Towards quantifying the good of success

Yesterday, I argued that the good of success contributes to one’s well-being at the time of one’s striving for success rather than at the time of the success itself.

It seems, then, that the longer you are striving, the longer the amount of time that you are having the good of success. Is that right?

We do think that way. You work on a book for five years. Success is sweeter than if you work on a book for one year.

But only other things being equal. It’s not really the length of time by itself. It’s something like your total personal investment in the project, to which time is only one contribution. Gently churning butter for an hour while multitasking other things (using a pedal-powered churn, for instance) does not get you more good of success than churning butter with maximum effort for fifteen minutes, if the outputs are the same.

We might imagine—I am not sure this is right—that the good of success is variably spread out over the time of striving in proportion to the degree of striving at any given time.

What else goes into the value of success besides total personal investment? Another ingredient is the actual value of the product. If you’ve decided to count the hairs on your toes, success is worth very little. Furthermore, the actual value of the product needs to be reduced in proportion to the degree to which you contributed.

Thus, if Alice and Bob both churned butter and produced n pounds, the value of the output is something like bn, where b is the value of butter per pound. If the investments put in by Alice and Bob are I_A and I_B, then Alice’s share of the value is bnI_A/(I_A+I_B). But since the value of success is proportional also to the absolute investment, I think that the considerations given thus far yield a formula for the value of success for Alice proportional to:

• bnI_A²/(I_A+I_B).

Next note that one way to think about the degree to which you contributed is to think as above—what fraction of the total investment is yours. However, even if you are the only person working on the project, the degree of your contribution may be low. Let’s say that you have moved into a house with a mint bush. Mint bushes are aggressive. They grow well with little care (or so we’ve found). But you do water it. The mint bush added half a pound to its weight at the end of the season. You don’t, however, get credit for all of that pound, since even if you hadn’t watered it, it would likely have grown, just not as much. So you only get credit for the portion of the output that is “yours”. Moreover, sometimes things work probabilistically. If the success is mostly a matter of chance given your investment, I think you only get good-of-success credit in proportion to the chance of success—but I am not completely sure of this.

But here is something that makes me a little uncertain of the above reasoning. Suppose that you have some process where the output is linearly dependent on the investment of effort. You invest I, and you get something of value cI for some proportionality constant c. By the above account, to get the value of success, you should multiply this by I again, since the value of success is proportional to both the value of the output and the effort put in. Thus, you get cI². But is it really the case that when you double the effort you quadruple the value of the success? Maybe. That would be interesting! Or are we double-counting I?

Another question. When we talk about the value of the output, is that the objective value, or the value you put on it, or some combination of the two? Counting the hairs on your toes has little objective value, but what if you think it has significant value? Doesn’t success then have significant value? I suspect not.

But what about activities where the value comes only from your pursuit, such as when you try to win at solitaire or run a mile as fast as you can? In those cases it’s harder to separate the value of the output from the value you put on it. My guess is that in those cases there is still an objective value of the output, but this objective value is imposed by your exercise of normative power—by pursuing certain kinds of goals we can make the goal have value.

Let’s come back to counting hairs on toes. If you’re doing it solely for the sake of the value of knowledge, this has (in typical circumstances) little objective value. But if your hobby is counting difficult to count things, then maybe there is additional value, beyond that of trivial knowledge, in the result.

I suspect there are further complications. Human normativity is messy.

And don’t ask me how this applies to God. On the one hand, it takes no effort for God to produce any effect. On the other hand, by divine simplicity God is perfectly invested in everything he does. But since my metaethics is kind-relative, I am happy with the idea that this will go very differently for God than for us.

The good of success is not at the time of success

It’s good for one to succeed, at least if the thing one succeeds in is good. And the good of succeeding at a good task is something over and beyond the good of the task’s good end, since the good end might be good for someone other than the agent, while the good of success is good for the agent.

Here’s a question I’ve wondered about, and now I think I’ve come to a fairly settled view. When does success contribute to one’s well-being? The obvious answer is: when the success happens! But the obvious answer is wrong for multiple reasons, and so we should embrace what seems the main alternative, namely that success is good for us when we are striving for the end.

Before getting to the positive arguments for why the good of success doesn’t apply to us at the time of success, let me say something about one consideration in favor of that view. Obviously, we often celebrate when success happens. However, notice that we also often celebrate when success becomes inevitable. Let’s now move to the positive arguments.

First, success at good tasks would still be good for one even if there were no afterlife. But some important projects have posthumous success—and such success is clearly a part of one’s well-being. And it seems implausible to respond that posthumous success only contributes to our well-being because as a matter of fact we do have an afterlife. Note, too, that in order to locate the good of success at the time of success, we would not just need an afterlife, but an afterlife that begins right at death. For instance, views on which we cease to exist at death and then come back into existence later at the resurrection of the dead (as corruptionist Christians hold) won’t solve the problem, because the success may happen during the gap time. I believe in an afterlife that begins right at death, but it doesn’t seem like I should have to in order to account for the good of success. Furthermore, note that to use the afterlife to save posthumous success, we need a correlation between the timeline the dead are in and the timeline the living are in, and even for those of us who believe in an afterlife right at death, this is unclear.

Second, suppose your project is ensure that some disease does not return before the year 2200. When is your success? Only in 2200. But suppose your project is even more grandiose: the future is infinite and you strive to ensure that the disease never returns. When is your success? Well, “after all of time”. But there is no time after all of time. So although it may be true that you are successful, that success does not happen at any given time. At any given time, there is infinite project-time to go. So if you get the good of success at the time of success, you never get the good of success here. Even an afterlife won’t help here.

Third, consider Special Relativity. You work in mission control on earth to make sure that astronauts on Mars accomplish some task. You are part of the team, but the last part of the team’s work is theirs. But since light can take up to 22 minutes (depending on orbital positions) to travel between Earth and Mars, the question of at what exact you-time the astronauts accomplished their task depends on the reference frame, with a range of variation in the possible answers of up to 22 minutes. But whether you are happy at some moment should not depend on the reference frame. (You might say that it depends on what your reference frame is. But there is no unambiguous such thing as “your” reference frame in general, say if you are shaking your head so your brain is moving in one direction and the rest of your body in another.)

Here is an interesting corollary of the view: the future is not open (by open, I mean the thesis that there are no facts about how future contingents will go). For if the future is open, often it is only at the time of success that there will be a fact about success, so there won’t be a fact of your having been better off for the success when you were striving earlier for the success. That said, the open-futurist cannot accept the third argument, and is likely to be somewhat dubious of the second.

Intending to lower the probability of one's success

It seems a paradigm of irrationality to intend an event E in an action A and yet take the action to lower the probability of E.

But it’s not irrational if my principle that intending a specification of something implies intending that which it is a specification of.

Suppose that Alice is in a bicycle race and is almost at the finish. If she just lets inertia do its job, she will inevitably win. But she carefully starts braking just short of the finish, aiming to cross the finish just a hair in front of Barbara, the cyclist behind her. She does this because she wants to make the race more exciting for the spectators, and she carefully calibrates her braking to make her win but not inevitably so.

Alice is aiming to win with a probability modestly short of one. This is a specification of winning, so by my principle, she is intending to win. But she is also, and in the very same action, aiming to decrease the probability of winning.

The possibility test for intentions

This test for whether one is intending some effect E of an action is often employed (e.g., by Germain Grisez) in the Double Effect literature:

1. If it is logically possible for an action with an intention J to be fully successful even though E does not happen, then E is not included in J.

Claim (1) follows in standard modal logic (with no need for anything fancy like S5) from:

2. If an intention J includes E, then the inclusion of E is an essential property of J.

3. Necessarily, if an action is done with an intention that includes E and E does not occur, then the action is not fully successful.

For suppose that E is included in J. Then in every possible world where an action is done with J, the action is done with an intention that includes E by (2)) and so in every possible world where an action is done with J, the action is not fully successful if E does not occur, by (3). Hence, there is no possible world where an action is done with J and is fully successful even though E does not happen. Thus, we have (1).

At the same time, (1) sounds awfully strong. Even if the possible world where the action is successful despite the lack of E requires a miracle, E is not included in J. For instance, suppose God is able to keep the soul of a human being bound to a single atom. That means that someone whose intention was to blow the man blocking the mouth of the cave literally to single atoms was not intending death, since there is a possible world where the person’s soul remains bound to a single atom, and in that world the action is clearly successful.

To deny (1), one needs to deny (2) or (3). I think the best route to denying (2) is a strong dose of semantic externalism: the content of an intention is dependent in part on things outside the individual. Perhaps on Earth the very same intention may be an intention to drink water, while on Twin-Earth the very same intention may be an intention to drink XYZ. I am sceptical of this: it seems to me that the best way to understand the water-XYZ issue is that intentions are partly grounded in facts outside the individual, and so it is a different intention on Twin-Earth than on Earth, even if it is partly grounded in the same facts in the individual.

But even if one is impressed by the water-XYZ issue, it seems one should be willing to accept the following variant on 2:

4. If an intention J includes E and occurs at t, then in any possible world that exactly matches the actual world up to an including t the intention J includes E at t.

The argument for (1) can now be modified to yield an argument for:

5. If an action with an intention J occurs at t, and if there is a possible world that matches the actual world up to and including t and where the action with J is fully successful but where E does not happen, then E is not included in J.

And if one’s motivation for denying (1) is to avoid the conclusion that intending to blow the man in the mouth of the cave to single atoms does not include intending death, then (5) is just as bad. For God could miraculously keep the soul bound to a single atom without anything being any different up to and including the time of the action.

If we don’t want (1), we won’t want (5), either.

So a better bet is to deny (3). A start towards a denial of (3) would be to talk of something like “stretch goals”. It seems that an action may have a stretch goal and yet be successful even if that stretch goal is unachieved. However, the stretch goal is surely intended.

I am not sure. If the stretch goal is intended, then it seems that the right thing to say is that the action is successful but not fully successful if the stretch goal is not met.

In any case, we might grant the claim about stretch goals, and introduce the concept of an intention being perfectly satisfied, which includes the satisfaction of all stretch goals, and then replace “fully successful” with “perfectly successful” in (1) and (5). And I think this will still generate the result about blowing the fat man to atoms, because the death of the fat man—the separation of soul from body—is not a stretch goal either. (If anything, one might imagine that his survival is a stretch goal.)

All this makes me want to say that (3) really is true, and we cannot avoid the conclusion that it is possible to intend to blow the man in the mouth of the cave to single atoms without intending to kill him. But I am now inclined to think that an intention to kill is not a necessary condition for murder, and so the action could still be a murder.

Deep Thoughts XXXVIII

If you don't try, you won't fail.

Some conjectures on intention, success and trying

Here are some conjectures:

1. x As out of a proximate intention to A if and only if x succeeds at trying to A.
2. x proximately intends to A if and only if x tries to A.
3. x proximately intends that s if and only if x proximately intends to bring it about that s.
4. x distantly intends to A if and only if x tries to bring it about that she* [quasi-indicator] As
5. x distantly intends that s if and only if x distantly intends to bring it about that s.

Proximate intentions are the intentions that normally directly result in action, as distinguished from distant intentions which are plans for future action that still require a proximate intention before the action. I am rather less confident of the theses on distant intention than those on proximate intention. But even the theses on proximate intention only have something like the following epistemic status: "They sound right and I can't think of a counterexample."

If (2) is right, then the intention condition in the Principle of Double Effect can be reformulated as saying that the agent isn't trying to bring about an evil. And indeed the following sounds exactly right to me:

6. You are never permitted to try to bring about an evil.

Of course, there are some difficult de re / de dicto issues in regard to (6).