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wedrifid comments on How to Convince Me That 2 + 2 = 3 - Less Wrong

53 Post author: Eliezer_Yudkowsky 27 September 2007 11:00PM

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Comment author: wedrifid 29 July 2011 12:40:12AM *  12 points [-]

waits for wedrifid

I hadn't actually read the grandparent beyond skimming and categorized it as an entirely non-trollish expression of personal belief. Given the prompt in the post it was appropriate to the context and as rational as can be expected given that the guys' beliefs are utter nonsense.

Having read through the first comment (before the "to be continued") the following part jumped out at me as the primary non sequitur.

So, if the archaeological evidences corroborate the Book's story, then we must consider the Book to be "true", and thereby accept either P-True or P-Alien.

That just isn't case. Archaeological corroboration provides evidence for the Book's story. That is, part of the story is validated which eliminates a whole lot of the bits that could be wrong and we can assume a correlated truthiness with the remainder of the story. We update p(Book's Story) upward, but not to one. Something along the lines of:

p(Arch | BS) = x
p(Arch | !BS) = y

p(BS | Arch) = p(Arch | BS) * p(BS) / p(Arch)

We do not have the logical deduction "IF Arch THEN BS" but rather a likelyhood ratio such that BS is more likely the less likely it is for the archaelogical evidence is to exist given that the BS is false. Because p(Arch | BS) > p(Arch | !BS), Arch does something to overcome the incredibly low prior probability p(BS).

To put it another way there is a critical observation that deductively "(Book's Story) = (Archeologically verifiable parts) && (parts that are not archeologically verifiable)". This is before we go ahead and calculate p(Mormonism | BS) vs p(Alien | BS).

Another interesting probability calculation to consider is how likely it is that wedrifid will write out a bunch of probability calculations given the clearly false 'truth' proposition is the acronym of "Book's Story" vs wedrifid writing out a bunch of calculations about bullshit given the acronym is not BS. From this we can go ahead and chain our inferences to calculate p(wedrifid is peurile | wedrifid writes out the calculations). For what it is worth I think you should find that the likelyhood ratio is small even if your posterior is enormous.

Comment author: TheOtherDave 29 July 2011 01:04:13AM 2 points [-]

Upvoted for amusement value.

Comment author: Arandur 29 July 2011 12:33:26PM 3 points [-]

I take offense to any implications about my posterior.

Heck, even I upvoted this. Your point is well made, and well taken; even if archaeological evidence corroborates parts of the Book of Mormon, that does not update its probability to 1. I should have been more clear... no, rather, I should have thought of it that rationally, but I was blinded by my own certainty. I apologize; thank you for showing me my error.

Were I to rewrite the above, it would take the form of something like this:

The Book consists of two pieces of information: data that are archaeologically verifiable, and data that are not archaeologically verifiable. If archaeological evidences corroborate the Book's story, then there are two possibilities: either the non-archaeologically-verifiable bits are also true, or they are not. If the former is the case, then Joseph Smith's story is correct, the Church is true, etc. etc. If the non-archaeologically-verifiable bits are not true, given that the a.v. bits are, then we must conclude one of two things: either a coincidence (which probability becomes smaller with each additional corroborating evidence), or something Stranger, e.g. alien teenagers. I am inclined, given the current state of the evidence, to believe the above scenarios in the following order, in descending order of probability: a) The Book Is True, b) Aliens Are Trolling Us, c) Magnificent Coincidence. I also think that these three possibilities, and their subgroups, comprise the entirety of the probability space, but please correct me if there's a possibility I have overlooked.

Oh, as an aside: The proposition that "The mainstream LDS church is not true, but the truth is had by one of the handful of splinter groups that split off from the LDS church and still believe in the Book of Mormon" does in fact fall under possibility a, though considering the legal troubles surrounding some of these groups, this seems rather unlikely to me. After all, Joseph Smith published this as one of our thirteen Articles of Faith: "We believe in being subject to kings, presidents, rulers, and magistrates; in obeying, honoring, and sustaining the law."

Comment author: MatthewBaker 29 July 2011 03:39:23PM *  0 points [-]

Again in 2008 that same team of genetic scientists republished essentially the same article under the same title, making a similar point: "Here we show, by using 86 complete mitochondrial genomes, that all Native American haplogroups, including haplogroup X, were part of a single founding population, thereby refuting multiple-migration models." (http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2427228/?tool=pmcentrez)

Only solid piece of evidence i found on the DNA route, most of the rest seems to be arguing that there remains a miniscule chance despite the current consensus on DNA data.

Comment author: Arandur 29 July 2011 04:12:49PM 0 points [-]

I'm not sure why you chose to post this as a response to my rewrite, but that doesn't detract form the validity of the post.

I'm well acquainted with the fallacy you linked to; that's actually been one of my favorite of Eliezer's articles. It is unfortunate that this and other fallacies abound in real-world arguments... however, I trust you understand that the existence of fallacies does not equate to a false conclusion. If I base my conclusion X on arguments A, B, C and D, and D is fallacious, X may still happily rest on A, B and C.

In particular, there's a difference between the hopeless grasping-at-straws of the "there's a chance it's a coincidence!" argument and the "This does not necessarily contradict what we're saying" argument. In the latter, there are also positive evidences to bolster the conclusion; it is true then that negative evidences (by that I mean, evidences which show no support for the conclusion, but do not disprove it) nudge the probability does, but not as much as the positive evidences nudge it up. In the former, all there is is wishful thinking.

Comment author: MatthewBaker 30 July 2011 04:17:11AM 0 points [-]

I trust you understand that the existence of fallacies does not equate to a false conclusion. If I base my conclusion X on arguments A, B, C and D, and D is fallacious, X may still happily rest on A, B and C.

I just think that if the DNA evidence isn't there then how can i consider the possibility of the book of Mormon having any truth to it. It feels a lot like considering the possibility of Intelligent Design as the origin of humanity. If A, B, and C preclude the existence of D then X is weakened more by the disproof of D then if it is a standalone piece of evidence.

Comment author: Arandur 30 July 2011 05:11:04AM 0 points [-]

But the DNA evidence is there. You pointed to a piece of it, and then said "but the rest is mostly bull". But that doesn't mean that the evidence you found ceases to be valid.

Comment author: wedrifid 29 July 2011 08:43:39PM 1 point [-]

While I do not accept certain of your premises (surprisingness of corroborated evidence) your reasoning from there is cogent and the update worthy of respect!

Comment author: Arandur 29 July 2011 11:33:33PM 1 point [-]

Oh! Well, thank you! I will attempt to be cogent the first time in the future. :3

Comment author: Bill_McGrath 14 September 2011 11:06:00AM 1 point [-]

Oh, as an aside: The proposition that "The mainstream LDS church is not true, but the truth is had by one of the handful of splinter groups that split off from the LDS church and still believe in the Book of Mormon" does in fact fall under possibility a, though considering the legal troubles surrounding some of these groups, this seems rather unlikely to me. After all, Joseph Smith published this as one of our thirteen Articles of Faith: "We believe in being subject to kings, presidents, rulers, and magistrates; in obeying, honoring, and sustaining the law."

I don't understand this - why would legal troubles make their beliefs any more or less likely to be true? Seems like an entirely irrelevant issue.

Comment author: gjm 14 September 2011 12:11:07PM 3 points [-]

I think the point is that not getting into legal trouble is an important tenet of Mormonism (since obeying the law was one of those 13 "Articles of Faith"), so that a group that's got into a lot of legal trouble is unlikely to be The One True LDS Church.

Comment author: Bill_McGrath 14 September 2011 07:03:52PM 1 point [-]

Cheers. I understand what he means now, but it still seems like a particularly peculiar belief.

Comment author: byrnema 29 July 2011 12:59:51PM *  0 points [-]

I gather the discussion of the whole thread rests on this unexpected premise:

we can assume a correlated truthiness with the remainder of the story

Stories always have a blend of fact and fiction. Accounts of travels, culture and civilizations may have some seeds of truth, but other parts about God's intentions and angels needn't be true.

My sense is that you are collectively underestimating how unpredictably information can pass down family lines and through traveling story-tellers, scholars and historians.

we must use archaeological evidence that would not have been available to Joseph Smith; that is, evidence lacking from what we must assume would be the knowledge available to a 21-year old unschooled farmhand in upstate New York in 1827

There's a lot packed into this. To give an analogy for a non-theistic example, if some details prove correct about the collective community's awareness of the lost location of Atlantis, Hans Christian Anderson shouldn't get credit for 'knowing' these details when he included them in The Little Mermaid.