Tuesday, October 27, 2009

A Refutation of Consequentialism? (I)

I'd like for someone to explain to me why the following isn't a sufficient refutation of consequentialism (at least of the maximalist or aggregative variety): One of the more over-reported anecdotes of the past century is Mao's retort to the question, "What was the significance of the French Revolution?" "It's too early to tell," Mao replied. Mao's point was partially tongue in cheek, but it managed to get across an important point: the effects of any action continue on into an indefinite, and at the limit, infinite, future. With that in mind, here's a refutation of consequentialism:

1) The right action in a given situation is a function of its net sum total consequences relative to alternative possible actions.
2) Sum net totals are calculated over total moments.
3) There are no total moments.
4) Hence, there are no sum totals.
5) Hence, there is no net sum total greater than all others.
6) Hence, there is no right action.

The key premise, obviously, is the third. It is also the least refutable. This is the insight captured in Mao's retort, and easily demonstrable: Let's take March 30th, 1794. You are Robesipierre, member the Committee for Public Saftey, deciding on the matter of Danton's execution. You think to yourself, What is the right thing to do? The answer, it is easy to demonstrate, depends upon what time frame is in question (and that, it should be stressed, is solely a matter of whim!). If the time frame is only through the end of the year, killing Danton will exacerbate the reign of terror (leading to your own execution!!), resulting in many more deaths. But, if your time frame is, say, up to 1814, it is precisely the excesses of the Reign of Terror and the Revolution that make Napoleon possible. Napoleon brings order finally to France, but he also harbingers war; yet without Napoleon there is no Congress of Vienna, which brings nearly a century of relative peace to Europe. But of course, without the developments that that century of peace engenders, there is no World War One and thus no World War Two. But without World War Two there is no United Nations....I could go on, but the point I take it is clear: whether it is right for you, Robespierre, to order the execution of Danton right now, in 1794, radically depends upon the time frame in question.

This is not an epistemic point. Of course it is hard to calculate out the consequences, and of course there is no reason whatsoever to believe that Robespierre could have made the considerations I just went over. But that is besides the point, which is that the consequentialist must be a realist about morality. The statement 'It is right in 1794 that Danton be executed' and its opposite, "It is wrong in 1794 that Danton be executed' must each have a determinate truth value. In general, any statement of the sort 'X is right' or 'X is good', if consequentialism is correct, must have a definite truth value, but no statement of that sort does. "It is right that Danton in 1794 be executed" is false in 1795, true in 1814, false again in 1816, true again maybe until 1914, false between 1914 and 1945, true again in 1946, and so on--which is just to say, "It is right that Danton is executed in 1794" has no definite truth value.

I suppose that one could argue that consequentialism is not a normative theory about what one ought to do, but is a descriptive theory that analyzes what we mean by statements of the sort 'X is right' and 'X is good'. But in that case, we have just shown that 'X is right' and 'X is good' have no definite truth values, and this, if any thing, speaks on behalf of error theory--and that, in turn, gets us to the same point: namely, that consequentialism is false.


  1. (Why can't I copy text into the comment box? It's really annoying)

    I take consequentialism as the proposition that the right action is the one that maximizes expected value according to some utility function. On that view, with standard probability theory, your 3 is confused and your 4 is false. You can get finite sums over infinite total moments. It's standard calculus. Whether or not you want to call the case where there are infinite total moments one in which there is "no total moments" is just semantics.

    That said, consequentialism as I've described it without further restrictions is pretty empty. Here's how to think about it: The problem of the consequentialist is to select the course of action a that maximizes utility according to some function U that takes a and some random
    variable x as arguments. For instance, if there are only 2 possible outcomes, each with equal probability, then the consequentilist chooses the a that maximizes (1/2)*U(a, x1)+(1/2)*U(a, x2). A more succinct notation for the above is:
    E[U(a,x)]. The E is for expectation. For instance, let's say there's a 50/50 chance that executing Danton will lengthen the reign of terror. Then I choose whether or not to execute by comparing E[U(execute,x)] with E[U(no execute, x)], and pick whichever is higher.
    Yes, probabilites change according to your information set, so consequentialism allows for the idea that if you learn more, you might choose a different action. In notation, if we call your information set O, the problem then becomes choosing the action a that maximize
    E[U(a,x)|0], i.e. maximize expected value conditional on information set O.

    The utility function can also take time as an argument. The reason this is all kind of empty and pointless, though, is that no restrictions have been imposed on the uility function. We can always rig the utiltiy function to conform to any a priori morality we want. For instance, we could say that U is always infinitely negative for actions in which we execute someome and infinitetly positive for actions in which we don't. This will means that no matter what the probability distribution, we always choose to not execute.


  2. Even if infinite sums converge to finite values, there is a problem with tractability and certainty. Can you really expect a human being to devise a mathematical function to describe all future results of an action? Given the complexity of the world, it is impossible for the mental capacities of humans to figure any definitive function. Moreover, given the severely limited scope of any one person's information, the certainty of any such prediction would be so close to zero as to make the utility function completely worhtless in practice.

    Furthermore, as Yobro pointed out, how one assigns 'values' to states of affairs is itself a tremendous issue.