@Tim:
It looks like you’re set on telling the authors of the paper what we really meant, despite us explicitly telling you what we really meant.
I think this is just an issue of reading comprehension. We wrote that “other theological concerns may make a historical Adam and Eve necessary”. “MAY make…”. And you somehow interpreted that that “as a matter of necessity not probability”.
Was the article poorly worded? Should we adjust the text? I don’t think so. “May” is a perfectly clear English word with well-understood denotations of conditionality and probability. The other authors have explained this in different ways, but I think the logic in this part of the paper is still best expressed probabilistically. And since I brought it up in my previous post, here’s how you frame a probabilistic proof by contradiction, using Bayes’ rule.
I’ll be using Bayes’ rule in the odds form. Let H be the hypothesis that you wish to discount (or disprove, in the “propositional logic” limit). Then let E be the existence of some claim, which is not likely to be true if H is true. Then Bayes’ rule says:
posterior_odds(H|E) = prior_odds(H) * bayes_factor(E|H)
To successfully discount H, all you have to do is show that E reduces the posterior odds, in comparison to the prior odds. That is, you need to show that the Bayes factor is < 1. No specific calculation of the exact prior odds is necessary.
The Bayes factor, by definition, is P(E|H) / P(E|~H). So if we show that P(E|H) < P(E|~H), then we’re done. In the “propositional logic” limit, P(E|H) is not merely smaller than P(E|~H), but is actually zero, because E and H together form a contradiction. So in that limit, P(H|E) = 0, and ~H must be true - exactly as we expect in a standard proof by contradiction.
How does this apply to the statement that “other theological concerns may make a historical Adam and Eve necessary”? Let H = “a non-historical Adam and Eve” (note the negation, to get this to fit in with our formulation above), and let’s choose E to be one of the theological concerns that was enumerated, say “a historical Fall”. So in full, E is “the existence of the theological claim of a historical Fall”. Now, as before, all we need to do is compute the Bayes factor: P(E|H) / P(E|~H)
P(E|H) is, of course, going to be small. A non-historical Adam and Eve is unlikely to lead to the theological claim of a historical Fall. People will want to dispute me on that, but it’s actually an irrelevant point: because the real thrust of the argument is that P(E|~H) is bound to be larger.
Because, for every meandering coincidence that may lead a non-historical Adam and Eve to the claim of a historical Fall, a historical Adam and Eve can take the same paths - except, in addition, they have the obvious alternative path, that everything in the Genesis creation account is true and was recorded accurately. You may not like this possibility, and may want to give it a very low probability. It doesn’t matter: its mere existence makes P(E|H) < P(E|~H). This is, of course, the obvious result: a historical Adam and Eve better explains the historical Fall. Thus H is successfully discounted, and a historical Adam and Eve becomes more likely.
Consider what we have achieved: the mere existence of the theological claim about the historical Fall, in conjunction with the mere possibility that it may be right, is enough to increase the probability of a historical Adam and Eve.
So, in terms of “appeal to consequences”: as long as the “consequences” have any truth-value implications, and is not just a simple matter of personal taste, “appeal to consequences” is not a fallacy in the Bayesian framework. If the “undesirable” consequence is that you’re forced to accept some E which is not well-explained by your H, then “appeal to consequences” is a perfectly valid way to think.
In general, I would not rely too much on crying “fallacy!” as a way to test an argument. Over-reliance on these so-called “logical fallacies” often creates a “only tool is a hammer” kind of problem. More importantly, many so-called “logical fallacies” only work in strict propositional logic, and speak more to the limitations of such methods rather than to actual sound thinking.
One example of such limits can be seen in “affirming the consequent” - a closely related cousin of “appeal to consequences” (note that it appears as the first link under the “See also” section in the Wikipedia page). This, too, has the imposing designation of a “logical fallacy”, but under a proper Bayesian formulation, it simply evaporates. “Affirming the consequent” is a GOOD thing, and is in fact one of the standard techniques in the scientific method. I write a lot more about it here.
@John_Harshman:
You write a lot of words, but you’re arguing against a mathematical law. P(H) is almost surely not equal to P(H|E), for any given H and E. So everything IS evidence. I do NOT draw any lines, and arbitrarily cut off whole realms from consideration.
Of course, as I have already said, this doesn’t mean that I find every claim to be convincing. Rather, I actually do the work of evaluating the evidence, instead of dismissing things from the onset. AFTER you’ve actually done that work, you may decide that the evidence is not enough, but that doesn’t mean that it’s “not evidence”. Again, as I’ve already said, we’ve explicitly included this kind of view in the original article itself, in discussing the position that Adam and Eve were not historical persons at all.