Philosophical apologetics book suggests replacing Bayes theorem with "Inference to the Best Explanation" (IBE)

jwhendy

4 Philosophical apologetics book suggests replacing Bayes theorem with "Inference to the Best Explanation" (IBE)

30th Aug 2011

4 min read

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I'm about 2/3 through an apologetics book that was recommended to me, Menssen and Sullivan's, The Agnostic Inquirer, and was quite surprised to run into a discussion of Bayes theorem and wanted some input from the LW community. The book is quite philosophical and I admit that I am probably not following all of it. I find heady philosophy to be one of these areas where something doesn't seem quite right (as in the conclusion that someone pushes), but I can't always identify what.

In any case, the primary point of the book is to attempt to replace the traditional apologetics method with a new one. The status quo has been to appeal to "natural theology," non-theological areas of discussion which attempt to bring one to the conclusion that some kind of theistic being exists, and from there establish that Christianity is the true formulation of what, exactly, this theistic being is/wants/does, etc by examining revealed theistic truths (aka the Bible). Menssen and Sullivan attempt to suggest that revelation need not be put off so long.

I don't want to get too into it, but think this helps set the stage. Their argument is as follows:

(1) If it is not highly unlikely that a world-creator exists, then investigation of the contents of revelatory claims might well show that it is probable that a good God exists and has revealed.

(2) It is not highly unlikely that a world-creator exists.

(3) So, investigation of the content of a revelatory claim might well show it is probable that a good God exists and has revealed.

(4) So, a negative conclusion concerning the existence of a good God is not justified unless the content of a reasonable number of leading revelatory claims has been seriously considered. (p. 63)

Issues Menssen and Sullivan have with Bayes applicability to this arena:

Then they begin trying to choose the best method for evaluating revelatory content. This is where Bayes comes in. The pages are almost all available via Google books HERE in Section 4.2.1, beginning on page 173. They suggest the following limitations:

Bayesian probability works well when the specific values are known (they use the example of predicting the color of a ball to be drawn out of a container). In theology, the values are not known.
The philosophical community is divided about whether Bayesian probability is reliable, and thus everyone should be hesitant about it too if experts are hesitant.
If one wants to evaluate the probability that this world exists and there are infinitely many possibilities, n, then no matter how small a probability one assigns to each one, the sum will be infinite. (My personal take on this is whether a literal infinity can exist in nature... 1/n * n is 1, but maybe I'm not understanding their exact gripe.)
In some cases, they hold that prior probability is a useless term, as it would be "inscrutable." For example, they use Elliott Sober's example of gravity. What is it's prior probability? If such a question is meaningless, they hold that "Has a good god revealed?" may be in the same category and thus Bayesian probability breaks down when one attempts to apply it.
There are so many components to certain questions that it would be nearly impossible or impossible to actually name them all and assign probabilities so that the computation accounted for all the bits of information required.
If Bayes' theorem produces an answer that conflicts with answers arrived at via other means, one might simply tweak his/her Bayes values until the answer aligned with what was desired.

Their suggested alternative, Inference to the Best Explanation (IBE)

They define IBE as follows:

If a hypothesis sufficiently approximates an ideal explanation of an adequate range of data, then the hypothesis is probably or approximately true.
h₁sufficiently approximates an ideal explanation of d, an adequate range of data.
So h₁is probably or approximately true.

Obviously the key lies in their definition of "ideal explanation." They cover this in great detail, but it's not all that specific. Basically, they want the explanation to be deductive (vs. inductive), grounded in "fundamental substances and properties" (basic, established truths), and to be overwhelmingly more true than contending hypotheses. You can read a bit more by reading the Google books section following the above.

I'm interested in takes on the above limitations that I've summarized in comparison with their suggested replacement, IBE. I'd be especially interested in hearing from those more familiar with philosophy. Menssen & Sullivan cover others' definitions of IBE prior to presenting theirs, which suggests that it's a common term in philosophy. My gut intuition is that Bayes should produce the same answer as the IBE, but should also be more reliable since it's not an inference by a defined method.

It seems like their proposal for IBE is doing precisely what Bayes' theorem is doing... but they've just formalized a way to do it more sloppily since they claim one can't know the exact numbers to use in Bayes' theorem. I can't tell what, exactly, is different. You take your priors, factor in your "adequate range of data" (new evidence), and figure out of the hypothesis, given the prior probability and adjusted for additional evidence, comes out more probabile than not (making it probably or approximately true).

Is this just funny games? Is there something to the proposed limitations of Bayes' theorem they present? I think Richard Carrier explained how he bypasses situations when exact numbers are not known (and how often are the numbers known precisely?) in his argument entitled Why I Don't Buy the Resurrection Story. He specifies that even if you don't know the exact number, you can at least say that something wouldn't be less likely than X or more likely than Y. In this way you can use the limits of probability in your formula to still compute a useful answer, even if it's not as precise as you would like.

If anyone is interested in this in more detail, I could perhaps scan the relevant 20 or so pages on this and make them available somewhere. There's only a few pages missing from Google books.

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4 Philosophical apologetics book suggests replacing Bayes theorem with "Inference to the Best Explanation" (IBE)

by jwhendy

30th Aug 2011

4 min read

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I don't want to get too into it, but think this helps set the stage. Their argument is as follows:

(1) If it is not highly unlikely that a world-creator exists, then investigation of the contents of revelatory claims might well show that it is probable that a good God exists and has revealed.

(2) It is not highly unlikely that a world-creator exists.

(3) So, investigation of the content of a revelatory claim might well show it is probable that a good God exists and has revealed.

(4) So, a negative conclusion concerning the existence of a good God is not justified unless the content of a reasonable number of leading revelatory claims has been seriously considered. (p. 63)

Issues Menssen and Sullivan have with Bayes applicability to this arena:

Bayesian probability works well when the specific values are known (they use the example of predicting the color of a ball to be drawn out of a container). In theology, the values are not known.
The philosophical community is divided about whether Bayesian probability is reliable, and thus everyone should be hesitant about it too if experts are hesitant.
If one wants to evaluate the probability that this world exists and there are infinitely many possibilities, n, then no matter how small a probability one assigns to each one, the sum will be infinite. (My personal take on this is whether a literal infinity can exist in nature... 1/n * n is 1, but maybe I'm not understanding their exact gripe.)
In some cases, they hold that prior probability is a useless term, as it would be "inscrutable." For example, they use Elliott Sober's example of gravity. What is it's prior probability? If such a question is meaningless, they hold that "Has a good god revealed?" may be in the same category and thus Bayesian probability breaks down when one attempts to apply it.
There are so many components to certain questions that it would be nearly impossible or impossible to actually name them all and assign probabilities so that the computation accounted for all the bits of information required.
If Bayes' theorem produces an answer that conflicts with answers arrived at via other means, one might simply tweak his/her Bayes values until the answer aligned with what was desired.

Their suggested alternative, Inference to the Best Explanation (IBE)

They define IBE as follows:

If a hypothesis sufficiently approximates an ideal explanation of an adequate range of data, then the hypothesis is probably or approximately true.
h₁sufficiently approximates an ideal explanation of d, an adequate range of data.
So h₁is probably or approximately true.

If anyone is interested in this in more detail, I could perhaps scan the relevant 20 or so pages on this and make them available somewhere. There's only a few pages missing from Google books.

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Philosophical apologetics book suggests replacing Bayes theorem with "Inference to the Best Explanation" (IBE) — LessWrong

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Logos0115y10

My initial response was, "No way Bayesians really believe that."

When I was first introduced to the concept of Bayesian statistics, I had rather lengthy conversations on just this very example.

Either way, what you mean by "sufficiently accurate" might need some explaining.

"Sufficiently accurate" means "sufficiently accurate", in this case. sufficient: being as much as needed; accurate. Synthesize the two and you have "being as without error and precise as needed". Can't get more clear than that, I fear.

Now, if I can read into the question you're tending to with the request -- well... let's put it this way; there is a phenomenon called stochastic resonance. We know that quantum-scale spacetime events do not have precise locations despite being discrete phenonema (wave-particle duality): this is why we don't talk about 'location' but rather 'configuration space'.

Now, which portion of the configuration space will interact with which other portion in which way is an entirely probabilistic process. To the Bayesians I've discussed the topic with at any length, this is where we go 'sideways'; they believe as you espoused: know enough points of fact and you can make inerrant predictions; what's really going to happen is set in stone before the trial is even conducted. Replay it a trillion, trillion times with the same exact original conditions and you will get the same results every single time. You just have to get the parameters EXACTLY the same.

I don't believe that's a true statement. I believe that there is and does exist material randomness and pseudorandomness; and I believe further that while we as humans cannot ever truly exactly measure the world's probabilities but instead only take measurements and make estimates, those probabilities are real.

jwhendy15y00

Can't get more clear than that, I fear.

Your "read into where I was tending with the request" was more like it. Sorry if I was unclear. I was more interested in what phenomenon such a machine would have at its disposal -- anything we can currently know/detect (sensors on the thumb, muscle contraction detection of some sort, etc.), only a prior history of coin flips, or all-phenomenon-that-can-ever-be-known-even-if-we-don't-currently-know-how-to-know-it? By "accurate"

I was more meaning, "accurate given what input information?"... (read more)

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