a) You know, it has not actually been demonstrated that human consciousness can be mimicked by Turing-equivalent computer. In any case, the only role of mentioning this in your argument seems to be to push your thinking away from Beauty as a human towards a more abstract notion of what the problem is in which you can more easily engage in reasoning that would be obviously fallacious if your thoughts were anchored in reality.
b) Halfer reasoning is invalid, so it’s difficult to say how this invalid reasoning would be applied in the context of this decision problem. But if one takes the view that probabilities do not depend on what decision problem they will be used for, it isn’t possible for possibilities 5) and 6) to have probability 1⁄4 while possibilities 3) and 4) have probability zero. One can imagine, for example, that Beauty is told about the balls from the beginning, but is told about the reward for guessing correctly, and how the balls play a role in determining that reward, only later. Should she change her probabilities for the six possibilities simply because she has been told about this reward scheme? I suspect your answer will be yes, but that is simply absurd. It is totally contrary to normal reasoning, and if applied to practical problems would be disastrous. Remember! Beauty is human, not a computer program.
c) You are still refusing to approach the Sallor’s Child problem as one about real people, despite the fact that the problem has been deliberately designed so that it has no fantastic aspects and could indeed be about real people, as I have emphasized again and again. Suppose the child is considering searching for their possible sibling, but wants to know the probability that the sibling exist before deciding to spend lots of money on this search. The child consults you regarding what the probability of their having a sibling is. Do you really start by asking, “what process did your mother use in deciding what name to give you”? The question is obviously of no relevance whatsoever. It is also obvious that any philosophical debates about indexicals in probability statements are irrelevant—one way or another, people solve probability problems every day without being hamstrung by this issue. There is a real person standing in front of you asking “what is the probability that I have a sibling”. The answer to this question is 2⁄3. There is no doubt about this answer. It is correct. Really. That is the answer.
Thanks for taking the time to write all of these responses, but I suspect that we’ve become stuck. At some point I’ll write up some posts aimed at trying to argue for my position, rather than primarily aimed at addressing rebuttal and perhaps it will clear up some of these issues.
a) You know, it has not actually been demonstrated that human consciousness can be mimicked by Turing-equivalent computer. In any case, the only role of mentioning this in your argument seems to be to push your thinking away from Beauty as a human towards a more abstract notion of what the problem is in which you can more easily engage in reasoning that would be obviously fallacious if your thoughts were anchored in reality.
b) Halfer reasoning is invalid, so it’s difficult to say how this invalid reasoning would be applied in the context of this decision problem. But if one takes the view that probabilities do not depend on what decision problem they will be used for, it isn’t possible for possibilities 5) and 6) to have probability 1⁄4 while possibilities 3) and 4) have probability zero. One can imagine, for example, that Beauty is told about the balls from the beginning, but is told about the reward for guessing correctly, and how the balls play a role in determining that reward, only later. Should she change her probabilities for the six possibilities simply because she has been told about this reward scheme? I suspect your answer will be yes, but that is simply absurd. It is totally contrary to normal reasoning, and if applied to practical problems would be disastrous. Remember! Beauty is human, not a computer program.
c) You are still refusing to approach the Sallor’s Child problem as one about real people, despite the fact that the problem has been deliberately designed so that it has no fantastic aspects and could indeed be about real people, as I have emphasized again and again. Suppose the child is considering searching for their possible sibling, but wants to know the probability that the sibling exist before deciding to spend lots of money on this search. The child consults you regarding what the probability of their having a sibling is. Do you really start by asking, “what process did your mother use in deciding what name to give you”? The question is obviously of no relevance whatsoever. It is also obvious that any philosophical debates about indexicals in probability statements are irrelevant—one way or another, people solve probability problems every day without being hamstrung by this issue. There is a real person standing in front of you asking “what is the probability that I have a sibling”. The answer to this question is 2⁄3. There is no doubt about this answer. It is correct. Really. That is the answer.
Thanks for taking the time to write all of these responses, but I suspect that we’ve become stuck. At some point I’ll write up some posts aimed at trying to argue for my position, rather than primarily aimed at addressing rebuttal and perhaps it will clear up some of these issues.