Focusing in on the sentence you identified…
There is no Q there in the summary of the sentence, and no evolution either.
Maybe so. I suppose we didn’t expect this particular angle of critique. Perhaps we will adjust the text in the future, especially if others are confused.
To add onto what Joshua said, regarding Q as “other theological concerns”, these are not things some people want to be true only for emotional reasons, but rather that they are independently justified by other reasons from theology, Scripture (other than Genesis), or common experience. In that case, the form of the argument would be:
If ~P, then ~Q.
Q is obviously true from other reasons besides considering the truth of P.
Therefore, P.
This is not that different from a particle physicist in 2011 saying (regarding the faster-than-light neutrino anomaly):
If neutrinos can indeed travel faster than the speed of light, then that means all previous experiments verifying special relativity are false.
It is obviously very unlikely that all previous experiments verifying special relativity are false.
Therefore, it is very likely that neutrinos cannot travel faster than the speed of light.
Therefore, there must have been a mistake in the experiment somehow and the data is false.
With regards to the other theological consequences I mentioned, it is not the case. Doctrines like the unity of humanity, a historical Fall, original sin - these all often interlock logically with other areas of Christian theology which are not drawn directly from the Adam and Eve story. Thus, denying these doctrines may necessitate revisions in these other areas to avoid logical inconsistency, and some people might have reservations about that. This is something that people (including Christians) focusing too much on the Genesis or evolution debates might not realize as much.
An example, in the GAE book workshops at some point we even ended up talking about the implications of the GAE for the virgin birth and the humanity and sinlessness of Jesus. Any explanation of original sin must preserve both the humanity and sinlessness of Jesus, which is a conclusion we take from the NT, not Genesis.
Another example: I’ve found that quite a few Reformed theologians argue for federalism instead of realism (with regards to Adam’s solidarity with humanity) because it nicely parallels the Reformed understanding of the doctrine of imputed righteousness, which is not originally derived from the A&E narrative at all, but from a completely different Reformation-era theological debate.
I take this to be a tacit admission that you finally understand my point - that you have been misinterpreting the intention of the authors of the text in question and projecting arguments that we never intended to make. I agree with Josh, though, that if many other people report the same sort of misunderstanding, then it is probably best to change the wording of the text to make it clearer.
You are confusing ways of knowing with ways of telling.
No, it’s part of theologizing. As the Wiki article explains, that fallacy is “true or false based on whether the premise leads to desirable or undesirable consequences. This is based on an appeal to emotion.” Looking for consistency is not necessarily an emotional appeal. Whether it’s good theologizing is open to critique, but I don’t see the fallacy.
Given that I am restricted to one post an hour on this thread, I’ll state my viewpoint and then try to address points that I feel are relevant. It will also mean that any clarifications that I think of later will have to be added to (hour) later posts.
Causality
This would appear to be crucial in determining if something is an Appeal to Consequence, as the chain of causality is what determines what is a consequence of what else.
The chain of causality would appear to be Biblical Inerrancy therefore acceptance of Adam and Eve as historical. The A&E story, therefore theology such as the Fall, Original Sin, etc. I would however be willing to entertain substantiated claims to the contrary.
In addition, other theological concerns may make a historical Adam and Eve necessary, such as maintaining the uniqueness of human beings as made in the image of God, the unity of all humans, a historical Fall from original sinlessness, and the doctrine of original sin.
**Q.**E.D.
“Theologizing” is on the basis of scripture, and thus is a consequence of scripture.
Undercutting a piece of scripture (e.g. by questioning its historicity) consequentially undercuts the theologising based upon it.
Having one’s theologising undercut is undesirable.
It is thus very easy, and in fact natural, to fit this into an Appeal to Consequences.
This is merely a bald assertion (and so no, not at all “obvious”). It requires substantiation to be given any credance. And I would point out that a vague claim of ‘interlocking theology’ does not count as substantiation. I have never seen any articulation of Original Sin that did not have Adam and Eve as its foundational bedrock, and would be surprised if such doctrines are solid independently of this story.
Bricks are ‘interlocked’ by mortar. This does not mean that a house will stand up without a foundation.
No Daniel. What I was saying was simply that the quoted statement was poor writing and muddy thinking. It presents (to anybody familiar with logic and the basis of such doctrines as the Fall and Original Sin in the A&E story) as an Appeal to Consequences, even if not intended in that way.
I would point out that I find it very irritating to be patronised by somebody whose command of logic is so poor as (i) to have created your ‘Proof by Contradiction’ hot mess, and (ii) to have been highly problematical in a number of previous conversations.
As I stated already:
@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.
Everyone is so restricted*, with the intent that it should encourage more thoughtful and constructive comments. You can still edit to add necessary clarification.
'* Except for us moderators, but we are busy people so it’s not much of a perk.
That’s an interesting assertion, but I see nothing to back it up. What if H is the hypothesis that there are spiders on Mars and E is the fact that I have a picture of Mount Fuji in my living room? Is P(H|E) greater than P(H)?
I agree with this, and with much of what precedes it. (To the extent that I’ve been following it – for me
the whole issue has the significance of a pinhead angel-occupancy debate, only this debate is actually happening.)
This, on the other hand, is utterly impossible. No human – not even ahistorical pre-Flood patriarchs – lives long enough to actually do the work of evaluating the evidence for all of the claims that have been made for and against things like astrology and phrenology.
I’m reminded of an English professor I heard about when I was in grad school. His specialty was the Victorian novel, so he decided to do a comprehensive study of the subject, starting by reading them all. He started reading, taking careful notes on each. He got through 20,000 of them, out of the 60,000 extant novels. Then he died.
This is true, but the fact that we have finite time to evaluate evidence should be viewed as a limitation and source of uncertainty in our ability to obtain complete and accurate knowledge, rather than becoming a criteria to determine what counts as knowledge or not. The latter (“X counts as evidence for claim A as long as it would take less than a certain time T for an “average” human being to evaluate its credibility”) would be a form of pragmatism (and possibly an actual instance of an Appeal to Consequences fallacy). Note that I’m not accusing you of actually saying this, but just trying to clarify a point.
Furthermore, I’m not sure @naclhv would say that everyone is obligated to evaluate all the evidence for every claim directly. In many cases it is fine to rely on the work of other specialists that we trust to evaluate the credibility of certain claims rather than doing all the work ourselves. So instead of evaluating the evidence directly, we evaluate the credibility of the expertise of these specialists and the coherence of their analyses - whether they fit with other pieces of knowledge that we are more familiar with.
After topic goes into slow mode, can people still edit their comments? I thought “No”…?
Sure, anything could be fit into an Appeal to Consequences if one accuses their interlocuter of believing certain propositions for emotional instead of rational reasons. But is that accusation true? So far, no one else has accused us of appealing to emotions, so I disagree that it’s a “natural” assessment.
First, you’ve misunderstood the claim again. The statement I wrote “Q is obviously true from other reasons besides considering the truth of P” is meant to depict the mindset of a certain type person that may read our article, not necessarily my own personal stance. Different people may have different epistemological and doctrinal commitments, and we wanted to accommodate that. That’s why we used the diplomatic language of “may make a historical Adam and Eve necessary”, to convey that we know these theological concerns are not universally held by all readers.
Second, even apart from our personal stances, it is a fact that many theologians regard certain doctrines as interlocking with Adam and Eve, original sin, and so on. I actually gave some examples of these (with some brief explanations) - doctrines and lines of argumentation that intersect with the A&E narrative, but are not primarily derived from them. We could have had an interesting conversation where we go into the details, but seeing that you chose to ignore them entirely and pretend that those examples don’t exist, I don’t think it’s fruitful to engage further. I’m not sure you’re disagreeing in good faith here.
No doubt original sin is massively influenced by the Adam and Eve narrative, but it is not the only piece of biblical evidence marshalled in favor of it. In fact, original sin is more frequently motivated by Romans 5:12-19, not Genesis 2-3. Thus, even if one is convinced that Genesis doesn’t teach that Adam and Eve existed as historical figures, there is still biblical evidence for the doctrine of original sin that we have to contend with. Thus there are plenty of theologians who still believe in a modified version of the doctrine of Original Sin even as they do not believe in a historical Adam and Eve. They keep the doctrine (in a modified form) instead of throwing it out entirely because it is an important part of Christian theology which helps to explain, for example, why Jesus needed to save all of humanity.
Note that I never actually said that the argument in the article was a “proof by contradiction” in a strict sense. I only brought it up as a useful comparison (that you are surely familiar with, as a mathematician), because there are important similarities - namely that arriving at a logical contradiction pushes up to give up one of the propositions used in an argument. In mathematics, this normally means we give up \neg P, where P is the original proposition meant to be proven. Thus, P is shown to be true. However, a PoC can only work if all the other thorems and lemmas invoked along the way are actually true. It is not unheard of that a certain theorem Q used towards arriving at the contradiction is later shown to be false, and so the PoC fails because there is no longer a contradiction when we assume \neg P. This is why good mathematicians make sure that they only rely on theorems that have been thoroughly verified and evaluated to be true, instead of unproven conjectures.
We can apply this concept to reasoning in systematic theology. There are similarities with mathematical PoC in that there are certain foundational doctrines that are practically regarded as absolutely true (e.g. the existence of God, Jesus’ divinity, universal sinfulness, etc.), and we also do not want to have contradictions in our overall theological system. However, in contrast to the relatively clear-cut situation we have for mathematical theorems, in theology claims or doctrines can often be modified, qualified, or revisited. Thus, it is not always the case that when we start at with \neg P and arrive at a contradiction it means that we must give up \neg P and affirm P. Instead, one has to weigh whether giving up \neg P (in this case, P = “Adam and Eve exist as historical figures”) makes sense over giving up or modifying other (non-foundational) theorems along the way (e.g. “Augustinian original sin is true”, “Doctrine of imputation is true”, etc.). This weighing likely requires more of a probabilistic evaluation, which is where what @naclhv said comes into play.
Hmmm … I can, but mods are exempt from the timer. Will test this when I have more time.
Tim, thanks for the interaction. I don’t think I necessarily disagree with everything you’re pushing at, but perhaps some clarity on terms would be helpful.
I’m not sure I know what you mean by this. Doing theology is more than rounding up Bible verses and providing a summary. The Scripture is a prominent, but not the only, source of data; other sources include reason, nature, tradition, culture, and experience. We could also add one’s particular orientation toward scripture as divine revelation (if by “scripture” you meant something more than a synonym for the Bible).
This needs some nuance. A text’s “historicity” is a much larger discussion–what do we mean by a text being “historical”? what determines if a text should be considered historical (and to what degree)? how would one verify or falsify “historicity”? So, I don’t see this as an either/or, such that a text is verified or “undercut” so simply. Also, even if one were to challenge another’s stance on a text (including it’s historicity), this only informs the theological process, not undercuts it.
That depends (especially on what “undercut” means). I assume a good scientist doesn’t mind (ideally) being challenged…it’s sort of the nature of scientific engagement, isn’t it? I’d same the same with theology (ideally…though i admit a lot of knuckleheads don’t like to be challenged at all). We (ideally) are in search of truth. So we should be willing to entertain evidence even if it challenges our set view and causes us to tweak and refine it.
One of the difficulties with theology is considering how much weight to give different, sometimes competing, angles (added to this is the difficulty of assessing a truth claim from outside one’s area of expertise, e.g., a theologian listening to the scientists). Some of the disagreement among theologians is at this very point.
Just a final note on the word “desirable.” The article you originally linked ties this to emotional appeal…which is what I was hitting on. If we broaden “desire” to include desire for consistency, cogency, and clarity, then wouldn’t almost all our discussions and conclusions (including scientific) be guilty of this fallacy?
@glipsnort , @dga471 :
Thanks for talking through what “evaluating evidence” means. And yes, nobody can evaluate “all the evidence” - especially if everything is evidence, as I have claimed. We often rely on only the tiniest slice of the evidence available to us, and that’s often enough.
I think that the example of astrology is illustrative here. I’d wager that very few people here have actually conducted a scientific study that disproves astrological claims. In all likelihood, few people have even done a decent exploration into the literature on the subject. To take it one step further, if we’re being honest, many of us are probably just going with the group consensus on this topic - because of hearsay.
And yet many of us have a strong belief that astrology is bunk, and we are not irrational for having that belief. Why? Because everything - even just hearsay - is evidence. And that’s enough for most of us in this case.
Does that mean that I can now categorically dismiss all astrological claims? No; I don’t categorically dismiss anything. I instead weigh the astrological claims according to the evidence, including the earlier evidence from hearsay. The conclusion of such weighing is that astrological claims are not enough to be convincing. As I have repeatedly said, this kind of thinking is explicitly included in the paper linked above.
Ah, then let me walk you through the contents behind that “almost surely” link.
If you click on that link, you’ll land on a Wikipedia page that describes events which are possible to specify, but have no chance of happening. In fact, the first example that you’ll see is the example of throwing a dart, on to a 1 x 1 square area. You can specify that the dart will land on the square’s diagonal, yet that actually has no chance of happening, because the diagonal, being a 1-dimensional line segment, has no area. That is to say, the dart will almost surely not land on the diagonal.
Now, let’s make the analogy explicit between this “diagonal of a square” and probability values. Probability values are a real number between 0 and 1. So, the value of P(H) can be mapped to the x-axis value of that 1 x 1 square, and the value of P(H|E) can be mapped to the y-value. In that case, “landing on the diagonal” translates directly to the statement that P(H) = P(H|E). And we’ve already shown that this will almost surely not happen.
Note that this conclusion relies only on the infinite cardinality of the real numbers, which all probability values must be. This is about as robust as a mathematical conclusion can be. This is why P(H) is almost surely not equal to P(H|E), and why everything is evidence. To argue against it is to argue against a mathematical law.
Let me know if you didn’t understand any of that, and I’ll try to walk though it with you again.
I don’t know if P(H|E) greater than P(H) in this particular case, but it isn’t terribly difficult to show through a physics calculation that they are almost surely different. I’d be glad to share that calculation, but again, it relies on you understanding the concept of “almost surely”. So let’s make sure that you understand that first.
Nope. Astrology is bunk at a far more basic level–it doesn’t make truly testable empirical predictions. IOW, one can twist just about any evidence to fit astrologers’ predictions. If you disagree, read up on how cold readings are done.
I deny that this analogy — and it is an analogy — applies to real probabilities. Sure, the probability that P(H) = P(H|E) is zero, but so is the probability that their difference is any other specific value you choose. It’s impossible to pick a random real number from 0 to 1, much less a random ordered pair. What you have there is an empty formalism.
Alright, I’m going to share the “picture of Mt. Fuji affecting the spiders on Mars” calculation here, because it’s just a really cool calculation. In fact, the actual calculation I carry out shows that the effect holds for far, far smaller causes. From the post:
That is the degree of the universe’s inter-connectivity and complexity. A SINGLE WATER MOLECULE, located in ANOTHER GALAXY, changing its orientation for a FRACTION OF A SECOND, will completely alter the microstate of the Earth’s atmosphere nearly instantly (after accounting for the speed-of-light delay), and change our macroscopic future in short order. Your life, brain, and very existence is the result of all these effects combining to create you in your current state. “Subtle is the LORD” indeed.
To bringing this back to the original “Adam and Eve” article, this shows the importance of taking everything into account. Some people, when faced with the idea that evolution may be in conflict with Adam and Eve, simply want to categorically reject entire realms of evidence. The calculation above shows the folly of doing that, and the “Adam and Eve” article shows that this is not at all necessary.
You have confused A affecting B with A being evidence that B exists, two quite differen things. A water molecule in the Andromeda galaxy is not evidence that a nitrogen molecule exists in earth’s atmosphere. What the heck?