus tends to go with a pragmatic approach. Otherwise one should be aware of the inevitable uncertainties. To say that X [possibly] causes Y is simply to say that one’s experience to date fits X causes Y, subject to certain assumptions. It may not be sensible to rely on this, for example where you are in an adversarial situation and your opponent has a broader range of relevant experience than you, or where you are using your notion of causality to influence something that may be counter-adapting. Any notion of causality is just a theory. Thus it seems quite proper for physicists to seek to redefine causality in order to cope with Quantum Physics.

Dave Marsay

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About Dave Marsay
Mathematician with an interest in 'good' reasoning.

One Response to Induction, novelty and possibilistic causality

  1. Pingback: Science advice and the management of risk | djmarsay

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