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The Laws of Thought

Over at Facing the Intelligence Explosion there is a page with the title of “the laws of thought”. This is a page that goes into a bit more detail about what it means to be skeptical. Many atheists know about these ideas, but they are inconsistently applied because they don’t know many of our cognitive biases, which are generally based on intuition, that make us use those vague tools selectively. What’s worse, one cognitive bias is called the sophistication effect, where the most knowledgeable people, because they possess greater ammunition with which shoot down facts and arguments incongruent with their own position, are actually more prone to succumb to one of these biases! Luke writes in one of his earlier writings:

Skepticism and critical thinking teach us important lessons: Extraordinary claims require extraordinary evidence. Correlation does not imply causation. Don’t take authority too seriously. Claims should be specific and falsifiable. Remember to apply Occam’s razor. Beware logical fallacies. Be open-minded, but not gullible. Etc.

But this is only the beginning. In writings on skepticism and critical thinking, these guidelines are only loosely specified, and they are not mathematically grounded in a well-justified normative theory. Instead, they are a grab-bag of vague but generally useful rules of thumb. They provide a great entry point to rational thought, but they are only the beginning. For 40 years there has been a mainstream cognitive science of rationality, with detailed models of how our thinking goes wrong and well-justified mathematical theories of what it means for a thinking process to be “wrong.”

As you might have guessed, I’ve written about many of those subjects before from the viewpoint of Bayes Theorem and other probability theory. For example, extraordinary claims require extraordinary evidence, claims should be specific and falsifiable, and Occam’s razor. Basically, if you want to be more efficient at being skeptical, you should know some probability theory. If you don’t know the basics then all you’re doing is professing and cheering, signalling that you are part of the Skepticism Tribe. *pom-pom pump* Gooooo Skepticism! *backflip*

He expands on this further in his “laws of thought” page. There are three general laws of thought: Logic, Probability Theory, and Decision Theory. Decision theory follows (almost) necessarily from Probability Theory, which (almost) necessarily follows from logic.

Luckily, not many people disagree about logic. As with math, we might make mistakes out of ignorance, but once someone shows us the proof for the Pythagorean theorem or for the invalidity of affirming the consequent, we agree. Math and logic are deductive systems, where the conclusion of a successful argument follows necessarily from its premises, given the axioms of the system you’re using: number theory, geometry, predicate logic, etc… Why should we let the laws of logic dictate our thinking? There needn’t be anything spooky about this. The laws of logic are baked into how we’ve agreed to talk to each other.

Logic follows from some basic axioms, like the law of identity (A = A) and the law of non-contradiction (A can’t be both A and ~A). If we disregard the laws of logic, then no one would be able to understand each other. Certain logical fallacies are predicated on violating the identity part of logic. My favorite example of this is the fallacy of equivocation. The relevant version of this fallacy is when people conflate “faith” in the general sense with “faith” in a probabilistic sense and then conclude with some variant of the fallacy of gray.

Say you’ve got two revolvers on a table, and you’re forced to play Russian Roulette. One revolver has 1 bullet chambered out of 6 and the other has 5 bullets chambered out of 6. A proponent of this fallacy of equivocation/fallacy of gray combo claims that everyone has faith and therefore no faith is better than any other. Yet if that were the case, then if we want to survive in the Russian Roulette game above, their logic dictates that it makes no difference which revolver they choose. Whereas a rational person would obviously choose the revolver with less ammunition chambered.

But logic is a system of certainty, and our world is one of uncertainty. In our world, we need to talk not about certainties but about probabilities…

What is probability? It’s a measure of how likely a proposition is to be true, given what else you believe. And whatever our theory of probability is, it should be consistent with common sense (for example, consistent with logic), and it should be consistent with itself (if you can calculate a probability with two methods, both methods should give the same answer).

Several authors have shown that the axioms of probability theory can be derived from these assumptions plus logic.1,2 In other words, probability theory is just an extension of logic. If you accept logic, and you accept the above (very minimal) assumptions about what probability is, then whether you know it or not you have accepted probability theory.

I really wish I could write a simpler guide on why probability theory — correct probability theory — follows from logic. Unfortunately the references that Luke provides at what I’ve indented at 1 and 2 are the simplest I’ve come across. Anything simpler and something essential will get left out. It suffices it to say that if we were to build an artificial intelligence, it would have to know probability theory in order to make sense of and function in the world. And when we think of computers and AI, we automatically think of “logic”, so the association (hopefully) makes intuitive sense.

Next he talks about Decision Theory which I’ve poked a little bit. This is the most subjective part of it, but even so, there are objective ways to assess your own subjective decision theory / utility function.

So there you have it. If you want to stop just sitting in the stands waving your Skepticism Banner to let everyone know which team you support and start actually practicing good skepticism, you should start learning these three areas.

 
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Posted by on May 21, 2013 in Bayes, skepticism

 

Absence of Evidence is Evidence of Absence

This is a quote from the blog of awesome Less Wrong:
Absence of proof is not proof of absence. But absence of evidence is always evidence of absence. According to the probability calculus, if P(H|E) > P(H) (observing E would be evidence for hypothesis H), then P(H|~E) < P(H) (absence of E is evidence against H). The absence of an observation may be strong evidence or very weak evidence of absence, but it is always evidence.
Αnd I think I'll apply this to the current tide rising in the Historical/Mythical Jesus debate.
 
To pick the most obvious example, the current JM hypothesis posits that Paul and other early epistle writers would have quoted a teaching of Jesus if they viewed Jesus as a preacher instead of a mythical/legendary/cosmological savior figure. Since they don't do this, then it fits their hypothesis. On the other hand, the HJ hypothesis posited by most scholars is a sort of floating ad-hoc explanation for this. That is, if the early epistle writers did quote a teaching of Jesus, this would be evidence for their hypothesis (a preaching Jesus). But, if the early epistle writers did not quote a teaching of Jesus… well, this is still evidence for their hypothesis (a preaching Jesus).
 
This is why Bayes theorem is useful. It points out glaring ad hoc hypotheses like these. It's a heads I win, tails you lose set up by scholars.
 
Let H be the hypothesis that a preaching Jesus existed. E is early epistle writers quoting from the preaching Jesus. Let's say that the probability of the preaching-historical or mythical Jesus is equally 50% (i.e. P(H) = 50%) just for pedagogical value. In the mythical Jesus model, P(H|E) > P(H); the probability of Jesus existing given the evidence of epistle writers quoting him is higher than the bare bones probability of Jesus existing. That is, the probability of Jesus existing is nudged higher than 50% if a letter writer like Paul quotes from Jesus. On the flip side, the P(H|~E) < P(H); the probability of Jesus existing given the lack of evidence of epistle writers quoting him is lower than the bare bones probability of Jesus existing. That is, the probability of Jesus existing is nudged lower than 50% if a letter writer like Paul does not quote from Jesus.
 
In the historical Jesus model, both P(H | E) AND the P(H | ~E) are the same. When this happens, it basically means that the probability stays at 50%. This violates the probability calculus inherent in Bayes Theorem. Since Bayes is formally/logically valid, this means that the set up that mainstream scholars have erected is logically invalid. E and ~E can't both be evidence for the same thing. The only time that happens is when you're dealing with ad hoc hypotheses: “A hypothesis that forbids nothing, permits everything, and thereby fails to constrain anticipation. Your strength as a rationalist is your ability to be more confused by fiction than by reality. If you are equally good at explaining any outcome (my emphasis), you have zero knowledge“.  
 
Take a look at the likelihood ratio (from E. Yudkowsky's Intro to Bayes Theorem): 
The likelihood ratio for X, p(X|A)/p(X|~A), determines how much observing X slides the probability for A; the likelihood ratio is what says how strong X is as evidence.  Well, in your theory A, you can predict X with probability 1, if you like; but you can't control the denominator of the likelihood ratio, p(X|~A) – there will always be some alternative theories that also predict X, and while we go with the simplest theory that fits the current evidence, you may someday encounter some evidence that an alternative theory predicts but your theory does not.  That's the hidden gotcha that toppled Newton's theory of gravity.  So there's a limit on how much mileage you can get from successful predictions; there's a limit on how high the likelihood ratio goes for confirmatory evidence.
 
On the other hand, if you encounter some piece of evidence Y that is definitely not predicted by your theory, this is enormously strong evidence against your theory.  If p(Y|A) is infinitesimal, then the likelihood ratio will also be infinitesimal.  For example, if p(Y|A) is 0.0001%, and p(Y|~A) is 1%, then the likelihood ratio p(Y|A)/p(Y|~A) will be 1:10000.  -40 decibels of evidence!  Or flipping the likelihood ratio, if p(Y|A) is very small, then p(Y|~A)/p(Y|A) will be very large, meaning that observing Y greatly favors ~A over A.  Falsification is much stronger than confirmation.  This is a consequence of the earlier point that very strong evidence is not the product of a very high probability that A leads to X, but the product of a very low probability that not-A could have led to X.  This is the precise Bayesian rule that underlies the heuristic value of Popper's falsificationism.
Now, what if you posit a Jesus that wasn't a preacher? This would also make sense of the evidence; P(non-preaching Jesus | ~E) > P (non-preaching Jesus). That is, we would expect the early epistle writers to not quote Jesus because they didn't view him as a preacher. 
 
As for ad hocness, take one of the comments over at Vridar:

Cross-posted from comments on Exploring Our Matrix:

So, according to mainstream scholarship…

Accurate geographical details = Evidence for historicity.

Absence of geographical details (e.g. Sepphoris) = more evidence of historicity, and it even tells us new facts about Jesus, e.g., that he deliberately avoided big cities.*
Inaccurate historical details = no problem for historicity/no effect on the historicist model.

You can see where this is going. Accurate and absence should be on either side of the probability formula. This time E would be accurate historical details; in the HJ hypothesis P(H | E) is still equivalent to P(H | ~E).
 
The problem here is with constraints. I hate to say it, but most scholars work under the assumption of a wandering, preaching Jesus without any constraints on what a wandering, preaching Jesus would entail. So they look at all of the evidence through the lens of a wandering, preaching Jesus. As the quote I posted above says, we should be looking for evidence that disconfirms our pet theories and not look for confirmation of our theories. Because the disconfirmation, as the blog of awesome that I quote from is named, helps us to become less wrong. And becoming less wrong is a lot more powerful than being “right”; implicit in the phrase “less wrong” is admitting to our own fallibility and trying to mitigate it. On the other hand, “confirmation” of our theories only feeds our ego (because it's the default human cognitive bias).
 
On a higher level, this lack of constraints/making beliefs pay rent seems to also apply to the Problem of Evil. We have this world that seems to be indifferent to our suffering. It would make sense that the ultimate reality (god, the matrix, etc.) actually is indifferent to our suffering. But theists posit that their god loves us and has some sort of plan for all of it or is so in love with Free Will that he will not abrogate it to ease our suffering. The problem is that this god would also explain a world that is 100% free of all suffering (heaven), and this god could also be used to explain a world that is 0% free of suffering… and every single percentage point in between the two extremes. While an indifferent god or no god at all would not explain either of those last two options.
 
Which worldview is operating on constraints, and which one is not? Which one is making their belief(s) pay rent and which one is letting their belief(s) squat? A theory/worldview that can be used to explain every single possible outcome is really no explanation at all.
 
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Posted by on July 7, 2011 in Bayes, scientific method, skepticism

 

My Rejection of Christianity

This is a conversation I’m having with a Christian at another forum. My response is a bit long so I’m going to post from about the middle of the conversation:

Me:

For example, studying Biblical criticism has led me to the conclusion that the historical Jesus didn’t say almost anything that has been presented in the gospel narratives. The “Jesus” in the gospels of Mark, Matthew, Luke, Thomas, John, Peter, etc. is simply the sockpuppet of the gospel authors, using Jesus as a polemical device to further their theological agenda(s). The same thing happened to a lesser degree with Paul and his writing – almost 50% of his writings in the New Testament are “forgeries”, for lack of a better word. The history of early Christianity is wrought with polemics and deception, using and abusing Christian (and Jewish) scripture to further their theological agenda(s). If a Christian in the 2nd century felt that “true” Christianity was a certain way, and they see a Jesus presented that differs from how they felt Jesus should be, they simply changed the scripture. There was no “Christian canon” in the 1st and 2nd centuries other than the Tanakh, so interpolations in not-yet canonical Christian documents was rampant. This is, again, why appealing to subjectivity is a fool’s errand. Faith takes precedence over fact, plain and simply. This inexorably leads to deception. And if subjectivity (faith) takes precedence over objectivity (fact), how can a Christian tell the difference between faith and self-deception?

Him:

I just don’t see that as the case, I mean your speculating that the early Christians felt comfortable in not altering OT scripture because it was sacred and yet felt comfortable altering a letter from Paul or a Gospel narrative.. and if they did, then to what possible end. What gain would come to them for such a thing. I mean these people went through round after round of severe persecution for their beliefs. It would stand better to reason that if there was a selfish intent then such a persons would have been better off working with the accepted beliefs that went without such punishments.

Now, I am not saying that there weren’t transmissional and translational discrepences and errors. Nor am I saying that there weren’t intentional interpolations.. the Johannine comma being the most notable. However, I am saying that I do believe that there are other plausible ways of looking at the situation, intents and so forth other than the way you have seemed to present it.

[H]ow can [I] as a Christian tell the difference between faith and self-deception? What methodology would [I] use? Hopefully I answered a bit of this earlier, but I’ll have to go with Ayn Rand on this one. The best answer would likely be to, “Check your premises.” 🙂

Me:

I urge you to actually study early Christianity. The most glaring interpolation is the synoptic problem: Luke and Matthew are basically interpolated versions of Mark. While Mark, the first gospel written, is generally seen to have been written around 70 CE, the first Christian document be to elevated to the level of “holy scripture” was Paul’s first letter to the Corinthians around 130 CE by the “heretic” Basilides. But prior to that, the only “holy scripture” was the Tanakh – thus Matthew and Luke had the freedom to change Mark as they saw fit, since Mark wasn’t “canon”. A gospel being canon doesn’t happen until 140 CE. And even so, Christians (like Justin Martyr in 150 CE) accused Jews of removing certain scripture that proof-texted evidence for Jesus’ messiah-hood – yet there’s no evidence of these supposed “deletions” in the oldest Hebrew bible texts.

Another example, the bishop Marcion is the first Christian to compile a “New Testament” in 140 CE and the first Christian to collect “all” of Paul’s letters. But Marcion’s canon only consisted of 10 Pauline epistles and one gospel. Not only that, but our current Pauline corpus is incompatible with Marcion’s Christology – so Marcion’s Pauline epistles couldn’t be the same ones found in our current New Testament. The only explanation is interpolation. Even worse, it’s an odd coincidence that Marcion’s canon didn’t contain the Pastoral Epistles (1 & 2 Timothy and Titus) and those are the three Pauline letters that most NT scholars conclude weren’t written by Paul… so they must not have existed when Marcion compiled his canon. Marcion’s canon consisted of the seven Pauline epistles that are generally agreed to be authentic to Paul and three that have undecided authorship.

Of course, Marcionites accused the proto-Catholics of interpolation, and the proto-Catholics accused the Marcionites of interpolation. But the only reason why we have almost half of the NT made up of Paul’s letters is due to the popularity of Marcionism. The proto-Catholics simply “catholicized” Paul to win over converts from the Marcionites. Hence the post-Marcion creation of Acts of the Apostles and the Pastorals.

And how about the Ebionites? Their name is Hebrew (ebionim means “poor ones” in Hebrew) and they apparently only regarded a Hebrew version of Matthew as sacred scripture along with the Tanakh. But our current Matthew shows no signs of being a translation from Hebrew, and the Ebionites didn’t believe in the virgin birth or Jesus’ status as the literal son of god – so their “Matthew” must have been different from our current Matthew.

And then the gospel of John probably had three different authors.

Of course, Christianity as a whole is one huge abuse of Jewish scripture. Jesus supposedly thought Daniel was a prophet, but prophecy ended upon the deaths of the last prophets like Zechariah and Malachi. Daniel was written during the Maccabean revolt of 164 BCE due to the “abomination causing desolation” (a statue of Zeus) that Antiochus set up in the temple. Thus Daniel isn’t a contemporary of any other prophets and lived less than 100 years before Jesus – a long time after prophecy had ended. This is why Daniel is Ketuvim (writings) and not Nevi’im (prophets) (the K and N in TaNaKh). The Psalms, also, are Ketuvim and not prophetic which invalidates all of the supposed “prophecies” about Jesus like Psalm 22, 26, 31, and 110.

There’s obviously a lot more abuse of the Tanakh by Christians who place their faith before fact, but that would probably take this post further into BC&H category.

[As for checking my premises] [t]hough I’m not much of an Objectivist, I do check my premises repeatedly 😉 I think I’ll list them here

1. I exist

2. A world exists independently of my senses (this is unfalsifiable, but the only other option is solipsism)

3. I’m an imperfect human being, thus my senses aren’t 100% reliable

4. Induction is an imperfect epistemology since it relies on the previous premise (and maybe the Problem of Induction).

5. Deduction is more robust than induction, but is reliant on the previous 2 premises.

Following these three premises, there are some conclusions one can draw:

1. Since my senses aren’t 100% reliable, I have to appeal to sources outside myself for reliable information about the world. Hence my constant appeal to objectivity when wanting to deal with objects (i.e. reality).

2. The vast majority of human beings in history have held inaccurate or just flat out wacky beliefs. This is from my undergraduate studies of history, sociology, psychology, and world religions. Thus an inductive argument against religious beliefs.

3. Confirmation bias is a well known psychological phenomenon [where we are quick to accept information that confirms what we already believe and are quick to reject information that doesn’t confirm what we already believe]. Since confirmation bias is ubiquitous, I should be skeptical of my beliefs that simply “feel good” without objective (P2) support. Quite ironically, that “feels right” feeling is a base emotion, just like anger or fear. The feeling of certainty can be stimulated by thoughts, not by logic or reason. Ergo, there’s no necessary correlation between what feels true and what actually is true. This is why I’m consistently trying to be less wrong than I currently am. Selection bias [where we count the hits and ignore the misses so that we erroneously have 100% success] is also a consistent pitfall of induction that many people do not realize they do.

This is really a fleshing out of my third premise above, and what I think constitutes “self-deception”.

4. Religions spread in the same exact way as other sociological beliefs. The reason most Americans are Christians is the same reason most Americans speak English.

These conclusions make me highly skeptical of the claims of the religious. In order for religious beliefs to be true without appealing to objectivity, my third premise has to be rejected. The only way you can trust your “feelings” on things is if you have perfect senses and confirmation/selection bias don’t apply to you because you are a superbeing. Evolutionary psychology basically states that our cognitive and empirical facilities only excel at helping us not end up dead. Beyond that, everything else isn’t really necessary, just surplus. So a person can have inaccurate beliefs but as long as those beliefs don’t kill them, they can be selected for.

And then, I’m of the belief that an interventionist, personal god invalidates my second premise. Miracles, signs, and other supernatural events that only one person can see that cannot be validated by unbiased (i.e. objective) sources means that this god can produce illusions that are only visible to the “believer” for the sole purpose of making them faithful to this god. How then, can we know anything is real? A miracle working god would naturally push me towards solipsism.

This is a basic summary of why I’m skeptical of and ultimately reject modern Christianity.

 
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Posted by on October 8, 2009 in Christianity, early Christianity, objectivity, skepticism

 

First Post

This is my first blog entry. I made this blog specifically for documenting my study of various religions.

I guess I should start with a little about myself. I recently graduated from Penn State with a B. S. in Information Sciences and Technology. Right now I’m waiting on the Army to give me a security clearance so I can start work… sometime soon. Anyway, I’ve been interested in religion since I first started seriously and critically thinking about it – which was around when I was 14 or 15. I was wearing a crucifix on the 4 train in NYC and one of my buddies asked if “I really believed that stuff” pointing to my crucifix. I said “I dunno” and then he poignantly rejoined “So why are you wearing that?”.

After that incident, I decided that I wanted find out what I really believed. Since I was (and still am) such a science-minded person, I wanted to verify Christianity – but well aware of human beings’ tendency towards Confirmation Bias (only looking for things that confirm our a priori assumptions and disregarding information that discredits it) I figured that the only way to prove something true was to try to prove it false. If that sounds strange, I’d like to point out that all of us follow that methodology to varying degrees (except when we have an emotional attachment to the outcome). Buying a TV, trying on clothes, doing our homework – the entirety of our school system is designed around the process of doubt. We wouldn’t have tests if that weren’t the case. We wouldn’t have to sit through job interviews if that weren’t the case. Antibiotics, house shopping, doing laundry… anything that we require some form of knowledge about, we go through a process of skepticism prior to arriving at our conclusion. The study of how people know what they know is called “epistemology”. I had no idea about even the existence of such a word in high school, but I did want to know “how people knew what they knew” and the most consistent methodology, as I just wrote, is examination through doubt.

So after high school in 1997, I joined the Air Force. At this time, I was an agnostic about my Christianity and the existence of god(s) in general. It wasn’t until I had full access to the Internet (1999) that my “verification” really started to go full steam ahead, and Christianity unfortunately, didn’t stand up to scrutiny. Most alarming about the concept of epistemology in the Christian paradigm is this concept of “faith”. You have to first have positive belief, and then you know. Which is a wacky epistemology to follow and downright dangerous if utilized in the wrong context. External critique and verification is absurd if “faith” is the ultimate arbiter of knowledge.

As an example of the profound epistemological deficiency of faith, here’s a less dangerous example. Let’s say two students are taking a math test and they finish at the same time. Someone who expresses some healthy skepticism might say “I’ll go over my test again to make sure I made all the right calculations”. Proponents of faith would simply say “I know it’s right, it feels right and I’ll hand in my test” without checking their answers. Naturally, the person who checked their answers before handing in the test would be doing the more rational thing. Most people would agree as well – mainly because there’s no emotional investment in a math test.

A more dangerous example of the intellectual bankruptcy of faith, let’s say two people have guns pointed at their head. The person of faith would say “I have faith that no harm will come to me if the trigger is pulled”. A more reasonable person would say “I want to check the gun first and make sure there are no bullets in the chamber or in the clip before pulling the trigger”. Obviously most people would still side with the more skeptical person and follow their example – except when it comes to religion!

As of this day, that’s always the final answer as to what Christianity boils down to – faith. Which is odd considering that fideism is frowned upon in at least Catholicism. Anyway, I’ll post more about Christianity in subsequent posts, since I’m constantly digging ever deeper into the history of Christianity. But after Christianity, I studied a bit about Islam (ironically in basic training I went to a Muslim church only because it met twice a week as opposed to the other churches that met once a week), some Judaism and eventually moved on to the religions of the “East”. Religions like Shintoism and Buddhism were more intellectually satisfying since they didn’t concentrate on a cosmic entity that cares that you touched a woman while she was menstruating, and more about living harmoniously with your surroundings.

While in the Air Force I became more of an Ontological Naturalist and most religions didn’t stand up to scrutiny once they posited the supernatural. But still, even eschewing the supernatural from Eastern religions didn’t hinder their message, while in Western religions the supernatural is where they derived their power from – right from might. As of right now, I consider myself an Ontological Naturalistic Pantheist of the Spinoza-Einstein variety and do meditate. My meditation, while it might sound sort of woo-woo supernatural-like, there’s definitely a verifiable change in my physiology while doing it, that other friends have been able to take note of.

As for the name of this blog, I named it “five” in Greek (pente – πέντε) because my last name means “five” in Latin, and my website is called deus diapente, which is Latin-esque for “fifth god” – which is ironic because a lot of the information in my website is incompatible with the [Western] view of god.

 
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Posted by on August 26, 2008 in Christianity, faith, naturalistic pantheism, skepticism

 
 
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