Counterfactual statements and the London Marathon

Dava asked:

Let’s assume I am running the London Marathon… if my feet were bigger would it be over sooner?

Answer by David Robjant

There are some marshalling issues connected with the definition of ‘running’. Overlooking width fitting problems, any athlete with a foot length over 26 miles and 385 yards would not be permitted to compete.

Answer by Geoffrey Klempner

My first reaction to this question was that it is surely a joke. However, on second thoughts there does seem to be a point here about the way we assess the truth of counterfactual conditionals, of the form, ‘If A had been the case then B would have been the case.’

If all the world was apple pie
And all the sea was ink
And all the trees were bread and cheese
What should we have to drink?

‘If all the world was apple pie…’ is the antecedent of a counterfactual. However, in this case, we have absolutely no idea how to assess its truth or falsity. To cite the analysis of David Lewis (in his book Counterfactuals, 1973) you look at the possible worlds most closely resembling the actual world, except for the fact that ‘all the world is apple pie and all the sea is ink’. Where do you start?!

Counterfactuals are unruly. It’s an idiom that allows you to ask questions, or make statements, where the question of truth or falsity isn’t something merely hidden or difficult to get at, but where the very idea that there ‘is’ an answer, in reality, is absurd. We don’t have to go as extreme as the nursery rhyme case. Do counterfactuals have truth conditions at all? Or are they merely more or less appropriate things to say, given the circumstances?

Keep everything the same and just make my feet one inch longer. I still take the same number of strides, at the same rate. If each stride is, say, one metre, then regardless of the size of my feet, with each stride I advance one metre. However, I do have one advantage, if we assume that one of my feet crosses the finishing line before the rest of me. I could beat my alter ego with one inch shorter feet, by one inch. (This rarely happens in real life, because the athlete’s nose or hand crosses the finish line first.)

So far so good, the problem is that lots of other things would be the case if my feet were longer by one inch. My body would be just that little bit heavier, my running shoes would also be just that little bit heavier, there would be slightly more wind resistance as I moved my feet forward. OK, you say, that’s just a matter of calculation. In principle, there would be answer, say, if we could devise a suitable computer simulation.

But that’s surely not the point of the question. We don’t want to change anything, at all, except foot size. We are not interested in the most likely or ‘similar’ scenario where my feet are larger, only in the effect that foot size has on the outcome of the race, and that effect alone. In short, what we are interested in is a specific causal relationship.

That is a condensed argument for a different analysis of counterfactuals from the one Lewis gives, where the key concept is causality rather than Lewis’s notion of ‘similarity of worlds’. The bad news is that, if we reject Lewis, then we also give up any hope of a reductive analysis of causal statements in terms of counterfactuals.

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