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At this point, if not before, I doubt Omega's reliability, not mine.
It is a traditional feature of Omega that you have confidence 1 in its reliability and trustworthiness.
Traditions do not always make sense, neither are they necessarily passed down accurately. The original Omega, the one that appears in Newcomb's problem, does not have to be reliable with probability 1 for that problem to be a problem.
Of course, to the purist who says that 0 and 1 are not probabilities, you've just sinned by talking about confidence 1, but the problem can be restated to avoid that by asking for one's conditional probability P(Islam | Omega is and behaves as described).
In the present case, the supposition that one is faced with an overwhelming likelihood ratio raising the probability that Islam is true by an unlimited amount is just a blue tentacle scenario. Any number that anyone who agrees with the general anti-religious view common on LessWrong comes up with is going to be nonsense. Professing, say, 1 in a million for Islam on the grounds that 1 in a billion or 1 in a trillion is too small a probability for the human brain to cope with is the real cop-out, a piece of reversed stupidity with no justification of its own.
The scenario isn't going to happen. Forcing your brain to produce an answer to the question "but what if it did?" is not necessarily going to produce a meaningful answer.
Quite true. But if you want to dispute the usefulness of this tradition, you should address the broader and older tradition of which it is an instance: that thought experiments should abstract away real-world details irrelevant to the main point.
This is a pet peeve of mine, and I've wanted an excuse to post this rant for a while. Don't take it personally.
That "purist" is as completely wrong as the person who insists that there is no such thing as centrifugal force. They are ignoring the math in favor of a meme that enables them to feel smugly superior.
0 and 1 are valid probabilities in every mathematical sense: the equations of probability don't break down when passed p=0 or p=1 the way they do with genuine nonprobabilities like -1 or 2. A probability of 0 or 1 is like a perfect vacuum: it happens not to occur in the world that we happen to inhabit, but it is perfectly well-defined, we can do math with it without any difficulty, and it is extraordinarily useful in thought experiments.
When asked to consider a spherical black body of radius one meter resting on a frictionless plane, you don't respond "blue tentacles", you do the math.
I agree with the rant. 0 and 1 are indeed probabilities, and saying that they are not is a misleading way of enjoining people to never rule out anything. Mathematically, P(~A|A) is zero, not epsilon, and P(A|A) is 1, not 1-epsilon. Practically, 0 and 1 in subjective judgements mean as near to 0 and 1 as makes no practical difference. When I agree a rendezvous with someone, I don't say "there's a 99% chance I'll be there", I say "I'll be there".
Where we part ways is in our assessment of the value of this thought-experiment. To me it abstracts and assumes away so much that what is left does not illuminate anything. I can calculate 2^{-N}, but asked how large N would have to be to persuade me of some fantastic claim backed by this fantastic machine I simply cannot name any value. I have no confidence that whatever value I named would be the value I would actually use were this impossible scenario to come to pass.
Fair enough. But if we're doing that, I think the original question with the Omega machine abstracts too much away. Let's consider the kind of evidence that we would actually expect to see if Islam were true.
Let us stipulate that, on the 1st of Muḥarram, a prominent ayatollah claims to have suddenly become a prophet. They go on television and answer questions on all topics. All verifiable answers they give, including those to NP-complete questions submitted for experimental purposes, turn out to be true. The new prophet asserts the validity of the Qur'an as holy scripture and of Allah as the one God.
There is a website where you can suggest questions to put to the new prophet. Not all submitted questions get answered, due to time constraints, but interesting ones do get in reasonably often. Are there any questions you'd like to ask?
I'll give a reworded version of this, to take it out of the context of a belief system with which we are familiar. I'm not intending any mockery by this: It is to make a point about the claims and the evidence:
"Let us stipulate that, on Paris Hilton's birthday, a prominent Paris Hilton admirer claims to have suddenly become a prophet. They go on television and answer questions on all topics. All verifiable answers they give, including those to NP-complete questions submitted for experimental purposes, turn out to be true. The new prophet asserts that Paris Hilton is a super-powerful being sent here from another world, co-existing in space with ours but at a different vibrational something or whatever. Paris Hilton has come to show us that celebrity can be fun. The entire universe is built on celebrity power. Madonna tried to teach us this when she showed us how to Vogue but we did not listen and the burden of non-celebrity energy threatens to weigh us down into the valley of mediocrity when we die instead of ascending to a higher plane where each of us gets his/her own talkshow with an army of smurfs to do our bidding. Oh, and Sesame Street is being used by the dark energy force to send evil messages into children's feet. (The brain only appears to be the source of consciousness: Really it is the feet. Except for people with no feet. (Ah! I bet you thought I didn't think of that.) Today's lucky food: custard."
There is a website where you can suggest questions to put to the new prophet. Not all submitted questions get answered, due to time constraints, but interesting ones do get in reasonably often. Are there any questions you'd like to ask?"
The point I am making here is that the above narrative is absurd, and even if he can demonstrate some unusual ability with predictions or NP problems (and I admit the NP problems would really impress me), there is nothing that makes that explanation more sensible than any number of other stupid explanations. Nor does he have an automatic right to be believed: His explanation is just too stupid.
Yes - I would ask this question:
"Mr Prophet, are you claiming that there is no other theory to account for all this that has less intrinsic information content than a theory which assumes the existence of a fundamental, non-contingent mind - a mind which apparently cannot be accounted for by some theory containing less information, given that the mind is supposed to be non-contingent?"
He had better have a good answer to that: Otherwise I don't care how many true predictions he has made or NP problems he has solved. None of that comes close to fixing the ultra-high information loading in his theory.
"The reason you feel confused is because you assume the universe must have a simple explanation.
The minimum message length necessary to describe the universe is long -- long enough to contain a mind, which in fact it does. There is no fundamental reason why the Occamian prior must be appropriate. It so happens that Allah has chosen to create a world that, to a certain depth, initially appears to follow that law, but Occam will not take you all the way to the most fundamental description of reality.
I could write out the actual message description, but to demonstrate that the message contains a mind requires volumes of cognitive science that have not been developed yet. Since both the message and the proof of mind will be discovered by science within the next hundred years, I choose to spend my limited time on earth in other areas."
Do you think that is persuasive?
It's not sufficient to persuade me, but I do think it shows that the hypothesis is not a priori completely impossible.
A Moslem would say to him, "Mohammed (pbuh) is the Seal of the Prophets: there can be none after Him. The Tempter whispers your clever answers in your ear, and any truth in them is only a ruse and a snare!" A Christian faced with an analogous Christian prophet would denounce him as the Antichrist. I ask -- not him, but you -- why I should believe he is as trustworthy on religion as he is on subjects where I can test him?
I might incidentally ask him to pronounce on the validity of the hadith. I have read the Qur'an and there is remarkably little in it but exhortations to serve God.
"Also, could you settle all the schisms among those who already believe in the validity of the Qur'an as holy scripture and of Allah as the one God, and still want to bomb each other over their interpretations?"
This is sect-dependent. The Mormons would probably be quite happy to accept one provided he attained prophet-hood through church-approved channels.
I wasn't aware of that particular tenet. I suppose the Very Special Person would have to identify as some other role than prophet.
If your prior includes the serious possibility of a Tempter that seems reliable until you have to trust it on something important, why couldn't the Tempter also falsify scientific data you gather?
"Indeed, the service of God is the best of paths to walk in life."
"Sure, that's why I'm here. Which point of doctrine do you want to know about?"
When I condition on the existence of this impossible prophet, many improbable ideas are raised to attention, not merely the one that he asserts.
To bring the thought-experiment slightly closer to reality, aliens arrive, bringing advanced technology and religion. Do we accept the religion along with the technology? I'm sure science fiction has covered that one umpteen times, but the scenario has already been played out in history, with European civilisation as the aliens. They might have some things worth taking regarding how people should deal with each other, but strange people from far away with magic toys are no basis for taking spooks any more seriously.
I find the alien argument very persuasive.
Suppose a server appeared on the internet relaying messages from someone claiming to be the sysadmin of the simulation we're living in, and asking that we refrain from certain types of behavior because it's making his job difficult. Is there any set of evidence that would persuade you to go along with the requests, and how would the necessary degree of evidence scale with the inconvenience of the requests?
This is a copout.