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.

Change without a plurality of times

Assume presentism. Then Aristotle’s definition of change as the actuality of a potentiality seems to have a serious logical problem. For consider a precise statement of that definition:

1. There is change just in case there is a potentiality P and an actuality A and A is the actuality of P.

Given presentism, quantification has to be over present items. Thus, the potentiality P and the actuality A are both present items (presumably, accidents of some substance). But if the actuality and potentiality can be simultaneous, then Aristotle’s definition of change does not logically require multiple times: one can have a moment t at which there is an actuality A of a potentiality P, and t could be the only time at which the underlying substance exists. But it seems obvious that if something changes, it exists at more than one time.

One way out of this problem is to deny presentism. I would like that, but Aristotle was probably a presentist.

A second way out is to be careful with tensing:

2. There is change just in case there was a potentiality P and there is an actuality A and A is the actuality of P.

This makes being the actuality of a cross-time relation. Cross-time relations are awkward for a presentist, but probably unavoidable anyway, so this isn’t so terrible. However, there are other problems with (2). First, it seems that tense depends on time, and for Aristotle, time depends on change, so (2) becomes circular. Second, if we can help ourselves to tense, we can just define change as being in a state in which one previously was not.

I want to suggest a more radical way out of the problem for (1). This more radical way starts by embracing the idea that a substance can change even if it exists only at one time. One way to motivate that is to think of Newtonian physics. Suppose that the universe consists of a number of particles that come into existence at time t₀. We may further suppose the state of the Newtonian universe at times after t₀ is deterministically caused by the state at t₀ (barring things like Norton’s dome). But this is only true if the state of the universe at t₀ includes the momenta of the particles, some of which we can assume to be initially non-zero. In other words, the fact about what the momenta are has to be a fact about what the universe is like at t₀, in the sense that even if God annihilated the universe right after t₀, it would still be true that the particles had the momenta at t₀ that they do. Thus, having a non-zero momentum at a time does not require existing at other times. But if one has non-zero momentum, then one is in motion. Hence, being in motion does not require existing at more than one time.

This sounds quite paradoxical, but I think it makes sense if we think of motion as that which explains the succession of states rather than as that which arises from the succession of states.

Next, let’s slightly tweak the English translation of Aristotle’s definition of change:

3. Change is the actualizing of potentiality.

One can be actualizing a potentiality without ever being in a state of having actualized it. Imagine a substance that is falling, and thus on Aristotle’s account in the process of actualizing the potentiality for being in the center of the universe, and yet which never reaches the center of the universe. At every moment of its existence, that substance is striving to be in the center. That striving, that actualizing of its potential, is what makes it be in motion. It would be in motion even if it only existed for an instant.

One cannot, I take it, have actualized a potentiality while still having the potentiality. But one can be actualizing it while still having it. One is actualing it until one has actualized it, and once one has actualized it, one is no longer actualizing it.

Granted, on this view, change does not entail a plurality of times. It is possible to have a changing universe that exists only for an instant. This complicates the Aristotelian projects of grounding time in change: change is not sufficient for time. Nor does Aristotle say it is. He says that time is a kind of number for change. But a single change may not be enough for number (Aristotle thought that one is not a number: number, for him, requires plurality). Thus, the single-moment universe may have change, but not enough change to have time on Aristotle’s view.

The pursuit of perfection and the great chain of being

Consider the following two plausible Aristotelian theses:

1. A substance naturally pursues each of its own perfections.

2. Every natural activity of a substance is a perfection of it.

This threatens an infinite regress of pursuits. Reproduction is a perfection of an oak tree. So by 1, the oak naturally pursues reproduction. But by 2, this natural pursuit of reproduction is itself a perfection of the oak. So, by 1, the oak naturally pursues the pursuit of reproduction. And so on, ad infinitum.

So, 1 and 2, though plausible, are problematic. I suggest that we reject 1. Perhaps the oak tree pursues reproduction but does not pursue the pursuit of reproduction. Or perhaps it pursues the pursuit of reproduction, but doesn’t pursue the pursuit of the pursuit of reproduction. How many levels of pursuit are found in the substance is likely to differ from substance to substance: it is one of those things that the substance’s form determines.

We might say that there are more levels of pursuit in a more sophisticated substance. Thus, perhaps, non-living things only have first order pursuits. To use Aristotle’s physics as an example, the stone pursues being in the center of the universe. But the stone does not pursue the pursuit of being in the center of the universe. But in living things, there are multiple levels. The oak tree grows reproductive organs with which it will pursue reproduction, and in growing the organs it pursues the pursuit of reproduction.

Here is an intriguing hypothesis: in human beings, 1 and 2 are both true. Thus there is thus a kind of (potential?) infinity at the heart of our pursuits. For we are capable of forming a mental conception of our perfection as such, which enables us to pursue our perfections as perfections. If an angel offers a dog food, the dog will take it, since it can conceive of food, and thereby become perfected. But even an angel cannot offer a dog perfection as such, since the dog cannot conceive of a perfection as such. However, we can: if an angel says: “If you ask for it, I will make you perfect in some respect or other, without any loss of perfection in any other respect”, that’s a deal we can understand, and it is a deal that is attractive to us, because we pursue perfection as such.

If the above is right, then we have a kind of deep teleological differentiation between three levels of being:

1. Non-living substances pursue first order perfections only.

2. Living substances have at least one meta-level of pursuit: they pursue the pursuit of some or all of their first order perfections.

3. Rational substances have infinitely many meta-levels of pursuit, at least potentially.

Progress

I was doing logic problems on the board in class and thinking about rock climbing, and I was struck by the joy of knowing one's made progress on a finite task. You can be pretty confident that if you've got an existential premise and you've set up an existential elimination subproof then you've made progress. You can be pretty confident that if you've got to a certain position on the wall and there is no other way to be at that height then you've made progress. And there is a delight in being really confident that one has made progress.

Moreover, the value of the progress doesn't seem here to be merely instrumental. Even if in the end you fail, still having made progress feels valuable in and of itself. One can try to say that what's valuable is the practice one gets, or what the progress indicates about one's skills, but that doesn't seem right. It seems that the progress itself is valuable. Of course, it has to be genuine progress, not mere going down a blind alley (though recognizing a blind alley, in a scenario where there are only finitely many options, is itself progress).

The value of progress (as such) at a task derives from the value of fulfilling the task, much as the value of striving at a task derives from the value of fulfilling it. But in both cases this is not a case of end-to-means value transfer. Maybe this has something to do with the idea developed by Robert M. Adams of standing for a good. Striving and a fortiori progress are ways of standing and moving in favor of a task. And that's worthwhile even if one does not accomplish the task.