There’s an interesting relationship with mathematizing of decision problems here, which I think is reflective of normal philosophy practice.
For example, in the Smoking Lesion problem, and in similar cases where you consider an agent to have “urges” or “dispositions” et c., it’s important to note that these are pre-mathematical descriptions of something we’d like our decision theory to consider, and that to try to directly apply them to a mathematical theory is to commit a sort of type error.
Specifically, a decision-making procedure that “has a disposition to smoke” is not FDT. It is some other decision theory that has the capability to operate in uncertainty about its own dispositions.
I think it’s totally reasonable to say that we want to research decision theories that are capable of this, because this epistemic state of not being quite sure of your own mind is something humans have to deal with all the time. But one cannot start with a mathematically specified decision theory like proof-based UDT or causal-graph-based CDT and then ask “what it would do if it had the smoking lesion.” It’s a question that seems intuitively reasonable but, when made precise, is nonsense.
I think what this feels like to philosophers is giving the verbal concepts primacy over the math. (With positive associations to “concepts” and negative associations to “math” implied). But what it leads to in practice is people saying “but what about the tickle defense?” or “but what about different formulations of CDT” as if they were talking about different facets of unified concepts (the things that are supposed to have primacy), when these facets have totally distinct mathematizations.
At some point, if you know that a tree falling in the forest makes the air vibrate but doesn’t lead to auditory experiences, it’s time to stop worrying about whether it makes a sound.
So obviously I (and LW orthodoxy) are on the pro-math side, and I think most philosophers are on the pro-concepts side (I’d say “pro-essences,” but that’s a bit too on the nose). But, importantly, if we agree that this descriptive difference exists, then we can at least work to bridge it by being clear about whether were’s using the math perspective or the concept perspective. Then we can keep different mathematizations strictly separate when using the math perspective, but work to amalgamate them when talking about concepts.
There’s an interesting relationship with mathematizing of decision problems here, which I think is reflective of normal philosophy practice.
For example, in the Smoking Lesion problem, and in similar cases where you consider an agent to have “urges” or “dispositions” et c., it’s important to note that these are pre-mathematical descriptions of something we’d like our decision theory to consider, and that to try to directly apply them to a mathematical theory is to commit a sort of type error.
Specifically, a decision-making procedure that “has a disposition to smoke” is not FDT. It is some other decision theory that has the capability to operate in uncertainty about its own dispositions.
I think it’s totally reasonable to say that we want to research decision theories that are capable of this, because this epistemic state of not being quite sure of your own mind is something humans have to deal with all the time. But one cannot start with a mathematically specified decision theory like proof-based UDT or causal-graph-based CDT and then ask “what it would do if it had the smoking lesion.” It’s a question that seems intuitively reasonable but, when made precise, is nonsense.
I think what this feels like to philosophers is giving the verbal concepts primacy over the math. (With positive associations to “concepts” and negative associations to “math” implied). But what it leads to in practice is people saying “but what about the tickle defense?” or “but what about different formulations of CDT” as if they were talking about different facets of unified concepts (the things that are supposed to have primacy), when these facets have totally distinct mathematizations.
At some point, if you know that a tree falling in the forest makes the air vibrate but doesn’t lead to auditory experiences, it’s time to stop worrying about whether it makes a sound.
So obviously I (and LW orthodoxy) are on the pro-math side, and I think most philosophers are on the pro-concepts side (I’d say “pro-essences,” but that’s a bit too on the nose). But, importantly, if we agree that this descriptive difference exists, then we can at least work to bridge it by being clear about whether were’s using the math perspective or the concept perspective. Then we can keep different mathematizations strictly separate when using the math perspective, but work to amalgamate them when talking about concepts.