On Philosophy

June 4, 2006

Causation: Update

Filed under: General Philosophy — Peter @ 12:53 pm

This post in an addendum to this post.

The equations that I used to define causation may need to be revised slightly to handle two kinds of cases, both of which used in the main body of the text, but which I did not explicitly define.

One case is where you are looking for the cause of a set of properties (“particles”). In this case we define z and DC as follows:

Under this definition the single particle case is covered when z is a set containing only one element.

A more complicated situation arises when the condition you wish to determine the cause of is not determined by any one state of the world. For example one of the applications I provided was determining the cause of a man’s death. However the state we are looking for, a dead man, is not determined uniquely by any one configuration. In this case we have to abandon first order logic and define z (or Z) as a predicate. We could then define Z to be true whenever the man is dead, and Z would then hold no matter how he died. In this case our definitions are like so:

The simpler cases where we are only testing for the cause of the state of a single “particle” or when we are testing for the cause of a set of particles can be recovered by defining Z as:
Single particle case: where p is the particle state we are interested in.
Set of particles case: where p1, p2, … are the particle states we are interested in.

Neither of these revisions however makes a difference to how C is defined, so they can be safely ignored when considering the cause of macroscopic objects, since we are only working with an approximation in those cases anyways.

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3 Comments

  1. Quick question…

    Do you have a way of addressing cases where:
    (i) e causes c.
    (ii) If e hadn’t occurred e’ would have caused c in just the same way at just the same time?

    It seems that according to your definition, such cases would be impossible for if (ii) were true, (i) couldn’t be.

    Comment by Clayton — June 13, 2006 @ 9:55 am

  2. In such a situation I would say that e wasn’t the cause of c at all, assuming that c was exactly the same in both cases. If it wasn’t the same in both cases then we could identify e as the cause of some property of c. If you construct an actual case where c is the same I think you will see that e really isn’t a cause of c after all. Consider if it was though; this would imply that everything could possibly be the cause of anything. For example let’s say the ball on my desk is the cause of me typing (instead of your comment). We say “let’s test that silly claim by taking away the ball”. Now I am still typing in the same way. If I were allowed to make claims of the kind you propose then I could still defend my claim saying NOW your comment caused me to keep typing, but really the ball was still a cause. I think if we are allowed to say that then it becomes much harder to do science.

    Comment by Peter — June 13, 2006 @ 12:19 pm

  3. I’ll modify that slightly, depending on the setup it might be that {e, e’} belongs to C(n, c), in which case you might say that even though e wasn’t a cause by itself it was part of a cause.

    Comment by Peter — June 13, 2006 @ 12:35 pm


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