Sunday, July 15, 2012

A problem for Lewis's account of counterfactuals

Let's say I have a bag of fifty ordinary chrome steel balls. They are of the same size up to a tolerance of 0.01 mm, but they do exhibit minor size variations below that tolerance. So one of these steel balls is smallest. On Lewis-type accounts of counterfactuals, we have to say that:

  1. If one of the balls were made of brass, it would be the smallest of them.
For worlds where the smallest of the balls is made of brass are more like our world than worlds where another of the balls is made of brass (keeping everything else equal) since the area of spatiotemporal mismatch is smaller when it is the smaller ball that is made of brass.

But while we intuitively think that (1) might turn out to be true, it shouldn't turn out to be true simply because of such size considerations.

This is a non-temporal version of the coat thief problem (see, e.g., p. 42 here).


Mike Almeida said...

I'm not sure how you can reach that conclusion. It is not like there is a single correct similarity relation operating here. What world is most similar is going to depend on contextual features, features of the discussion in which the counterfactual is asserted.

Alexander R Pruss said...

In "Time's Arrow", Lewis gives a specific ordered list of how one considers similarity:
1. Large scale nomic match.
2. Spatiotemporal volume of exact match.
3. Small scale nomic match.
4. (In some but not other contexts), spatiotemporal volume of approximate match.

Since we have large scale nomic match in all the most relevant worlds, the spatiotemporal volume of exact match criterion favors the world where the smallest ball is brass.

Mike Almeida said...

right, that's a familiar list. but Lewis says lots of other things about similarity that are not obviously consistent with there being a list. He says it is true, for instance, that Kripke could not have been born to other parents, provided this is what the context of discussion allows. But we can also truthfully and non-trivially utter, in other contexts, that were Kripke brought by a stork, it wold have been done 70 or so years ago. He says that in some contexts it is true to say that he can speak Finnish and in other contexts it is false to say he can speak Finnish. So I would not regard those rules as holding across all contexts of utterance.

Alexander R Pruss said...

The examples you give are about "can", not counterfactuals, right?

Mike Almeida said...

But counterfactuals just are cans.

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