It seems to me that this argument derives its force from the presupposition that value can be cleanly mapped onto numerical values. This is a tempting move, but it is not one that makes much sense to me: it requires supposing that ‘value’ refer to something like apples, considered as a commodity, when it doesn’t.
Begin with the intuition pump. For the intuition pump to function, we must grant that somebody would want to maximise the number of apples in the world; but I find it hard to see why anyone should grant this; this seems a pointless objective. The pump breaks.
It could be true that ‘If you’re an apple-maximizer, you mostly care about the first one because potential upside is unlimited. It wouldn’t be shocking if value worked the same way.’ But this conditional claim relies on a presupposition that I am not inclined to grant––namely that somebody might want to maximise the number of apples up to an arbitrarily large threshold––and that I think no-one should be inclined to grant. If value is like apples, we have no reason to maximise it up to an arbitrarily large threshold (a threshold large enough we cannot imagine it).
But value also doesn’t seem like apples as imagined in the intuition pump. Here are two apples:
🍎🍎
that together constitute two apples, which can be measured as two apple units. (We are to suppose, on the present picture, that every apple is the same.) But is value like this? By which I mean–is value like this:
🍎🍎
and so something we can count? It doesn’t seem like it to me. Maybe value is like this:
🍎🍎🍐 🍐
insofar as it is the product of combining apples and pears. But how do we combine apples and pears? The only kind of product we seem able to get when we add the above without further stipulations is: two apples and two pears. There is no natural unit.
The point I am getting at is this: a foundational assumption is that value is a quantity that is measured in value units; we can convert apples or pears or sensations or whatever into value units. But there seems no reason to suppose that this is how we should understand value.
Suppose, though, we allow that value is exactly like apples. A further problem comes out if we replace instances of ‘value’ with ‘apple’ in the remainder of the post. For instance, we now get:
A) If apple is bounded, you get 50,000 units of apple.
B) If apple is unbounded you get 10 billion units of apple.
C) If apple is unbounded you have a 1/googol chance of getting infinite units of apple.
Each of these is hard to parse. I don’t know how to make sense of ‘If apple is bounded’ except as ‘If the number of apples is bounded’. This presupposes that apples can be counted, which they can (although not without simplifying apples). But what does it mean to talk of ‘the number of values’ in this case? This picture doesn’t make sense to me.
Apples can be counted because apples are things; they sit there, one beside another, and can be collected into a pile. Value does not present itself this way. One might take ‘value’ to refer to something like: the importance of an action, or the significance of an outcome, or the excellence of a life, or the moral weight of a situation. But none of these are the sorts of things that naturally admit of cardinal measurement. They are appraised, not tallied. They are judged, not counted.
The further manoeuvres with credences and ‘deals’ simply repeat the same assumption in more elaborate clothing. Every comparison presupposes that value forms a countable currency: it can be translated into numbers that can be added, ranked, maximised, and even made infinite.
The structure is basically this:
Assume there is some thing X.
Assume X can be represented by a number Y.
Assume Y can take arbitrarily large or infinite values.
Assume we have credences over different theories T₁, T₂, …, each of which assigns Y-numbers to outcomes.
Assume that at least one of these theories treats higher Y as more choiceworthy.
When credences over Tᵢ are combined, the resulting ‘expected’ ranking is still defined over the Y-scale.
On any such scale, an infinite Y-outcome dominates all finite Y-outcomes.
Now let X = value.
Therefore a tiny credence in a theory allowing infinite Y forces fanaticism.
Therefore, under uncertainty about which attitude is correct, arbitrarily large (or infinite) value must dominate.
This argument makes sense only if we grant that X can be represented by a number Y in the first place. And that, even if we grant this, the Y-scale is common across theories. Neither of these make sense to me. Even if they can be made to make sense to you, this fact alone blocks the argument.
The general point is this: the whole argument only works if we accept a picture of value as something countable and fungible, like our apples. If we do not accept that picture, and there is no reason why we should, then nothing in the argument goes through. The fanatic conclusion simply reflects the structure of the picture, not the structure of value. It requires a picture of value I, for one, do not share.
I could say a lot about how this picture can be made to make sense. But I think the most useful additional thought is that this picture requires us to see value not so much as apples but as money: and that this is a painfully limited picture…
The apples being unbounded thing was just a brief intuition pump. It wasn’t really connected to the other stuff.
I don’t think the argument actually requires that different value systems can be compared in fungible units. You can just compare stuff that is, in one value system, clearly better than something in another value system. So, assume you have a credence of .5 in fanaticism and of .5 in bounded views. Well, creating 10,000 happy people given bounded views is less good than creating 10 trillion suffering people given unbounded views. But that’s less good than a one in googol chance of creating infinite people given unbounded views. So by transitivity, a 1/googol chance of infinite people given unbounded views wins out.
It seems to me that this argument derives its force from the presupposition that value can be cleanly mapped onto numerical values. This is a tempting move, but it is not one that makes much sense to me: it requires supposing that ‘value’ refer to something like apples, considered as a commodity, when it doesn’t.
Begin with the intuition pump. For the intuition pump to function, we must grant that somebody would want to maximise the number of apples in the world; but I find it hard to see why anyone should grant this; this seems a pointless objective. The pump breaks.
It could be true that ‘If you’re an apple-maximizer, you mostly care about the first one because potential upside is unlimited. It wouldn’t be shocking if value worked the same way.’ But this conditional claim relies on a presupposition that I am not inclined to grant––namely that somebody might want to maximise the number of apples up to an arbitrarily large threshold––and that I think no-one should be inclined to grant. If value is like apples, we have no reason to maximise it up to an arbitrarily large threshold (a threshold large enough we cannot imagine it).
But value also doesn’t seem like apples as imagined in the intuition pump. Here are two apples:
🍎🍎
that together constitute two apples, which can be measured as two apple units. (We are to suppose, on the present picture, that every apple is the same.) But is value like this? By which I mean–is value like this:
🍎🍎
and so something we can count? It doesn’t seem like it to me. Maybe value is like this:
🍎🍎🍐 🍐
insofar as it is the product of combining apples and pears. But how do we combine apples and pears? The only kind of product we seem able to get when we add the above without further stipulations is: two apples and two pears. There is no natural unit.
The point I am getting at is this: a foundational assumption is that value is a quantity that is measured in value units; we can convert apples or pears or sensations or whatever into value units. But there seems no reason to suppose that this is how we should understand value.
Suppose, though, we allow that value is exactly like apples. A further problem comes out if we replace instances of ‘value’ with ‘apple’ in the remainder of the post. For instance, we now get:
A) If apple is bounded, you get 50,000 units of apple.
B) If apple is unbounded you get 10 billion units of apple.
C) If apple is unbounded you have a 1/googol chance of getting infinite units of apple.
Each of these is hard to parse. I don’t know how to make sense of ‘If apple is bounded’ except as ‘If the number of apples is bounded’. This presupposes that apples can be counted, which they can (although not without simplifying apples). But what does it mean to talk of ‘the number of values’ in this case? This picture doesn’t make sense to me.
Apples can be counted because apples are things; they sit there, one beside another, and can be collected into a pile. Value does not present itself this way. One might take ‘value’ to refer to something like: the importance of an action, or the significance of an outcome, or the excellence of a life, or the moral weight of a situation. But none of these are the sorts of things that naturally admit of cardinal measurement. They are appraised, not tallied. They are judged, not counted.
The further manoeuvres with credences and ‘deals’ simply repeat the same assumption in more elaborate clothing. Every comparison presupposes that value forms a countable currency: it can be translated into numbers that can be added, ranked, maximised, and even made infinite.
The structure is basically this:
Assume there is some thing X.
Assume X can be represented by a number Y.
Assume Y can take arbitrarily large or infinite values.
Assume we have credences over different theories T₁, T₂, …, each of which assigns Y-numbers to outcomes.
Assume that at least one of these theories treats higher Y as more choiceworthy.
When credences over Tᵢ are combined, the resulting ‘expected’ ranking is still defined over the Y-scale.
On any such scale, an infinite Y-outcome dominates all finite Y-outcomes.
Now let X = value.
Therefore a tiny credence in a theory allowing infinite Y forces fanaticism.
Therefore, under uncertainty about which attitude is correct, arbitrarily large (or infinite) value must dominate.
This argument makes sense only if we grant that X can be represented by a number Y in the first place. And that, even if we grant this, the Y-scale is common across theories. Neither of these make sense to me. Even if they can be made to make sense to you, this fact alone blocks the argument.
The general point is this: the whole argument only works if we accept a picture of value as something countable and fungible, like our apples. If we do not accept that picture, and there is no reason why we should, then nothing in the argument goes through. The fanatic conclusion simply reflects the structure of the picture, not the structure of value. It requires a picture of value I, for one, do not share.
I could say a lot about how this picture can be made to make sense. But I think the most useful additional thought is that this picture requires us to see value not so much as apples but as money: and that this is a painfully limited picture…
The apples being unbounded thing was just a brief intuition pump. It wasn’t really connected to the other stuff.
I don’t think the argument actually requires that different value systems can be compared in fungible units. You can just compare stuff that is, in one value system, clearly better than something in another value system. So, assume you have a credence of .5 in fanaticism and of .5 in bounded views. Well, creating 10,000 happy people given bounded views is less good than creating 10 trillion suffering people given unbounded views. But that’s less good than a one in googol chance of creating infinite people given unbounded views. So by transitivity, a 1/googol chance of infinite people given unbounded views wins out.