a) Even if sleeping beauty is a human, they are still a deterministic (or probabilistically deterministic) machine, so their responses in any scenario can be represented by an algorithm.
b) The halfer gets the same solution (indifference) too as 1), 2), 5) and 6) are all assigned a probability of 1⁄4; whilst 3) and 4) are ignored.
c) My point isn’t that the child might not have a name. My point is that in order to evaluate the statement: “Radford Neal has a half-sibling” we have to define the scheme in which someone comes to be called Radford Neal.
So, suppose the two potential mothers are Amy and Barbara. The first possibility is that Amy calls their child, if they have one, “Radford Neal”. However, if this is the case, it may come to pass that Amy doesn’t have a child so no-one is called Radford Neal and the reference fails. Alternatively, we might want to ensure that there is someone always called Radford Neal. If they only have one child, this is trivial, if there’s two, we could pick randomly. My point is that there isn’t a unique way of assigning the name, so I don’t know what scheme you want to use to replace the indexical.
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) Even if sleeping beauty is a human, they are still a deterministic (or probabilistically deterministic) machine, so their responses in any scenario can be represented by an algorithm.
b) The halfer gets the same solution (indifference) too as 1), 2), 5) and 6) are all assigned a probability of 1⁄4; whilst 3) and 4) are ignored.
c) My point isn’t that the child might not have a name. My point is that in order to evaluate the statement: “Radford Neal has a half-sibling” we have to define the scheme in which someone comes to be called Radford Neal.
So, suppose the two potential mothers are Amy and Barbara. The first possibility is that Amy calls their child, if they have one, “Radford Neal”. However, if this is the case, it may come to pass that Amy doesn’t have a child so no-one is called Radford Neal and the reference fails. Alternatively, we might want to ensure that there is someone always called Radford Neal. If they only have one child, this is trivial, if there’s two, we could pick randomly. My point is that there isn’t a unique way of assigning the name, so I don’t know what scheme you want to use to replace the indexical.
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.