Wesley Salmon, Statistical Relevance and Causal/Mechanical Explanation

Filed under: — Bravus @ 2:49 pm

As you’ll know if you’ve been following along in this series of posts1 on the philosophy of explanation, or if you decide to go back and read them in chronological order before continuing to read this one, Wesley Salmon is a realist who has been working on the problems of explanation for some considerable time. He first advanced and then withdrew a ‘statistical-relevance (SR)’ approach to explanation, and later adopted what he called a ‘causal/mechanical’ approach. My aim here is to briefly explore both of these approaches and what they offer.

You’ll remember that Hempel advanced the ‘deductive-nomological (D-N)’ model for explanations when the causal laws that govern the scientific phenomena are deterministic: ‘if X happens then Y will definitely happen’. He also introduced the ‘inductive-statistical (I-S) model for when the laws are probabilistic (e.g. in quantum mechanics): ‘if A happens there is a 78% chance that B will happen’. Hempel insisted on a high probablity (close to 100% or 1.0) for explanations under the I-S approach. The main reason for this is that, if the probability is lower, A could presumably explain both the occurrence and non-occurrence of B. Say the probability is of B given A is .5, and A occurs, if B occurs we say ‘B happened because A’, but if B does not occur in some sense it also makes sense to explain this in terms of A, since there is a 50% chance that A will not lead to B.

There are also other helpful counter-examples. Jim (who is biologically male) did not become pregnant last year. Jim faithfully took birth control pills all year. Logically, we could say that Jim did not become pregnant because he took birth control pills, but our intuition tells us this is not a valid explanation. The birth control pills are not relevant to explaining the phenomenon. Similarly, being a lifelong smoker only yields about a 20% chance (probability of .2) of getting lung cancer, yet we consider that the smoking explains the cancer.

Similarly, the probability arguments can be complex. Someone who has pneumonia and is treated with penicillin has a higher probability of recovering than someone who does not have pneumonia. We would argue that the penicillin caused the recovery, or at least that it did so in conjunction with the immune system of the patient. (On the other hand, if we observe that taking Vitamin C correlates with recovering from the common cold after about a week we might consider that it is causal… until we realise that most people, Vitamin C or not, recover from the common cold in about a week.

Salmon suggested, therefore, that relevance is important in statistical cases. He also noted, as in the smoking example, that explanations for events with low probabilities can be explained, whereas Hempel’s approach insists on high probabilities.

Let’s go back the pneumonia patient, but add the information that there are penicillin-resistant strains of pneumonia. The simple argument that penicillin improves the odds of recovery is complicated by this new information, and the two classes of pneumonia patients initially – those treated with penicillin and those not – become four classes – those untreated who have the non-resistant strain, those treated who have the non-resistant strain, those untreated who have the resistant strain and those treated who have the resistant strain. In considering an individual patient’s likelihood of recovery, which of these quadrants s/he falls in is statistically relevant.

Salmon adds the additional criteria that (a) all relevant factors must be included and no irrelevant ones and (b) we must divide up our whole population of cases so that we look at an ‘objectively homogeneous’ class in trying to explain something. For example, in the case of our pneumonia patient, we can divde the population into four with two factors, and each of those four groups will be somewhat homogeneous (all members having the same characteristics). But there are potentially other relevant factors, like age, sex, obesity… the list is almost endless. In the end, while Salmon described objective homogeneity is an ideal, he conceded that practical problems mean it is unlikely to be actually useful in constructing and evaluating real explanations. He moved on to consider the important role of causality:

I no longer believe that the assemblage of relevant factors provides a complete explanation—or much of anything in the way of an explanation. We do, I believe, have a bona fide explanation of an event if we have a complete set of statistically relevant factors, the pertinent probability values, and causal explanations of the relevance relations. (Salmon, 1978)

His discussion of causation and explanation gets into Reichenbach’s ‘screening off principle’, conjunctive forks, interactive forks and other complexities that don’t really concern me for the moment.

The big contribution from Salmon to my project is (a) the very thorough overview his book ‘Four Decades of Scientific Explanation’ offers of Hempel’s work and the responses to it up until the late 1980s, (b) his realist approach in contrast to Hempel’s anti-realist approach and (c) the ways in which the statistical-relevance approach, despite shortcomings of its own, fixed some of the shortcomings of Hempel’s approach and led to other interesting work. He also enabled me to think carefully about which philosophers working in this field will need to be considered in depth in my book, for my purposes, and which can be mentioned in brief but not analysed in depth.

Next cab off the rank is Peter Achinstein, whose approach is less rigidly logical-philosophical and more directly focused on what human beings do when we explain. He calls it an ‘illocutionary’ approach, which is just a longer word for the process of giving and explanation and the ‘product’ of that explanation, whether it be written, spoken, animated etc. I’ll be reading Achinstein’s book over the next few days and will report in when I’ve done that.

  1. As you may have guessed, this series is in part a way of sharing the stuff I’m interested in and excited about with others, partly a way of taking notes for myself to remind me of some of the broader themes of what I’m reading… and partly just procrastination from writing the book I’m supposed to be writing about this stuff! I feel as though it’s worthwhile procrastination, though, because if I can explain it for a smart lay audience of my friends it will help me to better understand it for when I write about it more formally.


Salmon, W. (1978). “Why Ask ‘Why?’? An Inquiry Concerning Scientific Explanation”, Proceedings and Addresses of the American Philosophical Association, 51(6): 683–705. Reprinted in Salmon 1998: 125–141. doi:10.2307/3129654

Salmon, W. (1998).Causality and Explanation, New York: Oxford University Press. doi:10.1093/0195108647.001.0001

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