Hello! Sorry for the hiatus, work and school got a bit hectic — but I’m back and hopefully consistently so for at least the rest of the year. :)
This article is about a mistake that I have seen repeated many times in internet philosophy circles. This mistake is also deeply important, because once you see it, it makes less tenable some views of ethics and value.
This mistake is thinking that the Repugnant Conclusion (or, rather, the argument for the Repugnant Conclusion, which I will call ‘the Spectrum Argument’) is analogous, similar, or in any way parallel to the Sorites paradox (the “heap of sand” paradox). Many very smart people are under the impression that these two paradoxes are about the same issue, or commit the same kind of mistake (the legendary Flo seems to tentatively suggest this might be the case in their post on the Repugnant Conclusion). And it is often suggested that once we recognize that our everyday concepts like ‘hairy’ are vague/underdetermined, this too solves the paradox of mere addition.
Oh, if only population ethics were so simple. This is, unfortunately, far from the case. Despite appearances, the Spectrum Argument for the Repugnant Conclusion is simply a totally different puzzle from the Sorites Paradox.
I’m first going to start by explaining the Sorites, then I’ll explain the Repugnant Conclusion, and then I’ll explicate the differences between the two.
1 What is the Sorites Paradox?
The Sorites Paradox is a paradox about line drawing. Imagine that in front of you are 1 million grains of sand. This, we would say, is a heap of sand. Now, it also seems plausible that the following principle is true: If x is a heap of sand, then y (where y = x minus one grain of sand) is a heap of sand.
Basically, it seems as though one grain of sand could never be enough to make something that was a heap of sand no longer be a heap of sand. But this pretty quickly leads to issues: for, if this principle is true, it strictly follows that a single grain of sand is a heap of sand — which is obviously false!
To reject this conclusion, we must either say that there is a particular point at which a heap of sand, once it loses an additional grain of sand, is no longer a heap, OR, we must revise classical logic (e.g., by saying that truth comes in degrees and so as we remove more and more grains of sand from the heap it becomes less and less true that it is a heap).
No solution is perfect, but the general lesson is this: certain concepts we use (like ‘heap’ and ‘hairy’) are vague, and it may be indeterminate at various points whether they apply to an object. This is pretty general: for instance, it seems plausible that taking a single penny from a rich person is not enough to make them no longer rich. But, assuming Elon Musk is rich, accepting this principle would entail (in classical logic) that someone with a single penny is rich.
Put succinctly, the Sorites Paradox is about tolerance. A predicate like ‘is rich’ seems able to tolerate a slight change in the facts relevant to richness (money) while still obtaining. It seems, generally, that richness is tolerant of a single penny being taken away. But what the Sorites reveals is that that cannot be strictly right.
2 What is the Spectrum Argument?
Okay, let’s be clear on a few things.
First, we have the Repugnant Conclusion, which is the following proposition:
· Repugnant Conclusion: For any population A with billions of people living absolutely wonderful lives, there is an all-things-considered better population Z with some number n of people living lives barely worth living.
Next, there is the Spectrum Argument, which is an argument for the Repugnant Conclusion (again, a proposition). It relies principally on two propositions:
· Quality-for-Quantity: For any population X with n lives of well-being l, there is an all-things-considered better population Y with (10^100) * n lives of well-being 0.99999999999999 * l.
· Transitivity: If population X is all-things-considered better than Y, and Y all-things-considered better than Z, X is all-things-considered better than Z.
These two propositions entail the Repugnant Conclusion. Quality-for-Quantity provides us with a spectrum of populations, A, B, C, D, E, F, …, Z, where in each one everyone is enjoying a level of well-being almost as high as its predecessor, but there are 10^100 as many people enjoying those good lives. Transitivity secures that Z > A, i.e., the Repugnant Conclusion.
If you don’t think the Repugnant Conclusion is that crazy (a position I am sympathetic to), we can generate a parallel Spectrum Argument for the following proposition:
· Tortures over Pinpricks: A world of billions of horrific tortures is preferable to a world of n mild, barely noticeable pinpricks.
All we’d need is the principle that it is worse for a trillion times as many people to experience an almost identical pain than for a trillion times fewer people to experience a slightly worse pain, alongside transitivity.
It’s at this point that people will start pointing out the similarities between the Sorites series and the Spectrum Argument. In the Sorites series, we apply a very seemingly plausible principle, but repeated applications of this principle get us an absurd result. Same for the Spectrum! Quality-for-Quantity looks great, until you apply it repeatedly across a Spectrum of populations, and suddenly, alongside transitivity, you get a (repugnant!) result.
But this is way too quick.
First, what makes the Spectrum Argument so tricky is that it appears as though, every time you trade a bit of quality for a lot of quantity, things are getting better. But then you reach a point (Z), and compare it to what you started with, and it seems as though things have gotten worse!
This is not the puzzle involved in the Sorites. Every time I take out a penny from Elon Musk’s account, it’s not as though I think he is getting richer, and then, when I’ve finally gotten all his net worth down to 0, I suddenly think … wait, Elon seems poorer than when he started out! No, the Sorites, as we said earlier, is about tolerance. I do not think he is getting richer with every removed penny. The puzzle is that I think richness can always tolerate the miniscule change that a penny brings in richness. And, it turns out, richness cannot always tolerate such miniscule changes. And yet, despite this, I hesitate to say, at any particular point, that that is the point where Elon Musk went from rich to not rich.
There is no puzzle of tolerance involved in the Spectrum Argument. My intuition is not that trading a bit of quality for lots of quantity is something the goodness of a population can tolerate: it is that such a trade would make the population even better. However, simultaneously, I have the intuition that, if quality is too low, no amount of quantity could ever make up for it.
This also explains why the fundamental problem to be solved in each case is different. The problem to solve in the Sorites is a line drawing problem: where, in particular, is the boundary between rich and not-rich? Comparatively, the problem to solve in the Spectrum Argument is a question about tradeoffs: how could it be that trading off quality for quantity doesn’t make things better? Notice: the puzzle here is not “where, exactly in the sequence are you saying things don’t get better?”
Finally, one can see that the Sorites and Spectrum Argument are different simply by observing that the two involve differently structured concepts. The Spectrum Argument is about multidimensional concepts. For instance, how good a population of lives is seems to depend on (at least) two dimensions: quality (how good the lives in the population are) and quantity (how many lives there are). And the puzzle is that we have two (potentially conflicting) intuitions about this multidimensional concept: we believe that you can always trade off a slight loss along one dimension for huge gains in another dimension, and yet also that, if one dimension is very low, no amount of the other dimension can compensate.
Comparatively, the Sorites can be about unidimensional concepts. Whether something is a heap of sand can depend on literally only one dimension: how many grains of sand it has. And yet, we can still generate a line-drawing problem about where we want to draw the line between heaps and non-heaps.
To see my point most vividly, just consider that we can construct Spectrum Arguments concerning concepts that are usually the subject of the Sorites paradox. For instance: one version of the Sorites concerns the concept hairy. The plausible principle here is: if someone is hairy, and you remove one hair from their head, they are still hairy. But this will generate issues as, eventually, you’ll have plucked all the hairs from someone’s head and make them clearly not hairy.
Here's what a Spectrum Argument concerning hairy would look like (I steal this from Larry Temkin, who stole this from someone else): suppose that how hairy you are is actually a function of two factors. It is not just a function of the pure number of hairs around your head, but it is also a function of the distribution of your hairs. For instance, if you have hair, but it’s all around your neck and ears, such that you have a massive bald spot in the middle of your head, you are not hairy, even though the pure number of hairs you have isn’t too low.
Given this, we might be tempted to endorse the following principle, which trades off between the distribution of hairs for an additional number of hairs:
Distribution-for-Number: If I remove one hair from the middle of someone’s head, but double the number of hairs he has, this person has gotten hairier.
The trouble (maybe) with this principle is that, if we apply it repeatedly on a person who starts out with a normal amount of hair everywhere, we will eventually get someone who has a massive bald spot in the middle of their head, with a lot of hair on the side. This person (we might say) is less hairy than when he started, even though each individual move seemed to make him hairier overall.
Now, maybe this principle about trading off between the distribution of hair and the number of hairs isn’t too plausible. Or maybe the final verdict should just be that the person with the bald spot is actually hairier than the person we started out with. My point is merely: this is a different puzzle than the puzzle about plucking a single hair from someone until they are bald. The question here concerns trading off between two aspects of ‘hair’, whereas the question in the Sorites series of ‘hair’ is: is ‘hairiness’ intolerant of even a single hair being plucked off someone’s head?
Of course, I should be clear that this is not to say that the Sorites is totally irrelevant when thinking about the Spectrum Argument. It might be that some moves within the dialectic of the Spectrum Argument may eventually make use of resources from the work on vagueness. For instance, if one defends a lexical threshold view (a view on which no amount of x’s could ever be of more total value than some number of y’s) , one question from opponents may be about where such a threshold should obtain. Here, one can make analogies to the Sorites paradox and adopt one of those solutions to answer the lexical skeptic.
But that is compatible with the thrust of this post. My point here has merely been that the Sorites paradox and the Spectrum Argument are two different arguments, not that, within each argument, there aren’t moves you can make to defend one particular view that uses work on vagueness. Indeed, vagueness and line-drawing is part of most philosophical debates concerning some concept or other.
Do not be fooled by the fact that the Sorites and Spectrum Argument both involve applying a principle many times across many cases. The two arguments are subtly different. Next time you hear someone saying they are the same, send them this post! :)
Good post, absolutely true. I will say with this:
Tortures over Pinpricks: A world of billions of horrific tortures is preferable to a world of n mild, barely noticeable pinpricks.
This is just the dust specks vs torture debate, and I am firmly on the side that the torture is the more moral option. So as someone who accepts the repugnant conclusion, I think your version is actually weaker because your version doesn’t rely on the fact that creating barely net good lives is always good.
Note that the Repugnant Conclusion and Spectrum Argument apply to utility functions that try to add up a total amount of happiness. They don't apply to functions that just take an average of happiness. The post kind of just assumes we're talking about the former, but I think this is an important assumption to note!
Of course, we want to say more happy people is better than fewer happy people. A simple function you could choose is, "Pick the universe with the higher average happiness; if absolutely equal, then pick the one with more people." Of course, this immediately runs into its own weird Conclusion: A single super happy person would be picked over a universe full of billions of very happy people.
The natural next thing to try is combining the two measures, say, by calculating the worth of a universe by multiplying its average happiness by its total happiness to create a sort of custom happiness score (which will need extra tweaks to consider negative values, ie suffering, and other things we might care about, like just desserts, or qualities like "fulfillment" instead of "happiness").
My question: Does the Spectrum Argument still work on the simple multiplication function?
(If the answer to this isn't already known, I plan on exploring some examples and attempting a proof, one way or the other, when I find the time.)