That is, suppose you are considering whether or not to believe that you can fly by leaping off a cliff and flapping your arms. What is the expected utility of holding this belief?
I completely grant that this scheme can have disastrous consequences for a utility function that discounts consistency with past evidence, has short time horizons, considers only direct consequences, fails to consider alternatives, or is in any other way poorly chosen. Part of the point in naming it Pascal’s Goldpan was as a reminder of how naive utility functions using it will be excessively susceptible to wagers, muggings, and so on. Although I expect that highly weighting consistency with past evidence, long time horizons, considering direct and indirect consequences, considering all alternative hypotheses, and so on would prevent the obvious failure modes, it may nevertheless be that there exists no satisfactory utility function that would be safe using the Goldpan. That would certainly be compelling reason to abandon it.
That’s a little too vaguely stated for me to interpret. Can you give an illustration? For comparison, here’s one of how I assumed it would work:
A paperclip-making AI is given a piece of black-box machinery and given specifications for two possible control schemes for it. It calculates that if scheme A is true, it can make 700 paperclips per second, and if scheme B is true, only 300 per second. As a Bayesian AI using Pascal’s Goldpan formalized as a utilitarian prior, it assigns a prior probability of 0.7 for A and 0.3 for B. Then it either acts based on a weighted sum of models (0.7A+0.3B) or runs some experiments until it reaches a satisfactory posterior probability.
Occam’s razor is the basis for believing that those experiments tell us anything whatsoever about the future. Without it, there is no way to assign the probabilities you mention.
Clearly people who don’t know about Occam’s Razor, and people who explicitly reject it, still believe in the future. Just as clearly, we can use Occam’s Razor or other principles in evaluating theories about what happened in the past. Your claim appears wholly unjustified. Was it just a vague hifalutin’ metaphysical claim, or are there some underlying points that you’re not bringing out?
People who don’t know about Newtonian mechanics still believe that rocks fall downwards, but people who reject it explicitly will have a harder time reconciling their beliefs with the continued falling of rocks. It would be a mistake to reject Newtonian mechanics, then say “people who reject Newtonian mechanics clearly still believe that rocks fall”, then to conclude that there is no problem in rejecting Newtonian mechanics. Similarly, if you reject Occam’s razor then you need to replace it with something that actually fills the explanatory gap—it’s not good enough to say “well people who reject Occam’s razor clearly still believe Occam’s razor”, and then just carry right on.
I completely grant that this scheme can have disastrous consequences for a utility function that discounts consistency with past evidence, has short time horizons, considers only direct consequences, fails to consider alternatives, or is in any other way poorly chosen. Part of the point in naming it Pascal’s Goldpan was as a reminder of how naive utility functions using it will be excessively susceptible to wagers, muggings, and so on. Although I expect that highly weighting consistency with past evidence, long time horizons, considering direct and indirect consequences, considering all alternative hypotheses, and so on would prevent the obvious failure modes, it may nevertheless be that there exists no satisfactory utility function that would be safe using the Goldpan. That would certainly be compelling reason to abandon it.
The point is that to evaluate the utility of holding a belief, you need to have already decided upon a scheme to set your beliefs.
That’s a little too vaguely stated for me to interpret. Can you give an illustration? For comparison, here’s one of how I assumed it would work:
A paperclip-making AI is given a piece of black-box machinery and given specifications for two possible control schemes for it. It calculates that if scheme A is true, it can make 700 paperclips per second, and if scheme B is true, only 300 per second. As a Bayesian AI using Pascal’s Goldpan formalized as a utilitarian prior, it assigns a prior probability of 0.7 for A and 0.3 for B. Then it either acts based on a weighted sum of models (0.7A+0.3B) or runs some experiments until it reaches a satisfactory posterior probability.
That doesn’t seem intractably circular.
Occam’s razor is the basis for believing that those experiments tell us anything whatsoever about the future. Without it, there is no way to assign the probabilities you mention.
Clearly people who don’t know about Occam’s Razor, and people who explicitly reject it, still believe in the future. Just as clearly, we can use Occam’s Razor or other principles in evaluating theories about what happened in the past. Your claim appears wholly unjustified. Was it just a vague hifalutin’ metaphysical claim, or are there some underlying points that you’re not bringing out?
People who don’t know about Newtonian mechanics still believe that rocks fall downwards, but people who reject it explicitly will have a harder time reconciling their beliefs with the continued falling of rocks. It would be a mistake to reject Newtonian mechanics, then say “people who reject Newtonian mechanics clearly still believe that rocks fall”, then to conclude that there is no problem in rejecting Newtonian mechanics. Similarly, if you reject Occam’s razor then you need to replace it with something that actually fills the explanatory gap—it’s not good enough to say “well people who reject Occam’s razor clearly still believe Occam’s razor”, and then just carry right on.