So I’m having difficulty getting traction on the actual content- there is too much going on and you’re not especially systematic. You need more thesis and subthesis statements. Maybe we can diagram your argument?
Chalmers claims zombies are logically possible.
Thomas tries to form a trilemma by arguing that we can’t regard statements made by Zombie Chalmers about consciousness as true, or false, or meaningless.
This looks bad but I don’t see yet how this implies the logical impossibility of p-zombies.
But the important lemma requires an account of knowledge in order to work.
I take it this is the part you take on in your discussion of Gettier cases.
To run through the other two lemmas: we know the zombie statements have meaning or truth values for us, the people postulating them, so let the rest of the argument apply to those meanings. And if we call the statements true then they must by assumption refer to something other than consciousness — call it consciousness-Z. But then Zombie Hairyfigment will (by assumption) say, “I have real consciousness and not just consciousness-Z.”
Okay, so zombie statements about their consciousness will not be true- since they will insist they are conscious and they are not. I’m leaning toward ‘those statements are false’ at the moment.
The remaining lemma tries to draw a contradiction out of the zombiphile argument’s assumption that Chalmers has knowledge of his own consciousness. We need some way to recognize or rule out knowledge in order for this to work. Happily, on this one question standard philosophy seems to point clearly towards the answer we want.
In what way is Chalmers’s argument dependent upon this assumption?
Can you explain what your analysis of Gettier type cases is supposed to show about zombie statements about consciousness?
I need a basic outline of the primary claims before I can go farther. (Hopefully this will also help you organize and explain your argument better).
This looks bad but I don’t see yet how this implies the logical impossibility of p-zombies.
Er, what? It would rule out each of the exhaustive possibilities (if we can reduce the options to three, as I tried to do briefly.) This would imply the logical impossibility of Zombie World by reductio, because the assumptions of Zombie World include a p-zombie Chalmers making statements about qualia. (I edited the post after the fact to more clearly specify Chalmers’ particular version of the zombiphile argument and to state his conclusion.)
(I could have spent more time on the lemma that we can’t regard Z-Chalmers’ statements as meaningless. But the meanings that we the readers take from them derive from the assumptions of the zombiphile argument. As near as I can tell, an inherent contradiction in these ‘apparently conceivable’ meanings for Z-Chalmers’ statements would mean a contradiction in the argument, therefore etc. Q.E.D.)
The important lemma says we can’t regard the statements as false because that would make Chalmers’ own knowledge of the existence of qualia unreliable. Now this depends on his whole argument up to the “bridging law”, not just the zombie part. I have to assume that one of us knows “qualia” exist (as I think he has to assume it in order to draw any conclusion.) This would create a major flaw in my argument if the assumption seemed doubtful in any meaningful way, or if Chalmers didn’t seem so certain of it.
Even granting this, my analysis of Gettier cases leads me to call the lemma open to interpretation. If we try to find the best form of the zombiphile argument then we could technically save it from contradiction. This, however, requires us to call our belief in qualia less-than-perfect evidence for their existence. Our belief counts as evidence to the extent that it actually co-exists with qualia, or the bridging law that produces them from ‘matter’. But the fact of our consciousness appears as certain as any fact we know. I therefore argue that a priori (or rather, depending on that last sentence alone) we cannot assign the Zombie World more probability than any of the claims we casually reject in the field of math, like the claim that arithmetic contradicts itself, or the claim that every single mathematician or programmer who helped examine (say) the proof of Gödel’s Incompleteness Theorem actually made some hidden mistake than none of us can find. Likewise, we must assign at least the amount of probability that we laughably call ‘mathematical certainty’ to the link leading from the ‘physical’ or functional causes we postulated in p-zombies, to consciousness.
At some point I’ll try to spell out exactly which causes I think do the work. In particular I want to see if they exist within any process that spits out an argument for believing in qualia (probably not.) But first let’s try to nail these parts down.
Ah very good. That was clear enough for me to pinpoint exactly where I think you’ve wrong.
The analyticity of a claim does not correspond all that well to the probability human’s assign to it’s truth. In other words, it may be true that p(hairyfigment is a zombie) is no more likely than 2+2=3. But that doesn’t make ‘hairfigment is a zombie’ logically impossible even though 2+2=3 is. This is rather trivial to see actually. Right now I’m wearing Converse All-Star sneakers. I’m pretty certain of this and, in fact, I’m more certain of this than 4523199 x 66734=301851162066 (I’ve did this with a calculator, but lets pretend I did it by hand or that someone just handed me a piecer of paper with this equation on it). This is in fact true of the vast majority of mathematical and logical statements- statements whose negations are logically impossible. Nonetheless, it is not logically impossible that I am not wearing Converse All-Star sneakers. Humans are not logically omniscient and sufficiently complex truisms can involve a lot of uncertainty. In contrast, rather simple observations involve little uncertainty but are not logical truisms. It is also not logically impossible that you are being deceived by a Cartesian Demon.
Of course there is also the question of to what extent incorrect mathematical statements are actually logically possibilities and what it actually means for something to be a logical possibility (it may not be the same thing as a metaphysical possibility).
I’m not sure I see how the Gettier cases are fitting in though.
Take the assumptions that seem least convenient for my argument, as given in my previous comment. Say the probability that “arithmetic will never tell us ‘2+2=3’,” does in fact converge to 1.
Let lim{P(x)} mean the limit of x’s probability as we follow a sequence of evidence, such that no truths added to the middle of the sequence could change the limit. If A means “physical causes which duplicate Chalmers’ actions and speech, and duplicate the functional process producing them, would produce qualia,” and B means “arithmetic will never tell us ‘2+2=3’,” and C means all of Chalmers’ premises, I think my analysis of Gettier cases leads in part to this:
lim{P(B)} - lim{P(A|C)} ⇐ | P(B) - lim{P(B)} |
I’d also argue that we should interpret probabilities as rational, logical degrees of belief. For this it helps if you’ve read the Intuitive Explanation of Bayes’ Theorem. Then I can show a flaw in frequentism and perhaps in subjective-Bayesianism just by pointing out that EY’s first problem has a unique answer, whether or not you choose to call it a probability. It has a unique answer even if we call the woman Martha. From there we can go straight to the problem of priors, as I did in my third note.
Going back to the math, then: if you think the right-hand side has a non-zero value, then logically you should adjust P(B). Because you must expect evidence that would lead you to change your mind, and that means you should change your mind now.
Ergo, logic tells us to believe A|C at least as much as we believe B.
I could be wrong, but I think this doesn’t quite address it.
First, I don’t deal directly with P(hairyfigment is a zombie). We should replace that with something like P(someone talking about qualia is a zombie| Zombie World exists & knowledge of qualia exists). And while I do get that second premise from introspection, I believe I could also get it from Chalmers. After that I follow logic to get the result.
Second, and this may bring us closer to the real disagreement, you don’t know the claim “2+2=3” is logically impossible, at least not from logic itself. (If that sounds like what you wanted to say at the end there, you can skip to the next paragraph.) Gödel tells us that logic can’t prove its own consistency or that of arithmetic. For all we know mathematically, it may allow us to prove both “2+2=4″ and “2+2=3” from whatever set of assumptions you want to use. You can prove consistency from within a different set of assumptions, but that just pushes the problem elsewhere. In reality, we believe logic and arithmetic don’t contradict themselves because they never have.
This brings me to Gettier. I think if we accept the Gettier intuitions, we have to define knowledge using the laws of probability. And this definition applies to logic. I pointed out in one of my notes that this makes sense formally. I also believe it makes practical sense for the reason I just gave. If we reject the definition I think we have to say that we’ll never know if 2+2 can give us three, nor could any logically omniscient entity know.
Now, for the statement that “arithmetic will never tell us ‘2+2=3’,” you could say we have a large probability of certainty. For the statement that “physical causes which duplicate Chalmers’ actions and speech would produce qualia,” you could say we have certainty of a large minimum probability. But surely the two give us equal “knowledge” of the statement. My imaginary, logically and empirically omniscient reader might give the two claims different numbers. The first might get P=1 in the limit while the second has P=1-ε by assumption. But I defined ε as the difference we feel we can ignore when it comes to the most certain claim we could possibly make! If you feel we can’t ignore it then aren’t you thinking of the wrong number? (Technically ε could equal zero.)
I’ll have to think about this some more. For now, we can agree that I started by assuming all Chalmers’ premises and arrived at an overwhelmingly high probability for the link he wants to prove logically unnecessary, yes?
First, I don’t deal directly with P(hairyfigment is a zombie). We should replace that with something like P(someone talking about qualia is a zombie| Zombie World exists & knowledge of qualia exists).
Huh? If we live in a Zombie world than by assumption everyone, whether they’re talking about qualia or not, is a p-zombie.
I’m discussing whether or not you are a zombie (or that Chalmers is a zombie) because that becomes the crux of the issue once we stipulate that the cognitive mechanism by which we conclude we have qualia is not 100% reliable.
In reality, we believe logic and arithmetic don’t contradict themselves because they never have.
There is no reason for us to get into that. Your claim here is the same as saying that we can never determine what is and is not logically possible. That it isn’t an unreasonable claim but you can’t proceed from it and show that p-zombies are logically impossible. Obviously.
We use logic and math, plus some kind of ontology to draw our map of reality. Chalmer’s claim is that our physical ontology combined with logic and math is insufficient to describe the world we live in- namely the one where we have qualia. So by necessity we’re bracketing questions about the consistency of logic and mathematics and assuming they work. The question is whether or not qualia is a logical extension of our physical ontology. Chalmer’s claims it isn’t.
This brings me to Gettier. I think if we accept the Gettier intuitions, we have to define knowledge using the laws of probability. And this definition applies to logic.
I already endorse strict Bayesian epistemology and think talk of “knowledge” is basically meaningless- beliefs just have probabilites. This applies to statements I make about logic as well. But that doesn’t make logical claims that same as empirical claims! We might express our credence of them the same way but that doesn’t make them categorically indistinguishable. Chalmer’s point is that qualia isn’t included in our physical description of the universe nor is it part of any logical extension of that ontology. It’s a conceptually distinct phenomena that requires our description of the universe to have an additional term.
Now, for the statement that “arithmetic will never tell us ‘2+2=3’,” you could say we have a large probability of certainty. For the statement that “physical causes which duplicate Chalmers’ actions and speech would produce qualia,” you could say we have certainty of a large minimum probability. But surely the two give us equal “knowledge” of the statement.
Yes, claims based on self-observation can have similar probabilities to deductive claims. But that isn’t Chalmer’s point. The self-observation you use to conclude you have qualia isn’t a logical extrapolation from the physical description of your brain. When Chalmers says Zombie Dave is a logical or metaphysical possibility he isn’t making a statement about the size of the set of worlds in which zombies exist. Rather, he is saying in the set of epistemically possible worlds (which includes logically impossible worlds since we are not logically omniscient) there are zombie worlds in the subset which is logically/metaphysically possible.
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.
So I’m having difficulty getting traction on the actual content- there is too much going on and you’re not especially systematic. You need more thesis and subthesis statements. Maybe we can diagram your argument?
Chalmers claims zombies are logically possible.
This looks bad but I don’t see yet how this implies the logical impossibility of p-zombies.
I take it this is the part you take on in your discussion of Gettier cases.
Okay, so zombie statements about their consciousness will not be true- since they will insist they are conscious and they are not. I’m leaning toward ‘those statements are false’ at the moment.
In what way is Chalmers’s argument dependent upon this assumption?
Can you explain what your analysis of Gettier type cases is supposed to show about zombie statements about consciousness?
I need a basic outline of the primary claims before I can go farther. (Hopefully this will also help you organize and explain your argument better).
Er, what? It would rule out each of the exhaustive possibilities (if we can reduce the options to three, as I tried to do briefly.) This would imply the logical impossibility of Zombie World by reductio, because the assumptions of Zombie World include a p-zombie Chalmers making statements about qualia. (I edited the post after the fact to more clearly specify Chalmers’ particular version of the zombiphile argument and to state his conclusion.)
(I could have spent more time on the lemma that we can’t regard Z-Chalmers’ statements as meaningless. But the meanings that we the readers take from them derive from the assumptions of the zombiphile argument. As near as I can tell, an inherent contradiction in these ‘apparently conceivable’ meanings for Z-Chalmers’ statements would mean a contradiction in the argument, therefore etc. Q.E.D.)
The important lemma says we can’t regard the statements as false because that would make Chalmers’ own knowledge of the existence of qualia unreliable. Now this depends on his whole argument up to the “bridging law”, not just the zombie part. I have to assume that one of us knows “qualia” exist (as I think he has to assume it in order to draw any conclusion.) This would create a major flaw in my argument if the assumption seemed doubtful in any meaningful way, or if Chalmers didn’t seem so certain of it.
Even granting this, my analysis of Gettier cases leads me to call the lemma open to interpretation. If we try to find the best form of the zombiphile argument then we could technically save it from contradiction. This, however, requires us to call our belief in qualia less-than-perfect evidence for their existence. Our belief counts as evidence to the extent that it actually co-exists with qualia, or the bridging law that produces them from ‘matter’. But the fact of our consciousness appears as certain as any fact we know. I therefore argue that a priori (or rather, depending on that last sentence alone) we cannot assign the Zombie World more probability than any of the claims we casually reject in the field of math, like the claim that arithmetic contradicts itself, or the claim that every single mathematician or programmer who helped examine (say) the proof of Gödel’s Incompleteness Theorem actually made some hidden mistake than none of us can find. Likewise, we must assign at least the amount of probability that we laughably call ‘mathematical certainty’ to the link leading from the ‘physical’ or functional causes we postulated in p-zombies, to consciousness.
At some point I’ll try to spell out exactly which causes I think do the work. In particular I want to see if they exist within any process that spits out an argument for believing in qualia (probably not.) But first let’s try to nail these parts down.
(edited slightly for clarity)
Ah very good. That was clear enough for me to pinpoint exactly where I think you’ve wrong.
The analyticity of a claim does not correspond all that well to the probability human’s assign to it’s truth. In other words, it may be true that p(hairyfigment is a zombie) is no more likely than 2+2=3. But that doesn’t make ‘hairfigment is a zombie’ logically impossible even though 2+2=3 is. This is rather trivial to see actually. Right now I’m wearing Converse All-Star sneakers. I’m pretty certain of this and, in fact, I’m more certain of this than 4523199 x 66734=301851162066 (I’ve did this with a calculator, but lets pretend I did it by hand or that someone just handed me a piecer of paper with this equation on it). This is in fact true of the vast majority of mathematical and logical statements- statements whose negations are logically impossible. Nonetheless, it is not logically impossible that I am not wearing Converse All-Star sneakers. Humans are not logically omniscient and sufficiently complex truisms can involve a lot of uncertainty. In contrast, rather simple observations involve little uncertainty but are not logical truisms. It is also not logically impossible that you are being deceived by a Cartesian Demon.
Of course there is also the question of to what extent incorrect mathematical statements are actually logically possibilities and what it actually means for something to be a logical possibility (it may not be the same thing as a metaphysical possibility).
I’m not sure I see how the Gettier cases are fitting in though.
Take the assumptions that seem least convenient for my argument, as given in my previous comment. Say the probability that “arithmetic will never tell us ‘2+2=3’,” does in fact converge to 1.
Let lim{P(x)} mean the limit of x’s probability as we follow a sequence of evidence, such that no truths added to the middle of the sequence could change the limit. If A means “physical causes which duplicate Chalmers’ actions and speech, and duplicate the functional process producing them, would produce qualia,” and B means “arithmetic will never tell us ‘2+2=3’,” and C means all of Chalmers’ premises, I think my analysis of Gettier cases leads in part to this:
lim{P(B)} - lim{P(A|C)} ⇐ | P(B) - lim{P(B)} |
I’d also argue that we should interpret probabilities as rational, logical degrees of belief. For this it helps if you’ve read the Intuitive Explanation of Bayes’ Theorem. Then I can show a flaw in frequentism and perhaps in subjective-Bayesianism just by pointing out that EY’s first problem has a unique answer, whether or not you choose to call it a probability. It has a unique answer even if we call the woman Martha. From there we can go straight to the problem of priors, as I did in my third note.
Going back to the math, then: if you think the right-hand side has a non-zero value, then logically you should adjust P(B). Because you must expect evidence that would lead you to change your mind, and that means you should change your mind now.
Ergo, logic tells us to believe A|C at least as much as we believe B.
I could be wrong, but I think this doesn’t quite address it.
First, I don’t deal directly with P(hairyfigment is a zombie). We should replace that with something like P(someone talking about qualia is a zombie| Zombie World exists & knowledge of qualia exists). And while I do get that second premise from introspection, I believe I could also get it from Chalmers. After that I follow logic to get the result.
Second, and this may bring us closer to the real disagreement, you don’t know the claim “2+2=3” is logically impossible, at least not from logic itself. (If that sounds like what you wanted to say at the end there, you can skip to the next paragraph.) Gödel tells us that logic can’t prove its own consistency or that of arithmetic. For all we know mathematically, it may allow us to prove both “2+2=4″ and “2+2=3” from whatever set of assumptions you want to use. You can prove consistency from within a different set of assumptions, but that just pushes the problem elsewhere. In reality, we believe logic and arithmetic don’t contradict themselves because they never have.
This brings me to Gettier. I think if we accept the Gettier intuitions, we have to define knowledge using the laws of probability. And this definition applies to logic. I pointed out in one of my notes that this makes sense formally. I also believe it makes practical sense for the reason I just gave. If we reject the definition I think we have to say that we’ll never know if 2+2 can give us three, nor could any logically omniscient entity know.
Now, for the statement that “arithmetic will never tell us ‘2+2=3’,” you could say we have a large probability of certainty. For the statement that “physical causes which duplicate Chalmers’ actions and speech would produce qualia,” you could say we have certainty of a large minimum probability. But surely the two give us equal “knowledge” of the statement. My imaginary, logically and empirically omniscient reader might give the two claims different numbers. The first might get P=1 in the limit while the second has P=1-ε by assumption. But I defined ε as the difference we feel we can ignore when it comes to the most certain claim we could possibly make! If you feel we can’t ignore it then aren’t you thinking of the wrong number? (Technically ε could equal zero.)
I’ll have to think about this some more. For now, we can agree that I started by assuming all Chalmers’ premises and arrived at an overwhelmingly high probability for the link he wants to prove logically unnecessary, yes?
Huh? If we live in a Zombie world than by assumption everyone, whether they’re talking about qualia or not, is a p-zombie.
I’m discussing whether or not you are a zombie (or that Chalmers is a zombie) because that becomes the crux of the issue once we stipulate that the cognitive mechanism by which we conclude we have qualia is not 100% reliable.
There is no reason for us to get into that. Your claim here is the same as saying that we can never determine what is and is not logically possible. That it isn’t an unreasonable claim but you can’t proceed from it and show that p-zombies are logically impossible. Obviously.
We use logic and math, plus some kind of ontology to draw our map of reality. Chalmer’s claim is that our physical ontology combined with logic and math is insufficient to describe the world we live in- namely the one where we have qualia. So by necessity we’re bracketing questions about the consistency of logic and mathematics and assuming they work. The question is whether or not qualia is a logical extension of our physical ontology. Chalmer’s claims it isn’t.
I already endorse strict Bayesian epistemology and think talk of “knowledge” is basically meaningless- beliefs just have probabilites. This applies to statements I make about logic as well. But that doesn’t make logical claims that same as empirical claims! We might express our credence of them the same way but that doesn’t make them categorically indistinguishable. Chalmer’s point is that qualia isn’t included in our physical description of the universe nor is it part of any logical extension of that ontology. It’s a conceptually distinct phenomena that requires our description of the universe to have an additional term.
Yes, claims based on self-observation can have similar probabilities to deductive claims. But that isn’t Chalmer’s point. The self-observation you use to conclude you have qualia isn’t a logical extrapolation from the physical description of your brain. When Chalmers says Zombie Dave is a logical or metaphysical possibility he isn’t making a statement about the size of the set of worlds in which zombies exist. Rather, he is saying in the set of epistemically possible worlds (which includes logically impossible worlds since we are not logically omniscient) there are zombie worlds in the subset which is logically/metaphysically possible.
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.