It feels like this post starts with a definition of “coherence theorem”, sees that the so-called coherence theorems don’t match this definition, and thus criticizes the use of the term “coherence theorem”.
But this claimed definition of “coherence theorem” seems bad to me, and is not how I would use the phrase. Eliezer’s definition, OTOH is:
If you are not shooting yourself in the foot in sense X, we can view you as having coherence property Y.
which seems perfectly fine to me. It’s significant that this isn’t completely formalized, and requires intuitive judgement as to what constitutes “shooting yourself in the foot”.
Which makes the criticism feel unwarranted, or at best misdirected.
The point is: there are no theorems which state that, unless an agent can be represented as maximizing expected utility, that agent is liable to pursue strategies that are dominated by some other available strategy. The VNM Theorem doesn’t say that, nor does Savage’s Theorem, nor does Bolker-Jeffrey, nor do Dutch Books, nor does Cox’s Theorem, nor does the Complete Class Theorem.
But suppose we instead define ‘coherence theorems’ as theorems which state that
If you are not shooting yourself in the foot in sense X, we can view you as having coherence property Y.
Then you can fill in X and Y any way you like. Either it will turn out that there are no coherence theorems, or it will turn out that coherence theorems cannot play the role they’re supposed to play in coherence arguments.
Then you can fill in X and Y any way you like. Either it will turn out that there are no coherence theorems, or it will turn out that coherence theorems cannot play the role they’re supposed to play in coherence arguments.
That seems totally fine. A term like “coherence theorems” clearly is just like a rough category of things. The definition of the term should not itself bake in the validity of arguments built on top of the elements that the term is trying to draw a definition around.
It is not fine if, whichever way you interpret some premise, either:
(1) the premise comes out false.
Or:
(2) the premise does not support the conclusion.
Reserve the term ‘coherence theorems’ for whatever rough category you like. ‘Theorems which state that, unless an agent can be represented as maximizing expected utility, that agent is liable to pursue strategies that are dominated by some other available strategy’ refers to a precise category of non-existent things.
The title “There are no coherence theorems” seems click-baity to me, when the claim relies on a very particular definition “coherence theorem”. My thought upon reading the title (before reading the post) was something like “surely, VNM would count as a coherence theorem”. I am also a bit bothered by the confident assertions that there are no coherence theorems in the Conclusion and Bottom-lines for similar reason.
My use of the term matches common usage. See the Appendix.
‘There are no theorems which state that, unless an agent can be represented as maximizing expected utility, that agent is liable to pursue strategies that are dominated by some other available strategy’ would have been too long for a title.
I (reasonably, in my view) didn’t expect anyone to interpret me as denying the existence of the VNM Theorem, Savage’s Theorem, Bolker-Jeffrey, etc.
In any case, I explain how I’m using the term ‘coherence theorems’ in the second sentence of the post.
It feels like this post starts with a definition of “coherence theorem”, sees that the so-called coherence theorems don’t match this definition, and thus criticizes the use of the term “coherence theorem”.
But this claimed definition of “coherence theorem” seems bad to me, and is not how I would use the phrase. Eliezer’s definition, OTOH is:
which seems perfectly fine to me. It’s significant that this isn’t completely formalized, and requires intuitive judgement as to what constitutes “shooting yourself in the foot”.
Which makes the criticism feel unwarranted, or at best misdirected.
The point is: there are no theorems which state that, unless an agent can be represented as maximizing expected utility, that agent is liable to pursue strategies that are dominated by some other available strategy. The VNM Theorem doesn’t say that, nor does Savage’s Theorem, nor does Bolker-Jeffrey, nor do Dutch Books, nor does Cox’s Theorem, nor does the Complete Class Theorem.
But suppose we instead define ‘coherence theorems’ as theorems which state that
Then you can fill in X and Y any way you like. Either it will turn out that there are no coherence theorems, or it will turn out that coherence theorems cannot play the role they’re supposed to play in coherence arguments.
That seems totally fine. A term like “coherence theorems” clearly is just like a rough category of things. The definition of the term should not itself bake in the validity of arguments built on top of the elements that the term is trying to draw a definition around.
It is not fine if, whichever way you interpret some premise, either:
(1) the premise comes out false.
Or:
(2) the premise does not support the conclusion.
Reserve the term ‘coherence theorems’ for whatever rough category you like. ‘Theorems which state that, unless an agent can be represented as maximizing expected utility, that agent is liable to pursue strategies that are dominated by some other available strategy’ refers to a precise category of non-existent things.
The title “There are no coherence theorems” seems click-baity to me, when the claim relies on a very particular definition “coherence theorem”. My thought upon reading the title (before reading the post) was something like “surely, VNM would count as a coherence theorem”. I am also a bit bothered by the confident assertions that there are no coherence theorems in the Conclusion and Bottom-lines for similar reason.
Fair enough. I don’t think it’s click-baity:
My use of the term matches common usage. See the Appendix.
‘There are no theorems which state that, unless an agent can be represented as maximizing expected utility, that agent is liable to pursue strategies that are dominated by some other available strategy’ would have been too long for a title.
I (reasonably, in my view) didn’t expect anyone to interpret me as denying the existence of the VNM Theorem, Savage’s Theorem, Bolker-Jeffrey, etc.
In any case, I explain how I’m using the term ‘coherence theorems’ in the second sentence of the post.