Update (8/21/06, 10:15PM): I've now made the corrections described in the first update below. The differences were all too small to effect the interpretation, with the possible exception of (17): the probability of (7) increased by .002, (11) increased by .021, and (17) increased by .040.
Update (8/21/06, 2:33PM): Welcome Prosblogion readers! I've realized that there was a minor error in my math below. The numbers for (7), (11), and (17) should be marginally higher than they are. The numbers I have given are the probabilities that the Bible teaches the proposition in question AND that it is right. The numbers need to be corrected to add in the probability that the Bible doesn't teach the proposition and it is nonetheless true. I don't have time to correct the numbers right now, but in the meantime, for each one you can correct the numbers for yourselves by adding the product of P(Tx|~Bx) with P(~Bx) to the originally posted value. I think that should give the correct numbers, but hopefully will have a chance to look it over in more depth this evening (or maybe a reader would like to help me out).
A common argument levelled against Evangelicals (most recently by Neal in the comments to my post on Jesus' witness to the Hebrew Bible) is that if, as most Evangelicals believe, it is that autographs of the Biblical books that are inerrant, then the doctrine of inerrancy is irrelevant since the autographs no longer exist. (The 'autographs' are the original manuscripts handwritten by the original authors of the books.) If something other than the autographs is supposed to be inerrant, what would it be, since there is disagreement among the manuscripts, and no single manuscript seems uniquely priveleged over the others? What this amounts to is the claim that the inerrancy of the autographs is irrelevant because there is uncertainty about what the autographs in fact said. This is very similar to the claim that inerrancy is made irrelevant by the uncertainty in our interpretation. Both of these arguments are seriously flawed in precisely the same way. What I hope to do here is, by making some very simple applications of the Bayesian probability calculus (I haven't done this in a while - feel free to correct my math), to show just how deeply mistaken these arguments are, and how much impact the truth or falsity of the doctrine of inerrancy will still have on our reasoning, despite uncertainty about the teachings of the inerrant books.
There is uncertainty everywhere in this world. If we are (rationally, justifiably) certain about anything at all, it is only about very elementary logically necessary propositions like '2+2=4', and even here there is some question (uncertainty!) about whether we are, or ought to be, truly certain. However, human beings go through life, act, make decisions, and form beliefs despite all of this uncertainty, and acting and forming beliefs while still uncertain is not a violation of any rational principle - on the contrary it saves us from an extreme form of the Buridan's ass dilemma. The reasoning pattern a perfectly rational being goes through to make decisions and form beliefs under uncertainty is (thought to be) codified in the Bayesian probability calculus, which currently sees wide application in philosophy and artificial intelligence. I am not going to try to explain how the whole thing works here, but see Wikipedia on Bayesian inference.
So, first we must formulate the doctrine of inerrancy in the autographs more formally. We are going to be doing first order predicate logic on the universe of propositions here, which will be a little confusing. Just remember that the upper-case letters are predicates or functions and the lower-case letters are variables or constants.
(1) i = '∀xP(Tx|Bx) = 1'
That is, if we were to have absolute certainty that some book of the Bible taught x, we would have certainty that x was true. But, the critic replies, we never have certainty that the Bible teaches x, i.e.
This, however, does not mean that (1) tells us nothing. Let us consider some conditional probabilities on i. To take a simple example, suppose we are trying to determine whether such a person as King Saul ever lived. We know him as a legendary figure in Jewish and Christian traditions, but we haven't yet looked at the Bible. So:
That is, there is a 97% probability that the Biblical books, in the autographs, teach the King Saul really lived (historically). The 3% doubt here is mostly because we have less early evidence of the Old Testament than the New Testament (there's a little more possibility of transmission error) - I don't think there is much doubt that that is what the Bible we have now teaches. 3% is still a very generous helping of doubt, given the evidence (we're being a little skeptical). Now, from (1) we have:
This means that P(Ti|~Ts)&le.03 - the probability of inerrancy cannot be greater than the probability that the Bible doesn't teach that King Saul lived, if King Saul did not in fact live. From this we can conclude by Bayes' theorem that:
That is, if we know that the Bible is inerrant, there is a 93% chance that King Saul actually lived, but if we ignore the Bible, there is only a 30% chance. (We assume for simplicity that P(Ti|Ts) = 1 - that is, that we have no reason to doubt inerrancy as long as Saul actually lived.) This, clearly, makes a big difference! But what would happen if the Bible wasn't inerrant, if it was only right most of the time. Would the difference be significant? Suppose we say that there is a possibility that the Bible would say Saul lived even if he didn't, but it's fairly small. P(Bs|~Ts)=.2. However, since Saul was the first King of Israel, he is pretty important to the Bible's story, so if he did live, the Bible would probably tell us about it. P(Bs|Ts)=.85. On this account, we will conclude that:
Now, this is the probability that Saul actually lived if the Bible says he did. The overall probability that he actually lived is P(Ts|Bs)*P(Bs)+P(Ts|~Bs)*P(~Bs) (the first addend is the probability that the Bible teaches that Saul lived AND Saul did in fact live, the second is the probability that the Bible does NOT teach that Saul lived, but he nevertheless did), so:
So, if we take the Bible to be only generally accurate instead of inerrant, we have 62.9% probability that Saul lived, instead of 93%. This is still enough to base a belief on, but it is certainly (or at least probably) a significant difference! Furthermore, since probabilities are multiplicative, if we take something with higher uncertainty about the Bible's teaching, the difference will be larger. Suppose we take the statement:
So P(Ti|~Ta)<e;.4. In order to make our calculation we need to determine the prior probability of Ta. We would really have no idea about this without the Bible, so the prior probability P(Ta)=.5. Making the same simplifying assumption as before, we can conclude that:
This is not incredibly high, but enough to base our beliefs and actions on, at least tentatively. We often live and act on lesser probabilities than this! But what happens if we assume, as before, that the Bible is only generally reliable? Since this is a spiritual rather than historical matter, and the Bible is particularly trustworty on spiritual matters, let's use a somewhat higher probability than before; say, P(Ba|~Ta)=.1. Since this is an important spiritual statement for the life of the Church and we wouldn't know about it if the Bible didn't tell us, let's assign P(Ba|Ta)=.95. From Bayes' theorem we find:
Which is pretty high. However, when we add in our uncertainty about Ba, we get:
Which is barely better than even odds! When the uncertainty factor in the Bible's teaching is significant, even a small possibility that the Bible might be wrong will make a big difference in the justifications we can give for our beliefs. Note too that in this case we are trusting the Bible a lot more than we did in the Saul case (since we assume the Bible knows more about spirituality and how to run churches than about history). If we plugged in the same values we used for Saul with this much uncertainty (and the same prior probability for Ta), we would get:
There is another interesting point that comes out of this type of analysis: if the prior probability of the proposition is lower than, or even on near equal footing with, the probability of errors in transmission or interpretation, the low prior probability can overwhelm the probability increase due to the Biblical teaching, even on inerrancy. For instance, consider:
That is, there is a 7% probability that evolution is entirely on the wrong track. However, the early chapters of Genesis seem to teach something contradictory to the theory. Still, there is room for doubt about the genre conventions and truth-conditions of the early chapters of Genesis, so P(Be) has a not insignificant uncertainty factor. Let's say:
That is, there is a 75% probability that the teaching of the early chapters of Genesis is that evolutionary theory is entirely on the wrong track. What we want to know is P(Te|Ti). As before, we assume that evolution is our only reason to doubt Ti, so P(Ti|Te)=1. This gives us:
The low prior probability P(Te) overwhelms the Scriptural evidence so that - much to the chagrin of most Evangelicals - we conclude with .779 probability that evolution is on the right track to the truth. The point I'm trying to make is not that we should believe in evolution (I don't know nearly enough for the probabilities I made up above to be meaningful), but that incorporating outside data into our search for Biblical truth, especially in cases where the Biblical teaching is unclear, is not a reasoning mistake, even if we have an absolute belief in inerrancy. This is in some sense not sound Biblical interpretation - that is, we shouldn't conclude from this that the Bible teaches evolution (though we will come to the conclusion that it doesn't teach against it), or ask other Christians to accept it as part of our common faith - but it is sound reasoning in light of our assumptions and the evidence. It is the conclusion someone who comes to the Bible already believing (a) in it's inerrancy, and (b) that the probability of evolution being false is fairly low ought to come to (provided he concludes that there is significant uncertainty as to the teaching of the early chapters of Genesis - if P(Be) was .95, P(Te|Ti) would be .601. The clear teaching of Scripture - where it is truly clear - still overwhelms everything else). Another point to note here is that in this type of case, if the Bible is merely generally reliable, then it's impact on P(Te) will be essentially negligable. Inerrancy brought P(Te) from .07 up to .231, which is quite significant. However, assuming the Bible is merely generally reliable, the means of creation is pretty well outside its scope, so it would be thought less reliable here than elsewhere. P(Be|~Te) might be around .2 (since the Bible would be considered unlikely to talk about it in the first place) and P(Be|Te) might be .4. This will give us
When we add in our uncertainty factor and P(Te|~Be), we have:
That is, without the Bible the probability of evolution being wrong would be .07, and with the Bible it would be .138. In other words, if the Bible is merely 'generally accurate' it's barely worth considering it's view on an issue like evolution, but if it is inerrant then what it says will contribute quite significantly to our beliefs and our degree of uncertainty about them.
What I have tried to show here is not that inerrancy is true or false, but simply that it matters. In fact, what I think the application of Bayesian analysis here shows is that both inerrantists and more liberal Christians are reasoning correctly based on their beliefs about the place of the Bible. Of course, this discussion doesn't have too much to contribute to a discussion of whether inerrancy is true or false, but it certainly shows that it matters, and it matters a lot - even if there is a great deal of uncertainty in transmission and interpretation of the Bible. In fact, where there is uncertainty it matters more. However, I should point out that there are many cases where the uncertainty factor with regard to interpretation is pretty low (the uncertainty in transmission is almost always low, especially for the New Testament), and in these cases theological liberals and conservatives ought to be much more likely to agree, since the difference between the Bible being probably or absolutely right is not being multiplied across serious uncertainties of interpretation.Posted by Kenny at August 16, 2006 6:51 PM
Return to blog.kennypearce.net