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Customer Review

84 of 125 people found the following review helpful
1.0 out of 5 stars Mathematical Blasphemy, September 28, 2012
This review is from: Proving History: Bayes's Theorem and the Quest for the Historical Jesus (Hardcover)
As a mathematician, I really must object to Carrier's fast-and-loose treatment of mathematics and logic. While Bayes Theorem is a well established part of statistics, his methods press well beyond the confines of any form of axiomatic probability theory. Most irritating was Carrier's insistence that proving something to be unlikely is equivalent to proving something false. In general, heuristic arguments are not only invalid but also useless from a purely logical framework. One can easily conjure up a wide array of theorems in mathematics that hold true in spite of rather damning heuristic evidence, such as the Banach-Tarski Paradox. I would consider his entire premise suspect, due to his insistence on applying subjective quanities to an objective theorem and general lack of mathematical rigour.

That said, I am neither a theologian nor a historian: I can't make any claims to the validity or invalidity of Carrier's assertions about the "Historical Jesus." But if his usage of Bayes theorem is the cornerstone of his conclusions, I would certainly take them with a grain of salt.

I'm trying to keep this short, but if anyone wants me to expand and explain my reasoning, I will be happy to oblige.
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Showing 1-10 of 113 posts in this discussion
Initial post: Oct 2, 2012, 9:42:27 AM PDT
Last edited by the author on Oct 3, 2012, 9:57:21 AM PDT
Skepticus says:
"proving something to be unlikely is equivalent to proving something false."
Is this something you infer from Carrier's argument or is something that the author explicitly avers? I haven't read the book but am curious about the subject.
Just a bit of my own background: I've found Bayes' theorem very useful myself, for example in determining reasonable courses of treatment for medical conditions, where there are reasonably good prior probabilities available. and the incidence of the condition being tested is reasonably well-known. How this can be applied to historical studies is an interesting topic.
This is a complex subject and, if you like, go ahead and post. However, if you feel that this is too much to address intelligibly in a post on Amazon, is there some treatment of the subject on-line you could point to?

Answering my own question I see on Google that searching for Vridar, bayes theorem and historical method yields at least one hit where there is a discussion of this topic. Whether good or not I don't yet know.

In reply to an earlier post on Oct 9, 2012, 6:11:28 AM PDT
Godel says:
The main issue with using Bayes theorem for historical research is the lack of well defined probability. When determining the course of treatment for a person suffering from a disease, you have multiple samples: there are multiple people suffering from this disease you can give treatment. Herein is the definition of probability: as you treat more and more patients, the closer the percentage of those patients for whom treatment is successful gets to the calculated probability.

The issue with historical research is the lack of sampling because history only happens once. As a result, any rigorous probabilistic approach is useless because we only have a single data point to deal with.

Does that help clear things up?

In reply to an earlier post on Oct 19, 2012, 11:18:03 AM PDT
Matt Gerrans says:
Godel, Carrier talks about all this in his book. Did you read the book, or just do a review based on what you think it might be about?

"Most irritating was Carrier's insistence that proving something to be unlikely is equivalent to proving something false." -- can you cite some examples?

It seems to me that Carrier's main point is that having some better rigor in historicity arguments is much better than none at all and using things like "criteria" willy-nilly and inconsistently. I don't think he says that using BT is flawless and results in incontrovertible truths when the inputs are weak. In fact, he spends quite a lot of time and effort on just these problems.

Your review comes off as a straw man and it seems as if you may have skimmed the book in a bookstore, but not actually read it.

In reply to an earlier post on Oct 21, 2012, 7:32:54 PM PDT
Last edited by the author on Oct 21, 2012, 7:33:06 PM PDT
Godel says:
I'll admit my review is somewhat lacking in specific examples, which may be why you come to these conclusions. So I suppose I better make a more specific case. But, for the sake of succinctness, I focus on what I consider to be the most offensive fallacies.

First, on page 83, Carrier asserts that "given any belief about the past, you must believe it has some probability of being true or false." However, this is generally untrue. You cannot assume that a given probability exists, because we could be working in a probability space with unmeasurable sets. In other cases, the probability does exist, but it is impossible to calculate to any degree of accuracy. Carrier attempts to assuage these concerns with the concept of an "a fortiori" argument on page 85, but that doesn't help when dealing with unmeasurable or non-existent numbers. For example, consider the limit of sin(1/x) as x approaches 0. A first year calculus student can prove this value does not exist, but we can determine that, for all x in the neighborhood around 0, sin(1/x) is between -1 and 1. Thus, an "a fortiori" argument could be applied to this number, even though it does not actually exist. (I apologize that I had to use a calculus example here, but I could not think of a concrete example in history offhand).

Applying this and my previous observation about lack of sampling, I found his Bayesian analysis of the "smell test" and the "silence test" to be rather lacking. In particular, on page 116, Carrier's argument regarding the presence of miracles hinges on the fact that the presence of miracles now (or lack thereof) is evidence of the lack of miracles in the past. To the rigorous mathematician, this claim is not something you can just assume. On the contrary, this is not true in general. For instance, the probability of dying of the black plague was far higher in the middle ages than it is now. Granted, dying of the black plague is rather different than experiencing a miracle, but how do we seperate between data which remains constant over the years, and data which changes over the years? In fact, on reconsidering the argument, is it really reasonable to assume that miracles are uniformally distributed over time?

But perhaps I am being too hard on Carrier: historical deduction is an daunting task, and I do applaud his attempts to axiomize it. However, I do think his attempt to derive axioms from probability theory is lacking in rigour.

Thank you, Matt, for the question, and I hope this response explains my position better

In reply to an earlier post on Jan 1, 2013, 3:07:39 AM PST
Pen Name says:
"To the rigorous mathematician, this claim is not something you can just assume."

This is not something that is merely assumed. If testable miracle claims ALWAYS turn out to be false, that not only says something about claims of miracles, whether testable or not, it also says something about human nature, which can be inferred upon humans of the past. It's the view that miracles are not evenly distributed between the past and present that relies on too many assumptions. It depends on the actual existence of miracles (unproven), supernatural forces that are responsible for these miracles (unproven), and a motive (unproven) for why these supernatural beings would concentrate true miracles outside the realm of testability.

These are things rigorous mathemeticians should think about, since logic is just a branch of math.

In reply to an earlier post on Jan 6, 2013, 1:44:39 PM PST
Last edited by the author on Jan 6, 2013, 9:08:40 PM PST
Godel says:
But I'm not making any assumption about the temporal distribution of miracles. I am simply stating the possibility of miracles being irregularly distributed. And you don't know whether or not testable miracle claims always turn out to be false, because there could always be one that occurs tomorrow which turns out to be true. You could say that MOST testable miracle claims are false, and what that might say about human nature, but that is not sufficient to generalize to all miracle claims.

In reply to an earlier post on Feb 19, 2013, 12:37:32 PM PST
J. Jolin says:
Regarding miracle claims, all Godel has stated in this last post is that the prior probability for P(miracles|b) is very low and that any new miracle coming up tomorrow would have to be evaluated via P(e|miracles.b) versus P(e|not miracles.b). This is a Baysean argument. Our background knowledge b entails that no miracle claim thus far evaluated has turned out to be a true miracle but rather either a commonplace phenomenon mistaken for a miracle or a hoax. That makes P(miracles|b) vanishingly low.

Also, the statement made about how miracles not being common now does not mean they were not common in the past ignores the fact that our background knowledge includes knowledge of observations made by all of the sciences, which show that the laws that operate within the universe have shown no signs of change during the lifetime of the universe, but that the frequency that people make up stories about momentary changes in those laws (miracles) is high. This is true whether they are lying, delusional or just mistaken. Unless we have new evidence to show that the frequency of miracles was higher in the past than in the present, it is not fallacious or lacking in rigor to presume the null hypothesis that the frequency of miracles is the same now as in the past (in other words, no demonstration of a miracle has occurred that has survived scrutiny).

Actually, Godel's entire criticism of Carrier's argument is itself Bayesian. Given Godel's background knowledge of mathematics, Godel assigns a prior probability of Carrier's argument being true as less than 50%. Godel would evaluate new arguments coming in as either supporting Carrier's argument being true or being false or both. However, Godel admit to a low knowledge of history, so Godel don't know if history ever has situations where those criticisms (unmeasurable sets or nonexistent numbers) would apply. Godel therefore doesn't know if it is indeed generally untrue in history that any proposed event has a probability of being true or false. I would put it to you that since our background knowledge b includes the fact that every historical claim we've ever experienced indeed has some probability of being true or false that we can call this a null hypothesis against which extraordinary evidence must be provided to disprove. Given that, b should be much higher than Godel's initial evaluation. It should certainly be higher than 90% and I'd feel comfortable with a 99.9999% value for P(Carrier's Argument|b).

Finally, Carrier is very careful to state that he's not trying to use Bayes's Theorem to prove something true or false. Rather, he's using it to determine how confident we should be that a given claim is true based on what we know right now. It is the difference between stating "This is true" and stating "To the best of my knowledge I can accept this being provisionally true with X% confidence." He wants to use Bayes's Theorem as a consensus-building tool, where everyone's subjective (but well-founded) evaluations are drawn together by the gravity of everyone's common b and e. Even if this doesn't result in actual values, it will be close enough to have strong confidence in the results it does yield.

In reply to an earlier post on Feb 19, 2013, 7:45:49 PM PST
[Deleted by the author on Feb 28, 2013, 8:21:08 AM PST]

In reply to an earlier post on Mar 10, 2013, 4:58:00 PM PDT
Godel says:
Suppose we conduct an experiment to estimate the probability of a miracle occurring on a given day. Suppose further that no miracle claims tested were found to be true miracles, and that the probability of a miracle occuring on a given day (denoted "q") obeys the inequality:
0 <= q <= delta
Where delta is some small positive real number. Given this information, we compute the probability of any testable miracle claim being true. Notice that the probability of no miracles occuring on N different days is (1-q)^N. Thus, the probability of miracles never occuring is f(q) = Limit_{n -> Infinity} (1-q)^n. Basic calculus tells us that f(0)=1 and f(q)=0 for any 0<q<1. That means that, unless the probability of a miracle occuring on a given day is exactly 0, there will almost surely be a miracle at some point.

We can further take the average of f(q) over all possible values of q between 0 and delta as follows:
The integral from 0 to delta of f(q) with respect to q divided by delta = delta / delta = 1

So, given our experiment, there is almost surely a miracle at sometime, regardless how unlikely our experiment indicates that to be.

The point of this exercise is not to prove that miracles exist, but to show the limitations of Bayesian probability, and how we cannot use it to confront the infinite without getting paradoxical results. We cannot even reach an approximation.

In reply to an earlier post on Apr 19, 2013, 4:43:23 AM PDT
I am curious, do you think this applies equally to an event such as a rainbow-colored unicorn suddenly appearing in your bathtub? Can we not even reach an approximation about the likelihood of such an occurrence, or is our sudden absolute skepticism about skepticism limited only to the claims of Palestinian cultists?
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