One of my main objections to Bayesianism is that it prescribes that ideal agent’s beliefs must be probability distributions, which sounds even more absurd to me.
From one viewpoint, I think this objection is satisfactorily answered by Cox’s theorem—do you find it unsatisfactory (and if so, why)?
Let me focus on another angle though, namely the “absurdity” and gut level feelings of probabilities.
So, my gut feels quite good about probabilities. Like, I am uncertain about various things (read: basically everything), but this uncertainty comes in degrees: I can compare and possibly even quantify my uncertainties. I feel like some people get stuck on the numeric probabilities part (one example I recently ran to was this quote from Section III of this essay by Scott, “Does anyone actually consistently use numerical probabilities in everyday situations of uncertainty?”). Not sure if this is relevant here, but at the risk of going to a tangent, here’s a way of thinking about probabilities I’ve found clarifying and which I haven’t seen elsewhere:
The correspondence
beliefs <-> probabilities
is of the same type as
temperature <-> Celsius-degrees.
Like, people have feelings of warmth and temperature. These come in degrees: sometimes it’s hotter than some other times, now it is a lot warmer than yesterday and so on. And sure, people don’t have a built-in thermometer mapping these feelings to Celsius-degrees, they don’t naturally think of temperature in numeric degrees, they frequently make errors in translating between intuitive feelings and quantitative formulations (though less so with more experience). Heck, the Celsius scale is only a few hundred years old! Still, Celsius degrees feel like the correct way of thinking about temperature.
And the same with beliefs and uncertainty. These come in degrees: sometimes you are more confident than some other times, now you are way more confident than yesterday and so on. And sure, people don’t have a built-in probabilitymeter mapping these feelings to percentages, they don’t naturally think of confidence in numeric degrees, they frequently make errors in translating between intuitive feelings and quantitative formulations (though less so with more experience). Heck, the probability scale is only a few hundred years old! Still, probabilities feel like the correct way of thinking about uncertainty.
From this perspective probabilities feel completely natural to me—or at least as natural as Celsius-degrees feel. Especially questions like “does anyone actually consistently use numerical probabilities in everyday situations of uncertainty?” seem to miss the point, in the same way that “does anyone actually consistently use numerical degrees in everyday situations of temperature?” seems to miss the point of the Celsius scale. And I have no gut level objections to the claim that an ideal agent’s conceptions of warmth beliefs correspond to probabilities.
From one viewpoint, I think this objection is satisfactorily answered by Cox’s theorem—do you find it unsatisfactory (and if so, why)?
Let me focus on another angle though, namely the “absurdity” and gut level feelings of probabilities.
So, my gut feels quite good about probabilities. Like, I am uncertain about various things (read: basically everything), but this uncertainty comes in degrees: I can compare and possibly even quantify my uncertainties. I feel like some people get stuck on the numeric probabilities part (one example I recently ran to was this quote from Section III of this essay by Scott, “Does anyone actually consistently use numerical probabilities in everyday situations of uncertainty?”). Not sure if this is relevant here, but at the risk of going to a tangent, here’s a way of thinking about probabilities I’ve found clarifying and which I haven’t seen elsewhere:
The correspondence
beliefs <-> probabilities
is of the same type as
temperature <-> Celsius-degrees.
Like, people have feelings of warmth and temperature. These come in degrees: sometimes it’s hotter than some other times, now it is a lot warmer than yesterday and so on. And sure, people don’t have a built-in thermometer mapping these feelings to Celsius-degrees, they don’t naturally think of temperature in numeric degrees, they frequently make errors in translating between intuitive feelings and quantitative formulations (though less so with more experience). Heck, the Celsius scale is only a few hundred years old! Still, Celsius degrees feel like the correct way of thinking about temperature.
And the same with beliefs and uncertainty. These come in degrees: sometimes you are more confident than some other times, now you are way more confident than yesterday and so on. And sure, people don’t have a built-in probabilitymeter mapping these feelings to percentages, they don’t naturally think of confidence in numeric degrees, they frequently make errors in translating between intuitive feelings and quantitative formulations (though less so with more experience). Heck, the probability scale is only a few hundred years old! Still, probabilities feel like the correct way of thinking about uncertainty.
From this perspective probabilities feel completely natural to me—or at least as natural as Celsius-degrees feel. Especially questions like “does anyone actually consistently use numerical probabilities in everyday situations of uncertainty?” seem to miss the point, in the same way that “does anyone actually consistently use numerical degrees in everyday situations of temperature?” seems to miss the point of the Celsius scale. And I have no gut level objections to the claim that an ideal agent’s conceptions of
warmthbeliefs correspond to probabilities.