Bidirectionality in means and ends

I never seem to tire of this action-theoretic case. You need to send a nerve signal to your arm muscles because there is a machine that detects these signals and dispenses food, and you’re hungry. So you raise your arm. What is your end? Food. What is your means to the food? Sending a nerve signal. But what is the means to the nerve signal?

The following seems correct to say: You raised your arm in order that a nerve signal go to your arm. What has puzzled me greatly about this case in the past is this. The nerve signal is a cause of the arm’s rising, and the effect can’t be the means to the cause. But I now think I was confused. For while the nerve signal is a cause of the arm’s rising, the nerve signal is not a cause of your raising your arm. For your raising your arm is a complex event C that includes an act of will W, a nerve signal S, and the rising of the arm R. The nerve signal S is a part, but not a cause, of the raising C, though it is a cause of the rising R.

So it seems that the right way to analyze the case is this. You make the complex event C happen in order that its middle part S should happen. Thus we can say that you make C happen in order that its part S should happen in order that you should get food. Then C is a means to S, and S is a means to food, but while S is a causal means to food, C is a non-causal means to S. But it’s not a particularly mysterious non-causal means. It sometimes happens that to get an item X you buy an item Y that includes X as a part (for instance, you might buy an old camera for the sake of the lens). There is nothing mysterious about this. Your obtaining Y is a means to your obtaining X, but there is no causation between the obtaining of Y and the obtaining of X.

Interestingly, sometimes a part serves as a means to a whole, but sometimes a whole serves as a means to the part. And this can be true of the very same whole and the very same part in different circumstances. Suppose that as a prop for a film, I need a white chess queen. I buy a whole set of pieces to get the white queen, and then throw out the remaining pieces in the newly purchased set to avoid clutter. Years later, an archaeologist digs up the 31 pieces I threw out, and buys my white queen from a collector to complete the set. Thus, I acquired the complete set to have the white queen, while the archaeologist acquired the white queen to have the complete set. This is no more mysterious than the fact that sometimes one starts a fire to get heat and sometimes one produces heat to light a fire.

Just as in one circumstances an event of type A can cause an event of type B and in other circumstances the causation can go the other way, so too sometimes an event of type A may partly constitute an event of type B, and sometimes the constitution can go the other way. Thus, my legal title to the white queen is constituted by my legal title to the set, but the archaeologist’s legal title to the set is partly constituted by legal title to the white queen.

There still seems to be an oddity. In the original arm case, you intend your arm’s rise not in order that your arm might rise—that you don’t care about—but in order that you might send a nerve signal. Thus, you intend something that you don’t care about. This seems different from buying the chess set for the sake of the queen. For there you do care about your title to the whole set, since it constitutes your title to the queen. But I think the oddity can probably be resolved. For you only intend your arm’s rising by intending the whole complex event C of your raising your arm. Intending something you don’t care about as part of intending a whole you do care about is not that unusual.