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Monthly Archives: October 2012

Logical Fallacies as Weak Bayesian Evidence: Argumentum Ad Hominem

Ad hominem. The most well known logical fallacy (and probably most used) in the history of everything. Like most logical fallacies, in some instances it might not actually be fallacious; but again, the thing about straightforward logic is that the conclusion has to follow necessarily from the premises. And again, we don’t live in a world of deductive certainty but the world of inductive probability.

First I have to distinguish between an ad hominem (ad hom) fallacy and a personal attack. The following is an ad hom:

Bob: All instruments that have strings are made out of wood. My guitar has strings. Therefore it is a wood instrument
Sue: Your guitar isn’t a wood instrument because you are a well known liar

This is a personal attack:

Bob: All instruments that have strings are made out of wood. My guitar has strings. Therefore it is a wood instrument
Sue: My electric violin has strings but isn’t made out of wood. You are a known liar.

The tricky part is that there can be non-fallacious ad hom arguments. This might be seen as a valid ad hom:

Bob: All instruments that have strings are made out of wood. My guitar has strings. Therefore it is a wood instrument
Sue: You are a known liar so I have no reason for accepting your say-so that all instruments that have strings are made out of wood. Therefore I can’t follow you to your conclusion that your guitar is a wood instrument.

Pedantically, an ad hom is fallacious because one is rejecting an argument or the conclusions of an argument based on the qualities of the person presenting it. However, a premise can be accepted or rejected for any reason; it’s up to the person presenting the argument to support their premises. The personal attack, however, is simply attacking the person gratuitously.

It’s a pretty good rule of thumb that an untrustworthy source isn’t to be trusted. If I read a story in the National Enquirer, there’s a high probability that it won’t be true. But people confuse themselves when, instead of “National Enquirer” we switch to “Bob from accounting”. If Bob was also a well known liar, then it might be perfectly reasonable to not accept a story from Bob as true.

But this is about arguments, not stories. So what if Bob was well known for concocting arguments that sound true but are actually fallacious? What if Bob was well known for his sophistry? Let’s say you hear argument E from Bob. The hypothesis, H, is whether Bob’s argument is a good one or a shitty, sophist-actic argument. The probability of E given H would be pretty low, since it is basically asking what the probability hearing about Bob’s argument given that he made an actual good argument. The converse would be the probability of hearing about Bob’s argument given that he is intentionally being tricky.

Let’s solidify this example a bit. Let’s say you overhear that Bob has recently argued that glutamine makes a good dietary suppliment for bodybuilding. What is the probability that this would be a good argument given that Bob argues for it? This depends on the probability that Bob would posit an argument given that it’s good versus the probability that Bob would posit an argument given that it’s sophistry. Or:

P(Good Arg) is our prior probability
P(Bob Said | Good Arg) is our success rate
P(Bob Said | Bad Arg) is our false positive rate
P(Good Arg | Bob Said) is what we are trying to find out

So let’s say that we are perfectly agnostic about whether glutamine is a good dietary suppliment for bodybuilding. If Bob has almost never presented a good argument for something, then this means that P(Bob Said | Good Arg) would be extremely low. However, knowing that Bob is constantly presenting sophisticated yet false arguments, P(Bob Said | Bad Arg) would be extremely high. So our Bayes Factor in this instance would be P(Bob Said | Good Arg) / P(Bob Said | Bad Arg), which is low / high, which is less than 1.

This means that, given that Bob has presented an argument that we are unsure about the conclusion, it is more likely that glutamine is not a good dietary suppliment for bodybuilding based only on the fact that Bob has argued in the positive. So depending on how disparate Bob’s success and false positive rates are for his arguments, an ad hominem argument could be either strong or weak Bayesian evidence against Bob’s argument. Maybe Bob has an invalid premise in his argument? Usually that’s how sophistry works. And remember, premises can be accepted or rejected for any reason and it’s up to the person presenting the argument to support their premises.

So here is the apparent contradiction: It is definitely deductively fallacious to reject an argument based on who says it. But it is not inductively fallacious to reject an argument based on who says it because based on their history, there could be a high probability of them hiding away false premises tucked in the argument (like a complex question). This makes a bit of sense, since induction and deduction are a bit at odds. What’s true by induction isn’t necessarily true by deduction, and what’s true by deduction isn’t necessarily true by induction.

But again, this is weak Bayesian evidence. Just like absence of evidence being evidence of absence, it’s not enough to rest an entire conclusion on. You would have to continually collect evidence besides the fact that Bob presented an argument to arrive at a definitive conclusion. The most straightforward way to do that would be to deductively check Bob’s premises and see if they follow logically to his conclusion.

 
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Posted by on October 23, 2012 in Bayes, logical fallacies as weak bayesian evidence

 

Criterology Was Born From Form Criticism; Form Criticism Was Never About Historicity

Therefore, criteriology was never about historicity.

Neil Godfrey reviews the recent bookJesus, Criteria, and the Demise of Authenticity:

So the form critic’s task is to separate the various strata in the Gospels. Some details belong to “the original historical tradition” and other strata belong to the author. How to separate these is the aim of form-criticism.

But why should their be a difference between the “original historical tradition” and the overlay from the author?

The form critic answers this by pointing to another assumption: that the gospels were composed by “Hellenistic Christians” who were removed from the original Palestinian Christians who were responsible for creating the earliest traditions about Jesus. The Palestinian Christians initially created oral traditions, not literary ones. It is these oral traditions that were taken by the later literary Christians and reshaped into written narratives expressing a particular theological point of view.

The form critic’s job was to break apart the units of early Jesus tradition from the theologically influenced narrative of the Gospels.

Once this was done the form critic would use these “free-standing units” to reconstruct the earlier oral tradition of the Palestinian church. […]

Form criticism was meant to discover the pre-literary oral tradition.

From the 1950s on scholars sought to discover something else: they sought to find the authentic Jesus traditions — the historical Jesus with the tools that had been designed to find the pre-Gospel tradition.

So for instance, the Criterion of Embarrassment was never meant to find out what the historical Jesus did. It was meant to separate what served the interests of “the Church”  from oral traditions that (might) have gone before it. Current historical Jesus scholars have taken an extra step: assuming that “oral tradition” meant “historical Jesus”.

Over time, the “oral tradition” part is completely ignored and criteriology is assumed to uncover information about the historical Jesus full stop.

 
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Posted by on October 18, 2012 in historical jesus, historicity, historiography

 

Other Ways Of Knowing

If you look at my blogger homepage, I list what my interests are in making this blog. One of them is epistemology. That is the study of how we know what we know. The biggest boost to my own epistemology, something that cleared up how I know what I know, is Bayes Theorem (BT).

Because BT is a simple formulation of how the scientific method is supposed to work, I should be accused of “scientism”. But since most people who accuse people of scientism don’t know about BT, they don’t know to level that charge against me. But I don’t even think I’m a proponent of just scientism. As Eliezer Yudkowsky says, [scientism] isn’t strict enough, bayesianism is stricter. As a bayesian, I’m much more critical of “other ways of knowing” than mere scientism.

What is the most important part of BT? If you read my most recent post on starting with different priors you’ll know that the most important part of BT is Bayes Factor, or dividing the conditional probabilities. This shows you how strongly or weakly the evidence favors or disfavors your hypothesis. For any binary test (true or false), the conditionals can be called the Success Rate (SR) and the False Positive Rate (FPR). This is real important to note, since it’s a blow against “other ways of knowing”.

At work, I’ve helped develop a program that can automatically generate100% valid messages according to a military standard. Other software developers use this program to test their systems. Now, this program was started before I became a project lead, so my input for how the program would work didn’t start until earlier this year.

In the language of BT, this means that the SR of this program is 100%. But what about the FPR? This program doesn’t automatically generate invalid messages, so it is actually of very little use to other software engineers who want to test their systems to make sure they are correctly validating messages. It’s actually very easy to make a system that will successfully validate 100% of the valid messages it receives: Just make it say that every message it receives is valid!

What would really make this automatic message generating application strong is being able to test both the SR and the FPR. This would help to ensure that other programs are successfully validating actual valid messages and correctly identifying invalid messages. So not only should the SR of this program be 100%, but the FPR of the program should be pretty close to zero. So for this next development cycle, I snuck in some BT language in the requirement 😉

If this isn’t clear enough, I’ll use a more hypothetical example. Let’s say that the TSA implements some new computer system that identifies 100% of the trial-terrorists during development. If this system is put into the field and identifies someone as a terrorist, does this mean that they actually are a terrorist? No. You would have to also know the system’s FPR (and also the prior probability / base rate) in order to guage how likely it is that a person caught is a terrorist. If the FPR for this TSA system is 100% or close to 100%, then this is either very weak or no evidence the person caught is a terrorist.

That actually seems to be how the current TSA system works, so it’s not as hypothetical as I thought…

Anyway, what about these so-called “other ways of knowing”? What is the success rate of these other ways of knowing? The false positive rate? If some other way of knowing had a 100% SR does this mean that you actually know something? No. It would be just like my automatic message generator.

One way that proponents of other ways of knowing would attempt to get out of it would be to claim that BT doesn’t apply. But that would be like Christian apologists claiming logic doesn’t apply when talking about the existence of god. Sure, maybe logic doesn’t apply, but then you wouldn’t be able to talk about god in any meaningful way. Apologists in this case are confusing ontology with epistemology: Logic is a function of epistemology, not ontology. The less something can fit into a logical framework, the less we can know and understand about it. Since BT is just an extention of the laws of logic the same argument would be applicable. The less something fits in with the laws of probability (BT), the less we can know about it.

But there’s another angle for where the charges of scientism, and appeals to “other ways of knowing”, might be coming from:

“Traditional Rationality” [i.e. scientism] refers to the memes of rationality which are in general circulation. It is good enough to get Science done, but lacks the technical precision of Bayesian probability. Unsharpened by curiosity, it demands only the least effort needed to push forward human knowledge.

Traditional Rationality is phrased in terms of social rules, with violations interpretable as cheating – as defections from cooperative norms. If you want me to accept a belief from you, you are obligated to provide me with a certain amount of evidence. If you try to get out of it, we all know you’re cheating on your obligation. A theory is obligated to make bold predictions for itself, not just steal predictions that other theories have labored to make. A theory is obligated to expose itself to falsification – if it tries to duck out, that’s like trying to duck out of a fearsome initiation ritual; you must pay your dues.

This, I would bet, is where the majority of charges of scientism come from. They are talking about the social rules of the scientific method. You can violate social rules (because this means you are no longer participating in that social ritual), but you can’t violate the rules of probability. Well you can, but if you are willing to put money on breaking those rules, you will lose money. This also seems to explain another phenomenon: That of religious scientists. Again, they consider the scientific method a social contract, only applicable when “doing science”. Because it is only a social contract, we have Non-Overlapping Magisteria between religion and science; religion is one social setting, doing science is yet another.

So I’ll make a bold statement: There aren’t any “other ways of knowing”. The only ways of knowing that we have are according to the laws of logic and the laws of probability. Break those rules, and you simply don’t know what you claim to know.

 
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Posted by on October 9, 2012 in Bayes

 

The Perpetual Virginity of Mary

So I was reading Matthew chapter 1 in Greek and I stumbled upon this little gem:

1.25 καὶ οὐκ ἐγίνωσκεν αὐτὴν ἕως [οὗ] ἔτεκεν υἱόν: καὶ ἐκάλεσεν τὸ ὄνομα αὐτοῦ Ἰησοῦν

That reads, in my own translation “And he did not know her (Mary) until she gave birth to a son: and called him Jesus”

So it looks like the straightforward meaning of this is that Joseph had sex with (i.e. “knew”) Mary after she had given birth to Jesus. Of course, there is a ready made apologetic for the plain meaning of this sentence, since Catholics have had over a thousand years to debate and prepare it:

Till she brought forth her firstborn son… From these words Helvidius and other heretics most impiously inferred that the blessed Virgin Mary had other children besides Christ; but St. Jerome shows, by divers[e] examples, that this expression of the Evangelist was a manner of speaking usual among the Hebrews, to denote by the word until, only what is done, without any regard to the future. Thus it is said, Genesis 8:6 and 8:7, that Noe sent forth a raven, which went forth, and did not return till the waters were dried up on the earth. That is, did not return any more. Also Isaias 46:4, God says: I am till you grow old. Who dare infer that God should then cease to be: Also in the 1 Maccabees 5:54, And they went up to mount Sion with joy and gladness, and offered holocausts, because not one of them was slain till they had returned in peace. That is, not one was slain before or after they had returned. God saith to his divine Son: Sit on my right hand till I make thy enemies thy footstool. Shall he sit no longer after his enemies are subdued? Yea and for all eternity. St. Jerome also proves by Scripture examples, that an only begotten son, was also called firstborn, or first begotten: because according to the law, the firstborn males were to be consecrated to God; Sanctify unto me, saith the Lord, every firstborn that opens the womb among the children of Israel, etc. Exodus 13:2.

The problem is that this makes sense if you assume the Perpetual Virginity of Mary from the start. But was that what Matthew intended? Matthew wasn’t a Catholic, so we have no idea whether he subscribed to the perpetual virginity of Mary, thinking of her as though she were some sort of vestal virgin. Maybe he put that in there to cement the idea that Jesus was born before Joseph had sexual relations with her.

Catholics, having syncretized a lot of their dogmas/traditions with the mores of the (pagan) Roman Empire, would be more likely to argue for that tradition based on being Romans. They would also have had traditions of aceticism since this undercurrent was around from at least the 2nd century; the idea of flesh and sexual relations being “sinful” inherited from the Gnostics and Marcion. They did get the basic layout of their NT from Marcion anyway.

There’s also no reason why Joseph would keep Mary around, being wed with her, and break the traditional Jewish requirement to be fruitful and multiply with his young nubile wife; Mary was probably around 13 or 14 when she gave birth to Jesus (assuming a modicum of the story is true). Joseph being a celibate, also, implies proto-Orthodoxy traditions of acetisim and not any legitimate (that we know of) early 1st century CE / late 1st century BCE Judaism.

Anyway, we should take Matt’s own writing in and of itself into account to determine what he meant. Earlier in the same chapter, a couple of verses before 25, he writes:

17 Πᾶσαι οὖν αἱ γενεαὶ ἀπὸ Ἀβραὰμ ἕως Δαυὶδ γενεαὶ δεκατέσσαρες, καὶ ἀπὸ Δαυὶδ ἕως τῆς μετοικεσίας Βαβυλῶνος γενεαὶ δεκατέσσαρες, καὶ ἀπὸ τῆς μετοικεσίας Βαβυλῶνος ἕως τοῦ Χριστοῦ γενεαὶ δεκατέσσαρες.

That is, “All of the generations from Abraham until David were fourteen generations, and from David until the Babylonian Exile fourteen generations, and from the Babylonian Exile until Christ fourteen generations.”

So what is the evidence we have? For one, we don’t know whether Matt was a Catholic, so apologetics from Catholic Jerome two centuries later might not represent what Matt himself was thinking. Second, Matt doesn’t seem to use ἕως in other contexts to signify “never”. Third, the phrasing of the sentence seems to have been written to emphasize that Joseph didn’t have sex with Mary until after Jesus was born because Matt’s emphasis was on the virgin birth of Jesus, not the perpetual virginity of Mary. Mary all but disappears from Matt’s special material after this introduction, meaning that her role as the immaculate conduit for Jesus’ birth was over in Matt’s mind. If Matt had intended for Mary to be depicted as a virgin for the rest of her life, he might have mentioned it elsewhere.

Of course, none of this is intended to dialogue with Catholics. Just my own lucubration.

 
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Posted by on October 5, 2012 in apologetics, greek, virgin birth

 

The Mormon Church’s Migration to the Global South

This is an interesting article on Slate that describes in short how the Mormon church grew. It mostly focuses on the economics side of the church, but it is also a nice succint history lesson as well.

But even the most devout Mormons in Africa and Latin America can only provide a fraction of the church’s annual tithing revenues. Which is why, as the Mormon population outside the United States rises—and as demands for temples, meetinghouses, and other church resources in the global south rises—the church may find it has backed itself into a corner. It has closely bound Mormon faith to the tastes and mores of the American middle class. As its growth outside the United States continues, the costs of such things will be considerable. Hence, it appears, the church’s investments in real estate and shopping malls. Eventually, as has happened already to Roman Catholicism, Pentecostalism, and Methodism, Mormonism will become a religion of the global south. And when that shift takes place, the money to keep the Christmas lights on in Temple Square will have to come from somewhere.

In general, it seems as though the big hierarchical religions are moving towards areas below the equator. Which are areas that are typically more economically unstable than the West.

 
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Posted by on October 3, 2012 in economics/sociology

 

Bayes Theorem and Starting With Different Priors

One critique of using Bayes Theorem is the problem of subjective priors. The criticism is that, if multiple people start with different priors then the whole formula is useless for arriving at any sort of consensus due to the inherent subjectivity of the priors. The actual problem isn’t the priors but the conditionals, which is something you ideally should have no control over. Even if your priors are the same, if the conditionals are different then this is where Bayes’ Theorem would disintegrate into postmodernist subjective-silliness.

So for example, if we have two people who are dealing with the Synoptic Problem — one starts with a prior of 90% that Mark was written first and the other starts with a prior of 22% that Mark was written first — it almost doesn’t matter where you start at because accumulating all of the evidence will push the two priors towards each other. As long as your priors aren’t 0 or 1 since those aren’t probabilities. And actually, if your prior is really in line with reality, then it won’t move much no matter how much evidence is gathered. So for example:

Person 1 assumes the prior probability that Mark was written first, or P(Mark) = 90%. P(Mark) for the second person is 22%. The first evidence they analyze is the length of Mark. It is a fact that Mark is the shortest Synoptic Gospel (MSSG), so this is our evidence E (if Mark being the shortest gospel was only hypothetical, then the logic behind Occam’s Razor would apply, not BT). How likely is it that Mark would be the shortest gospel given that Mark was written first? A historian might look at this by doing a large survey of ancient works and see how many of the newer versions are shorter than the older versions. I’m not a historian so I wouldn’t know, but I would guess that the usual way it happens is that original compositions are shorter than the ones derived from them, though there could be shorter versions that came after the long version (like what’s argued is Marcion’s relation to Luke, at least until relatively recently). The word “usually” could be quantified in some way somewhere around 80% (since I don’t have the experience with historical documents that actual historians do). The third value we need is the false positive rate, or how many times a shorter document is actually a rewrite of a longer document. Again, not a historian, but this doesn’t seem like it happens a lot (5%). So for the sake of example BT would look like this:

Person 1: P(Mark | MSSG) = P(MSSG | Mark) * P(Mark) / [P(MSSG | Mark) * P(Mark)] + [P(MSSG | Not Mark) * P(Not Mark)]
: = .8 * .9 / [.8 * .9] + [.05 * .1]
: = .9931

Person 2: P(Mark | MSSG) = P(MSSG | Mark) * P(Mark) / [P(MSSG | Mark) * P(Mark)] + [P(MSSG | Not Mark) * P(Not Mark)]
: = .8 * .22 / [.8 * .22] + [.05 * .78]
: = .8186

Both priors moved up, which makes sense since shorter documents are usually earlier versions of longer documents (but again, not a historian here).

With our new priors, we look at some other evidence. Like the content only found in Mark such as Mk 8.22-26. How likely is it that this pericope would be in Mark given Mark’s priority? How likely is it that this pericope would be in Mark given some other Gospel’s priority, or restated, Mark added this pericope after reading the other Synoptics?

Again, just for example since I’m not a historian, P(Mk 8.22-26 | Mark) is “probable” or 80% and P(Mk 8.22-26 | Not Mark) is “extremely improbable” or 1%.

Person 1: P(Mark | Mk 8.22-26) = P(Mk 8.22-26 | Mark) * P(Mark) / [P(Mk 8.22-26 | Mark) * P(Mark)] + [P(Mk 8.22-26 | Not Mark) * P(Not Mark)]
: = .8 * .9931 / [.8 * .9931] + [.01 * .0069]
: = .9999

Person 2: P(Mark | MSG) = P(MSG | Mark) * P(Mark) / [P(MSG | Mark) * P(Mark)] + [P(MSG | Not Mark) * P(Not Mark)]
: = .8 * .8186 / [.8 * .8186] + [.01 * .1814]
: = .9972

As you can see, the two priors are starting to converge. And you would repeat the process for each piece of evidence both for and against Markan Priority, with the priors changed from the previous use of BT (i.e. the posteriors) functioning as the priors for the next line of evidence. Again, the driving force here is the conditional probabilities. Which makes sense since these two numbers are crucial for figuring out Bayes Factor, which determines how strongly the evidence either favors or disfavors your hypothesis.

Of course, in the example above, my conditionals actually are subjective since I’m not a historian.

 
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Posted by on October 1, 2012 in Bayes

 
 
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