I see your objection, and I see more clearly than before the need for thesis statements.
I want to show that given only a traditional assumption of philosophy (a premise of cogito ergo sum, I think), we must believe in the claim: “physical causes which duplicate Chalmers’ actions and speech, and which we could never physically distinguish from Chalmers himself, would produce qualia.” Let’s call this belief A for convenience. (I called a different statement A in a previous comment, but that whole version of the argument seems flawed.) It so happens that if we accept this claim we must reject the existence of p-zombies, but we care about p-zombies only for what they might tell us about A.
To that end, I argue that if we accept Chalmers’ zombiphile or anti-A argument C, which includes the assumption I just mentioned, we must logically believe A.
Therefore, I don’t argue that “the cognitive mechanism by which we conclude we have qualia is not 100% reliable.” I argue that we would have to accept a slightly more precise form of that claim if we accept C, and then I show some of the consequences. (Poorly, I think, but I can improve that part.)
Likewise, I don’t argue that “we can never determine what is and is not logically possible.” I argue that we must believe certain claims about logic and math, like the claim B that “arithmetic will never tell us ‘2+2=3’,” due to the same thought process we use to judge all rational beliefs. Now that seems less important if the argument in that previous comment fails. But I still think intuitively that if the probability of you the judge having qualia (call this belief Q) would not equal 1 in the limit, then lim{P(B)} would not equal 1. This of course seems consistent, since we don’t need to assign P(B)=1 now, and we’d have to if we believed with certainty that the limit = 1. But on this line of thinking we have to call ¬B logically possible without qualification, thereby destroying any practical or philosophical use for this kind of possibility unless we supplement it with more Bayesian reasoning. The same argument leads me to view adding a new postulate, like a bridging law or a string of Gödel statements, as entirely the wrong approach.
I think this allows me to make a stronger statement than Robert Bass, who as I mentioned near the start of the post turns out to make a closely related argument in the linked PDF, but does not explicitly try to define what philosophers normally call “knowledge”. (I don’t know if this accounts for the dearth of Google or Google Scholar results for “robert bass” and either chalmers or zombie.) Once I give my definition perhaps I should have just pointed out that P(A|C)=P(Q|C) in the limit. Thus if someone who treats Q as certain has knowledge of Q (as I think C asserts), we can only escape the conclusion that we know A when we treat it as certain by giving P(A|C) a smaller acceptable difference ε from the limit. (Edited to remove mistake in expression.) Now I can certainly think of scenarios where the exact P(A|Q) would matter a lot. But since A has more specific conditions than ‘uploading’ and rules out more possible problems than either this or sleep, and since P(A|Q)>P(A|C), I think knowing the latter has a margin of error no greater than P(Q) would fully reassure me. (I guess we’re imagining Omega telling me he’ll reset me at some later time to exactly my current physical state, which carries other worries but doesn’t make me fear zombie-hood as such.) And it seems inarguable that P(A|Q)>P(A|C), since C makes the further assumption that we’ll never find a contradiction in ¬A. You’ll notice this works out to P(A|Q)>P(Q|C), which by assumption seems pretty fraking certain.
“physical causes which duplicate Chalmers’ actions and speech, and which we could never physically distinguish from Chalmers himself, would produce qualia.”
As written this is under-defined and doesn’t even obviously contradict anything Chalmers says. What set of worlds does this ‘would’ apply to?
Better answer with slightly less snow-shoveling fatigue:
Chalmers assumes for the sake of argument that his actions and speech have physical causes. So the quoted claim A, by my argument in the fourth-to-last paragraph of the post, already stipulates the presence of the evidence that we gain from introspection and use to argue for qualia. Thus “would” applies to any logically possible world chosen at random, which may or may not have a “bridging law” to produce qualia. Chalmers doesn’t seem to address the probability of it having such a law given the physical causes or ontology that we find in A. I show this chance exceeds P(that we actually have qualia | the aforementioned evidence for qualia & the assumption that we’ll never prove A logically) -- long derivation at the end of this comment, since previous comments had flaws. Chalmers’ argument against physicalism depends on treating this long conditional proposition as certain enough for his purpose, as its denial would leave us with no reason to think qualia exist and indeed no clear definition of qualia. Without the proposition Chalmers would not have an argument so much as an assertion. I’ll look at what all of this means in a second.
In the grandparent I compare it to the situation in math. Gödel showed that we can’t prove arithmetic will never contradict itself (we can’t prove B logically) and I wanted to express this by saying that in any random logically possible world P(B)<1. Below you express it differently, saying the probability that we live in a logically possible world does not equal 1. According to that way of speaking, then, the chance that at least one logically possible world exists does not equal 1. It equals P(B), since if we could find a contradiction in one world then logic ‘leads to’ a contradiction in all worlds. And yet I argue that we know B, by means of Bayesian reasoning and the neglect of incredibly small probabilities that we have no apparent way to plan for. This would mean we know in the same way that logically possible worlds might tell us something about reality. The form of argument that Chalmers uses therefore takes its justification from Bayesian reasoning (and the neglect of incredibly small probabilities that we have no apparent way to plan for). If we can show that this process offers greater justification for A than for Chalmers’ argument, then we should place more trust in A. This would of course increase the probability of physicalism, which requires A and seems to deny Chalmers’ conclusion.
(In a prior comment I tried connecting the chance of A directly to the chance of B. But that version of the argument failed.)
What follows depends on the claim that our actions and speech have physical causes. If you accept my take on Chalmers’ actual defense, and use C’ to mean the claim that we’ll never find a contradiction in ¬A, while E means the aforementioned evidence for the evidence-finder having qualia (claim Q),
P(A|E&C’)=P(Q|E&C’)
and P(A|E) seems redundant, in which case
P(Q|E&C’)=P(A|E&C’)=P(A|C’)
Now,
P(Q|E)= P(Q|E&C’)P(C’) + P(Q|E&¬C’)P(¬C’)
and since ¬C’ means P(A)=1 within logic, P(Q|E&¬C’) means the chance of Q, given the evidence plus certainty that physical causes duplicating the evidence would produce qualia. So
P(Q|E&¬C’)=1
P(Q|E)= P(Q|E&C’)*P(C’) + P(¬C’)
As for A,
P(A)= P(A|C’)P(C’) + P(A|¬C’)P(¬C’)
and since P(A|¬C’) means the chance of A if ¬A contradicts itself,
P(A)= P(A|C’)*P(C’) + P(¬C’)
by substitution,
P(A)= P(Q|E&C’)*P(C’) + P(¬C’)
P(A)=P(Q|E)
¬C’ would clearly increase the chance of Q|E and C’ would decrease it,
I’m starting to think we shouldn’t talk about sets of worlds at all. But in those terms: once we make that assumption of knowledge in our own world, “would” applies to the set of logically possible worlds, which may or may not have a “bridging law” to produce qualia. Chalmers doesn’t seem to address the probability of them having such a law given the physical causes or ontology that we find in A. I show that it exceeds P(that we actually have qualia | we know we have qualia & we’ll never prove A logically).
As I argued in the grandparent, saying we need to add a “bridging law” therefore seems like a terrible way to express the situation.
You need to be a lot more precise. It is a chore to figure out what you’re talking about in some of these comments and we’ve gone several rounds and I’m still not sure what your thesis is.
once we make that assumption of knowledge in our own world, “would” applies to the set of logically possible worlds, which may or may not have a “bridging law” to produce qualia. Chalmers doesn’t seem to address the probability of them having such a law given the physical causes or ontology that we find in A.
I think what you’re saying here is that qualia will be found in the entire set of logically possible worlds physically identical to our world (any bridging law is non-physical we’ll stipulate). Some of these worlds might have some kind of ‘redundant’ bridging law- but even if that isn’t nonsensical we can ignore it.
Now, we can recognize that someone could discover that 2+2=3 but that doesn’t mean 2+2=3 is a logical possibility in the sense that there exists a logically possible world in which 2+2=3. Rather, we would just conclude that the world we live in isn’t logically possible under whatever system of logic is shown to be contradictory. If you want to do calculations that don’t assume classical logic and the system of real numbers then you need do them over a larger set of worlds than those that are merely logically possible (what business you have doing calculations at all if those worlds are ‘live’ possibilities, I’ll leave to you).
Now I agree with you that if we can be certain about the internal observation that leads us to conclude we have qualia then it follows that a bridging law is unnecessary as p-zombies also believe they have qualia for the same reasons non-p-zombies do. For p-zombies to be possible then, requires that mechanism to be unreliable. I’d be surprised if Chalmers actually argues we can be 100% certain we are not p-zombies-but alright lets say he does argue that. We can easily strengthen the argument as you suggest by simply saying that the cognitive mechanism that produces the belief that we possess qualia is not 100% reliable.
And in fact the worlds in which this cognitive mechanism fails are the worlds which, according to Chalmers, have no bridging law. As far as I’m concerned that solves the problem. We’ve answered the question which is- are there logically possible worlds physically identical to this one where Chalmers has no qualia. The answer is yes- those worlds in which the cognitive mechanism which alerts him of his qualia fails.
Whether or not those worlds are common, that is whether or not it is probable we are in such a world, is totally tangential to Chalmers argument. I don’t see the point of your equations and what they mean doesn’t make much sense to me- you seem to be conditionalizing on an argument and not evidence at times, which is confusing and controversial.
I see your objection, and I see more clearly than before the need for thesis statements.
I want to show that given only a traditional assumption of philosophy (a premise of cogito ergo sum, I think), we must believe in the claim: “physical causes which duplicate Chalmers’ actions and speech, and which we could never physically distinguish from Chalmers himself, would produce qualia.” Let’s call this belief A for convenience. (I called a different statement A in a previous comment, but that whole version of the argument seems flawed.) It so happens that if we accept this claim we must reject the existence of p-zombies, but we care about p-zombies only for what they might tell us about A.
To that end, I argue that if we accept Chalmers’ zombiphile or anti-A argument C, which includes the assumption I just mentioned, we must logically believe A.
Therefore, I don’t argue that “the cognitive mechanism by which we conclude we have qualia is not 100% reliable.” I argue that we would have to accept a slightly more precise form of that claim if we accept C, and then I show some of the consequences. (Poorly, I think, but I can improve that part.)
Likewise, I don’t argue that “we can never determine what is and is not logically possible.” I argue that we must believe certain claims about logic and math, like the claim B that “arithmetic will never tell us ‘2+2=3’,” due to the same thought process we use to judge all rational beliefs. Now that seems less important if the argument in that previous comment fails. But I still think intuitively that if the probability of you the judge having qualia (call this belief Q) would not equal 1 in the limit, then lim{P(B)} would not equal 1. This of course seems consistent, since we don’t need to assign P(B)=1 now, and we’d have to if we believed with certainty that the limit = 1. But on this line of thinking we have to call ¬B logically possible without qualification, thereby destroying any practical or philosophical use for this kind of possibility unless we supplement it with more Bayesian reasoning. The same argument leads me to view adding a new postulate, like a bridging law or a string of Gödel statements, as entirely the wrong approach.
I think this allows me to make a stronger statement than Robert Bass, who as I mentioned near the start of the post turns out to make a closely related argument in the linked PDF, but does not explicitly try to define what philosophers normally call “knowledge”. (I don’t know if this accounts for the dearth of Google or Google Scholar results for “robert bass” and either chalmers or zombie.) Once I give my definition perhaps I should have just pointed out that P(A|C)=P(Q|C) in the limit. Thus if someone who treats Q as certain has knowledge of Q (as I think C asserts), we can only escape the conclusion that we know A when we treat it as certain by giving P(A|C) a smaller acceptable difference ε from the limit. (Edited to remove mistake in expression.) Now I can certainly think of scenarios where the exact P(A|Q) would matter a lot. But since A has more specific conditions than ‘uploading’ and rules out more possible problems than either this or sleep, and since P(A|Q)>P(A|C), I think knowing the latter has a margin of error no greater than P(Q) would fully reassure me. (I guess we’re imagining Omega telling me he’ll reset me at some later time to exactly my current physical state, which carries other worries but doesn’t make me fear zombie-hood as such.) And it seems inarguable that P(A|Q)>P(A|C), since C makes the further assumption that we’ll never find a contradiction in ¬A. You’ll notice this works out to P(A|Q)>P(Q|C), which by assumption seems pretty fraking certain.
To clarify before proceeding:
As written this is under-defined and doesn’t even obviously contradict anything Chalmers says. What set of worlds does this ‘would’ apply to?
Better answer with slightly less snow-shoveling fatigue:
Chalmers assumes for the sake of argument that his actions and speech have physical causes. So the quoted claim A, by my argument in the fourth-to-last paragraph of the post, already stipulates the presence of the evidence that we gain from introspection and use to argue for qualia. Thus “would” applies to any logically possible world chosen at random, which may or may not have a “bridging law” to produce qualia. Chalmers doesn’t seem to address the probability of it having such a law given the physical causes or ontology that we find in A. I show this chance exceeds P(that we actually have qualia | the aforementioned evidence for qualia & the assumption that we’ll never prove A logically) -- long derivation at the end of this comment, since previous comments had flaws. Chalmers’ argument against physicalism depends on treating this long conditional proposition as certain enough for his purpose, as its denial would leave us with no reason to think qualia exist and indeed no clear definition of qualia. Without the proposition Chalmers would not have an argument so much as an assertion. I’ll look at what all of this means in a second.
In the grandparent I compare it to the situation in math. Gödel showed that we can’t prove arithmetic will never contradict itself (we can’t prove B logically) and I wanted to express this by saying that in any random logically possible world P(B)<1. Below you express it differently, saying the probability that we live in a logically possible world does not equal 1. According to that way of speaking, then, the chance that at least one logically possible world exists does not equal 1. It equals P(B), since if we could find a contradiction in one world then logic ‘leads to’ a contradiction in all worlds. And yet I argue that we know B, by means of Bayesian reasoning and the neglect of incredibly small probabilities that we have no apparent way to plan for. This would mean we know in the same way that logically possible worlds might tell us something about reality. The form of argument that Chalmers uses therefore takes its justification from Bayesian reasoning (and the neglect of incredibly small probabilities that we have no apparent way to plan for). If we can show that this process offers greater justification for A than for Chalmers’ argument, then we should place more trust in A. This would of course increase the probability of physicalism, which requires A and seems to deny Chalmers’ conclusion.
(In a prior comment I tried connecting the chance of A directly to the chance of B. But that version of the argument failed.)
What follows depends on the claim that our actions and speech have physical causes. If you accept my take on Chalmers’ actual defense, and use C’ to mean the claim that we’ll never find a contradiction in ¬A, while E means the aforementioned evidence for the evidence-finder having qualia (claim Q),
P(A|E&C’)=P(Q|E&C’)
and P(A|E) seems redundant, in which case
P(Q|E&C’)=P(A|E&C’)=P(A|C’)
Now, P(Q|E)= P(Q|E&C’)P(C’) + P(Q|E&¬C’)P(¬C’)
and since ¬C’ means P(A)=1 within logic, P(Q|E&¬C’) means the chance of Q, given the evidence plus certainty that physical causes duplicating the evidence would produce qualia. So
P(Q|E&¬C’)=1
P(Q|E)= P(Q|E&C’)*P(C’) + P(¬C’)
As for A,
P(A)= P(A|C’)P(C’) + P(A|¬C’)P(¬C’)
and since P(A|¬C’) means the chance of A if ¬A contradicts itself, P(A)= P(A|C’)*P(C’) + P(¬C’)
by substitution, P(A)= P(Q|E&C’)*P(C’) + P(¬C’)
P(A)=P(Q|E)
¬C’ would clearly increase the chance of Q|E and C’ would decrease it,
so P(A)>P(Q|E&C’)
I’m starting to think we shouldn’t talk about sets of worlds at all. But in those terms: once we make that assumption of knowledge in our own world, “would” applies to the set of logically possible worlds, which may or may not have a “bridging law” to produce qualia. Chalmers doesn’t seem to address the probability of them having such a law given the physical causes or ontology that we find in A. I show that it exceeds P(that we actually have qualia | we know we have qualia & we’ll never prove A logically).
As I argued in the grandparent, saying we need to add a “bridging law” therefore seems like a terrible way to express the situation.
You need to be a lot more precise. It is a chore to figure out what you’re talking about in some of these comments and we’ve gone several rounds and I’m still not sure what your thesis is.
I think what you’re saying here is that qualia will be found in the entire set of logically possible worlds physically identical to our world (any bridging law is non-physical we’ll stipulate). Some of these worlds might have some kind of ‘redundant’ bridging law- but even if that isn’t nonsensical we can ignore it.
Now, we can recognize that someone could discover that 2+2=3 but that doesn’t mean 2+2=3 is a logical possibility in the sense that there exists a logically possible world in which 2+2=3. Rather, we would just conclude that the world we live in isn’t logically possible under whatever system of logic is shown to be contradictory. If you want to do calculations that don’t assume classical logic and the system of real numbers then you need do them over a larger set of worlds than those that are merely logically possible (what business you have doing calculations at all if those worlds are ‘live’ possibilities, I’ll leave to you).
Now I agree with you that if we can be certain about the internal observation that leads us to conclude we have qualia then it follows that a bridging law is unnecessary as p-zombies also believe they have qualia for the same reasons non-p-zombies do. For p-zombies to be possible then, requires that mechanism to be unreliable. I’d be surprised if Chalmers actually argues we can be 100% certain we are not p-zombies-but alright lets say he does argue that. We can easily strengthen the argument as you suggest by simply saying that the cognitive mechanism that produces the belief that we possess qualia is not 100% reliable.
And in fact the worlds in which this cognitive mechanism fails are the worlds which, according to Chalmers, have no bridging law. As far as I’m concerned that solves the problem. We’ve answered the question which is- are there logically possible worlds physically identical to this one where Chalmers has no qualia. The answer is yes- those worlds in which the cognitive mechanism which alerts him of his qualia fails.
Whether or not those worlds are common, that is whether or not it is probable we are in such a world, is totally tangential to Chalmers argument. I don’t see the point of your equations and what they mean doesn’t make much sense to me- you seem to be conditionalizing on an argument and not evidence at times, which is confusing and controversial.
Ha, I wrote that answer in haste. Let me try once more.
Cool, take your time.