Friday, August 06, 2004

Battle Tactics / Future Truths

Allan at FBC asks what's wrong with the following argument:
Premise 1: Either we will win the battle, or we will lose the battle.
Premise 2: If we will win the battle, then we ought to attack with a small force.
Premise 3: If we will lose the battle, then we ought to attack with a small force.
Conclusion: We ought to attack with a small force.

As The Ethical Werewolf put it:
I recommend that you reject premise 3: "If we will lose the battle, then we ought to attack with a small force."
Suppose the antecedent is true: We're going to lose the battle. There are many reasons why this might be the case. One of them is that we aren't going to bring a large enough force. Then it's the case that we ought to bring a large force including many werewolves and some hippogriffs. In this case, the ought-claim that is the consequent of the conditional -- "we ought to attack with a small force" is false. Since the antecedent is true and the consequent is false, the conditional is false.

I think he's exactly right there. Though I think that we should also reject premise 2: "If we will win the battle, then we ought to attack with a small force". For suppose it is true that we will win the battle with a large force - so the antecedent is true - but that with a lesser force we would have been defeated. (This is a plausible enough scenario, and indeed it is due to cases like this that we know the conclusion is false. So it is worth seeing how this case affects the premises.) Is the consequent also true? Ought we attack with a small force? Quite simply: no. If we were to attack with a small force, then we would lose. So we ought not attack with a small force.

"But we cannot lose," you object, "because we've already stipulated that we will win!". Okay [but see section on 'future truths' below]. So by attacking with a small force, we would bring about a logically inconsistent state of affairs. This is impossible. So we cannot attack with a small force. And since ought implies can, it is not the case that we ought to attack with a small force (in the given scenario).

Before anyone gets worried that I've just argued us out of free will, note that the claim "we cannot attack with a small force" is conditional on the supposition that we will win. And the truth of that claim is one that will be affected by our choices (i.e. whether to attack with a small or large force). That is, I'm merely pointing out that in this scenario, the following material conditional holds: "If we will win the battle, then we will not attack with a small force". That shouldn't be controversial, given how I described the scenario (i.e. both the antecedent and consequent are true). Now take the contrapositive: "If we will attack with a small force, then we will not win the battle". This is confusing because the consequent contradicts our assumption. Nevertheless, it is clear enough that we ought not attack with a small force. So in the above scenario, premise (2) would be false.

Future Truths:
Consider the following, analogous, argument (based on the assumption that I really enjoy free-fall):
(1) Either I will die tomorrow, or I will not
(2) If I will not die tomorrow, then I should jump off a cliff (fun and safe! Let's assume I either won't get injured, or don't care if I do.)
(3) If I will die tomorrow, then I should jump off a cliff (so I at least have some fun before I die).
(4) Therefore, I should jump off a cliff (tomorrow).

Premises (2) & (3), here as in the battle argument, seem to be based on an assumption of fatalism. That is, future truths exist in the present, and we cannot possibly make them false (they are, after all, truths.)

A better way to understand future truths might be to say that as a matter of convention, we will call a statement about the future 'true' if (in retrospect) it turns out to be accurate. The truth itself is in no way embedded in the present, however.

This is why it is not true that "If we will win the battle, then we ought to attack with a small force". The truth value of our winning the battle, is not decided until after we have made our attack. Once this has been done, we can look back and say "in retrospect, it was true all along that 'we will win the battle'". But I think talking of truth in this way is just a matter of convention, and not actually saying anything much about reality.

So here's the problem in a nutshell: the truth of "we will win the battle" (W) may well be dependent upon the falsity of "we will attack with a small force" (S). If S is true, then W is false. So it just doesn't make any sense to argue from the truth of W to the claim that we ought to make S true. That combination is inconsistent (in the particular scenario being discussed). You can't just stipulate the truth of W and then fiddle with other propositions on the assumption that W will stay true. It won't. And that's why we ended up with all those contradictions in the previous section.

Update: see my Better Battle Tactics post.

2 comments:

  1. [Copied from old comments thread]

    What if we add an additional premise to the original argument: "If we attack with a small force, it is possible that we will win and possible that we will lose. If we attack with a large force, it is possible that we will win and possible that we will lose."

    We want to say that the argument is garbage even when this new premise is true and the dependence of W (we will win) on S (we will attack with a small force) is probabilistic rather than deterministic. I'm not sure if your argument can be extended to that case.
    dan | Email | 7th Aug 04 - 9:33 am | #

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    Ah, good point. I wasn't clear enough in explaining how my counterexample was supposed to fit into the argument. Let me try again here:

    The truth of premises 2 & 3 will depend not only on the actual world, but also on various other possible worlds. This is because we're dealing in unknowns - "probabilistic" cases, as you say - and we do not know which of these cases obtains in the actual world. The way that I'm understanding this (this may or may not be the best interpretation of those premises - I'm certainly open to other suggestions) is to say that each premise is true only if the conditional it expresses is true at all of the relevant possible worlds (i.e. epistemically possible worlds).

    My argument involved a particular scenario (namely: we will win, but only if we take a large force). However, my argument does not require that scenario to be the actual case. It merely needs to be a relevant possibility. In which case, the failing of the conditionals in that world demonstrates the falsity of the premises actually.

    So even if we include your extra premises, the scenarios I discuss are still relevant possibilities, and so they still serve as counterexamples to premises 2 & 3.
    Richard | Email | Homepage | 7th Aug 04 - 1:39 pm | #

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