Monthly Archives: March 2012

Real Academic Work?

James McGrath left this nasty comment on P.Z. Myers’ blog about Richard Carrier and his use of Bayes’ theorem:

PZ, I have to say that I am very disappointed to find someone who stands for mainstream science against its bogus pseudoscientific critics, cheering on someone who represents the equivalent in the domain of history.

I’ve tried to offer some explanations regarding why Carrier’s attempt to engage in denialism ought to be found no more persuasive than the similar attempts to sow doubt regarding evolution, climate change, or anything else about which the vast majority of experts agree.

Evolution? Bayes’ Theorem. Climate Change? Bayes’ Theorem. Historical Jesus studies? Oh… well… when you attempt to use Bayes Theorem in that domain, you are the equivalent of a bogus pseudoscientific critic.

So make no mistake! Real academic work is not about method. It’s about appeals to authority and consensus.


Posted by on March 30, 2012 in Bayes


Epiphenom: Religious Students Have Fewer Interracial Friends

From here:

What she found was that the most religious students (based on self-reported religiosity, their frequency of religious service attendance, and their religious observance) also had the fewest friends from other races.

What’s more, Protestant or Jewish (but not Muslim, Hindu or Buddhist) students also had the fewest mixed-race friendships. That’s probably because these are the two major religious groups.

These two effects were independent – so the most mono-cultural people were the most religious Protestants and Jews. This held even after controlling for a bunch of other factors, including the racial diversity of the college, the diversity of their previous school, and the race of the student.

And on top of all this, belonging to a religious club reduced the chances of inter-racial friendship still further! That wasn’t the case with other clubs (except explicitly ethnic clubs – and even here the effect was smaller than for religious clubs).

Now, the interesting thing about these three factors – religiosity, religious denomination, and membership of a religious club – isn’t that they weren’t highly correlated. That means that they seem to have independent, additive effects.

I guess this makes sense in a way. It’s been well known for decades that there is a strong correlation between racism and religion. That is, the more religious someone is, the more likely it is that they’re racist. This is counterintuitive if you only look at the dogmas of religion and their pretense to inclusion, but we all know how well intuition works.

Of course my own anecdotal experiences confirm that religious people are more racist than the non-religious; a mother of an ex gf of mine apparently disapproved of interracial relationships (which was ours, but she didn’t know about it) and was one of the reasons why she didn’t approve of Obama, who was running for president at the time. Other religious parents of friends of mine also didn’t approve of interracial relationships going so far as to disown children for marrying outside of their race.

This probably isn’t a knock on religion per se; it probably means that racism and religion both appeal to the same sort of brain module that separates us vs them. This is evidenced by the fact that there is also a relationship between religiosity and nationalism. So it could be that people become religious just because they are also the type of people who are predisposed to racism and nationalism.

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Posted by on March 29, 2012 in cognitive science


French commune home to 20,000 ‘doomsday cultists’ awaiting alien salvation

I mean…

An estimated 20,000 New Age believers who say the “upside down” mountain is home to aliens who will rescue them from an impending apocalypse have saturated a small French commune near the foot of the picturesque Pic de Bugarach.

What is this I don’t even

“The apocalypse we believe in is the end of a certain world and the beginning of another,” one of the New Age pilgrims going only by the name “Jean,” tells the paper. “A new spiritual world. The year 2012 is the end of a cycle of suffering. Bugarach is one of the major chakras of the earth, a place devoted to welcoming the energies of tomorrow.”

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Posted by on March 28, 2012 in This is madness


The Existence Of Jesus Is Just A Theory

This should be the most common response to Creationists who insist that the theory of evolution is “just a theory”. And that feeling of being taken aback when you say “well, Jesus is just a theory” is the same feeling that normal people get when Creationists say that “evolution is just a theory”.

Make no mistake. Jesus is a hypothetical construct posited to make sense of Christianity, much in the same way the theory of evolution is posited to make sense of biology. The evidence for evolution is much better than the evidence for the existence of Jesus. So if Creationists want to doubt the theory of evolution because it’s “just a theory”, then they should be even more doubtful of the existence of Jesus based on the same logic. This is based on the simple fact that the hard sciences have more evidence to work with than history.

On the flip side of that, if the existence of Jesus is beyond reasonable doubt for the Creationist, then how much more solid is the existence of evolution? They are really stuck between a rock and a hard place if they assert that one is open to questioning and the other one is beyond questioning. This statement should really expose the hypocrisy of their “it’s just a theory” statement.

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Posted by on March 27, 2012 in apologetics, creationism, jesus myth


The Lord Works In Mysterious Way

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Posted by on March 26, 2012 in Funny


The Problem With Ad Hoc Hypotheses (Bayes’ Theorem And Coin Flips)

This post was originally part of a longer post I’m writing which is a follow up to these two posts. But I thought it would be good to dedicate a single post to it because I think it’s an important concept.

For Bayes’ theorem, evidence can only support hypotheses. Hypotheses can be used to support other hypotheses, but unlike evidence, this usually brings down the probability. Right now I’m having a bit of a discussion on my Facebook with someone who believes in ghosts. He says he knows he’s been haunted and been in haunted houses, therefore there is more to life than this universe because there are
other planes of existence. My response was that I thought it was more likely that he was mistaken about his encounter with ghosts instead of the human mind being immortal and entire other planes of existence being true.

It’s hard to get people to understand why his reasoning is wrong. He is stacking multiple hypotheses to explain an event. I didn’t disagree that he experienced something, but his interpretation of that experience is what I was questioning. I kept my explanation simple since I didn’t need to posit any other hypothesis besides human fallibility, which we all know is a large number.

When you add hypotheses to explain some event, the probability of each of those hypotheses has to be multiplied together. When a hypothesis is no longer hypothetical, that is, when we have confirmation of it and it becomes unquestioning fact, *that* is when you can add it as evidence for some initial hypothesis. And that is when you use Bayes’.

For example, in order to flip a coin and get three flips of heads in a row, I would have to first flip two heads in a row. In order to flip two heads in a row I have to flip heads on the first flip. Three heads depends on two heads which depends on one heads. Since the probability of flipping heads once is .5, and each additional heads depends on the previous heads, they all multiply together: .5 * .5 * .5 = .125.

In this case, .125 is the prior probability of flipping three heads in a row. What then happens once I flip heads once? It becomes:

P(H) = prior probability of flipping three heads in a row, .125
P(E) = probability of flipping heads, .5
P(E | H) = probability of flipping heads given that I will flip three heads in a row, 1.00 (it is absolutely necessary to flip heads given that I will flip three heads in a row)
P(E | ~H) = probability of flipping heads given that I won’t flip three heads in a row, ??? (not really necessary since I already know P(E), though it can be figured out as I demonstrated in the other two posts).

What is the probability that I will flip three heads in a row given that I have flipped heads once?

P(Flipping Three Heads In A Row | Flipping Heads Once) = P(E | H) * P(H) / P(E)
= 1.00 * .125 / .5
= .125 / .5
= .25

Given that I have flipped heads once, my prior has moved from .125 to .25. Which is what we would expect, since all we are really doing is subtracting one of the .5 probabilities from the three coin flips .5 * .5 * .5 and end up with only two flips to go — .5 * .5 — which equals .25.

And of course, absence of evidence is evidence of absence; I posted the Bayes’ theorem formula for that adage:

P(H | ~E) = P(~E | H) * P(H) / P(~E)

P(~E | H) is the compliment to P(E | H), both have to equal 1.00. Since P(E | H) in this example is already 1.00, this leaves nothing left for P(~E | H). Now we go through the anti-Bayes’ for absence of evidence:

P(H | ~E) = P(~E | H) * P(H) / P(~E)
= 0 * .125 / .5
= 0 / .5
= 0

So upon flipping tails, or the absence of the evidence of flipping heads, my prior probability of flipping three heads in a row plummets to zero.

Back to the ghost hypothesis to explain whatever it was that my friend experienced, he is doing the equivalent of flipping heads three times in a row. I have only flipped heads once. Notice the chain of probability:

1. Experience I can’t explain
2. It must be ghosts
3. Other planes of existence

Only 1 is in evidence. 2 is the explanation for 1, and 3 is the explanation for 2. The experience happened, so that is in evidence. The existence of ghosts is a hypothetical used to explain the experience, and the other planes of existence is a hypothetical used to explain ghosts. Since those two hypotheses aren’t in evidence, their probability — whatever they are — gets multiplied together just like the coin flips. If each of them was 60% probable, his ghost hypothesis used to explain the event is only 36% probable.

On the other hand, my chain of reasoning went like this:

1. Experience he can’t explain
2. The ghost explanation is probably hyperactive agency detection

Again, only 1 is in evidence. 2 is just the alternative to his ghost explanation and is 1 – P(Ghosts). In the above I assumed 60%, so this would be 40%. Since my total hypothesis has a 40% chance of being true, and his total hypothesis has a 36% chance of being true, my explanation is more probable even though I favored his hypothesis much more than I should have (60% probability that ghosts exist? 60% probability of another plane of existence? Really?).

In discussions with people, it’s important to distinguish between evidence and hypotheses. Evidence is anything that is factual, and the hypothesis is whatever framework is used to explain those facts. Lots of people equivocate between the two. If someone keeps adding hypotheticals to explain some event, this will exponentially lower the probability of their initial hypothesis being true. That is the problem with ad hoc hypotheses, and why Occam’s Razor makes sense.

For example, in historical Jesus research, scholars apply criteriology to discover facts, but this is equivocating between fact and hypothesis. Criteriology can only determine hypotheticals; the probability that some saying or event actually happened. Anything discovered via criteriology is not firmly in the fact bin but in the hypothetical bin. People can disagree about the cogency of some hypothetical, but no one should disagree about certain facts (“people are entitled to their own opinions but not their own facts”).

Even though both facts and hypotheticals have a certain probability, their probabilities are not utilized in the same way as hopefully the coin flip analogy showed.


Posted by on March 24, 2012 in Bayes


The Possible Therefore Probable Fallacy

The possible therefore probable fallacy. This is something that I have often encountered so many times in religious debates that there is no way I could put a finger on when I first ran into it. Not only that, but it was hard to explain why it was fallacious before I started studying probability theory. And there was no official name for this fallacy.

But make no mistake. It’s a fallacy. If you study probability theory, you will learn that everything is possible. Everything. Even though everything is possible, not everything is probable. This is the heart of the matter; we should always go by whichever idea or explanation has the highest probability of being correct, since this will minimize the probability of us being incorrect. If we didn’t do that, then things like the Base Rate Fallacy wouldn’t be, well, a fallacy.

The way it goes, someone posits some hypothesis that has a high probability of being correct. The person on the losing side, not content with being on the low end of the probability stick, spouts out his sore-loser argument: “I have this alternative argument. Even if it’s less probable than your argument it’s still possible! Therefore it’s true/I’m justified in believing it/na-na-nah-boo-boo.” While not as obvious as that, this is the basic gist of the thread of conversation.

Since Richard Carrier has recently published his book Proving History (p 26 – 29), there is now an actual peer reviewed publication that addresses this fallacy. Which means it is now an “official” fallacy since he gave it a Latin name lol: Possibiliter ergo probabiliter.

This can be added to the list of fallacies that can be analyzed by Bayes’.

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Posted by on March 23, 2012 in Bayes


Was Paul Against Homosexuals?

The passage which is quoted that shows that the New Testament is hostile to homosexuals is 1 Corinthians 6.9. This reads as follows:
"Or do you not know that wrongdoers will not inherit the kingdom of God? Do not be deceived: Neither the sexually immoral nor idolaters nor adulterers nor men who have sex with men."
Get that context: Men who sleep with men are "wrongdoers"! A note in the New International Version reads "The words men who have sex with men translate two Greek words that refer to the passive and active participants in homosexual acts". The Wescott-Hort version of this reads:
"ἢ οὐκ οἴδατε ὅτι ἄδικοι θεοῦ βασιλείαν οὐ κληρονομήσουσιν; Μὴ πλανᾶσθε: οὔτε πόρνοι οὔτε εἰδωλολάτραι οὔτε μοιχοὶ οὔτε μαλακοὶ οὔτε ἀρσενοκοῖται"
The words that I underlined — ουτε μαλακοι ουτε αρσενοκοιται::oute malakoi oute arsenokoitai — literally mean "nor the soft (μαλακοι) nor men who lie with men (αρσενοκοιται)". The only other two times that the word "soft" occurs in the NT is at Luke 7.25 (But what did you go out to see? A man clothed in soft clothing [ἄνθρωπον ἐν μαλακοῖς ἱματίοις ἠμφιεσμένον]? Behold, those who are gorgeously dressed, and live delicately, are in kings' courts.) and the Synoptic parallel Matt 11.8 (But what did you go out to see? A man in soft clothing [ἐν μαλακοῖς ἠμφιεσμένον]? Behold, those who wear soft clothing (τὰ μαλακὰ) are in king's houses).
But there's a bit of an oddity here. At least, how it seems to me. It just so happens that μαλακός (malakos) sounds a bit familiar to, uh, μαλακία (malakia) which means to be a person who pleases themselves. The Synoptic evolution between Matt and Luke using this phrase might give it away. Why would Luke reinterpret Matt's people who wear soft clothing living in kings' houses to people who are gorgeously dressed and live delicately in kings courts? Was Luke comparing John the Baptist (who was wearing "soft clothing") which is a "good" thing, to people who live in the king's court, who are ostensibly better off than people living in the wilderness? Does this mean that Matt originally had a pun between soft and masturbate? As in, people who wear soft clothing compared to people who are self-gratifying?
So "the soft" is in male plural form so it probably implies "sissies" or "weak men" who are on the, uh, receiving end of the men who lie with men. On the other hand, Paul might be talking about people who masturbate instead of "soft" men. But the last word that Paul uses – αρσενοκοιται – most definitely means men who sleep with men.
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Posted by on March 23, 2012 in early Christianity, paul


Richard Carrier Takes On Bart Ehrman

Richard Carrier has posted on his blog a response to Bart Ehrman’s article over at the Huffington Post discussing Jesus Mythicism. Here is an excerpt from Ehrman’s peice:

With respect to Jesus, we have numerous, independent accounts of his life in the sources lying behind the Gospels (and the writings of Paul) — sources that originated in Jesus’ native tongue Aramaic and that can be dated to within just a year or two of his life (before the religion moved to convert pagans in droves). Historical sources like that are pretty astounding for an ancient figure of any kind.

I couldn’t believe when Ehrman said this, because it’s simply not true. We don’t have multiple “independent” accounts of Jesus’ life; all accounts of Jesus’ life comes from one context: Early Christianity. And none of the gospels are independent because they all derive from Mark in some fashion, and Paul is useless for recovering the historical Jesus.

And then there is a problem with appealing to hypothetical documents behind prima facie sources. It would be fine if the hypothetical source had 100% certainty of existence, but anything less than that drags down the probability of any hypothesis that depends on the hypothetical. That’s why it’s called hypothetical. There’s a chain: Probability that Jesus exists * probability of the hypothetical source * probability of the main source. If the prior probability of Jesus’ existence was unknown, say 50%, and the hypothetical source had a probability of 80%, then this drags down Jesus’ probability of existing to 50% * 80% = 40%. The more hypothetical sources you add to that chain, the less probable Jesus becomes (which is why we need something like Bayes’ theorem to have a responsible way of adding hypothetical sources along with their probability of existence).

Anyway, this is a snippet of Carrier’s response:

He actually says we have such sources. We do not. That is simply a plain, straight-up falsehood. I can only suppose he means Q or some hypothesized sources behind the creedal statements in Paul or the sermons in Acts, but none of those sources exist, and are purely hypothetical. In fact, barely more than conjectural. There is serious debate in the academic community as to whether Q even existed; and even among those who believe it did, there is serious debate about whether it comes from Aramaic or in fact Greek sources or whether it’s one source or several or whether it even goes back to Jesus at all. The background to the creeds and sermons are even more conjectural (the creeds might go back to Aramaic sources, but none attest to a historical Jesus in the required sense of the term; and the sermons almost certainly do not go back to Aramaic sources, but are literary constructions of the author of Acts, writing in a Semitized Greek heavily influenced by the Septuagint

Don’t be too alarmed of a falling out. At least hopefully. Carrier has glowing praises of Ehrman’s other works. But…

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Posted by on March 22, 2012 in jesus myth


Moving Beyond Logical Fallacies

So I have an entire web page dedicated to describing logical fallacies that I encounter(ed) a lot when arguing with people on the web. In the course of learning Bayes’ Theorem, and knowing that valid math should be applicable to valid logic, I’ve been thinking of ways to apply Bayes’ to logical arguments. Due to Bayes’, we already know why extraordinary claims require extraordinary evidence, why the Prosecutor’s Fallacy is a fallacy, why something that equally explains everything in reality explains nothing, and that — contrary to its oft-repeated negation —  absence of evidence could be evidence of absence.

Just to go over these implications and fallacies of Bayesian reasoning quickly, here are their examples.

Extraordinary Claims Require Extraordinary Evidence

What does it mean when we say that some claim is extraordinary? It means that it is out of the ordinary, or not very mundane. In other words, and extraordinary claim is any claim that has a low probability of being true. So if the existence of god is ordinary, it would be a high probability claim. If the existence of god is extraordinary, then it would be a low probability claim.

Let’s take an extraordinary claim, like aliens abducted me and that’s the reason why I didn’t go to work yesterday. We would need some extraordinary — that is low probability — evidence to corroborate it. Simply missing a day of work is not improbable. Walking into work the next day with some super awesome alien technology is very improbable; it doesn’t happen every day.

So our Bayes’ formula is this: P(H | E) = P(E | H) * P(H) / P(E). P(H) is the extraordinary (i.e. low probability) claim. P(E) would be the evidence. If P(H) is close to or equal to P(E), then they will cancel each other out and the remainder will be P(E | H). If P(E) is nowhere near P(H), then they will not cancel each other out and the Bayesian update might be closer to P(H)’s original improbability.

Let’s say the probability of getting abducted by aliens is .1%, and the probability of missing work given that I was abducted by aliens is 99%. What is the probability of missing work period? Or, how many people missed work yesterday? This is a much, much higher number than .1%. Maybe 10% of the entire population decided not to go to work yesterday for various other mundane reasons. This, in turn, only updates our prior from .1% to .99%.

On the other hand, let’s say that there is a .1% probability of getting a super awesome alien weapon. Given that I was abducted by aliens, there would also be a high probability of getting the weapon just like there would be a high probability of me missing work. This in turn updates the prior from .1% to around 99%. The .1% in the numerator is canceled out by the .1% in the denominator and we are left with the conditional probability being equal to the posterior probability.

And that’s why extraordinary claims require extraordinary evidence.

Prosecutor’s Fallacy

Ok, let’s say that we have our extraordinary evidence. Does this mean that we have free reign to posit any extraordinary claim? If the claim is too extraordinary then this renders it null and void; the newly posited claim can’t be too out of left field or it will make the evidence relatively high probability.

Let’s say that you were driving along one day and started getting lost in your thoughts. You get so distracted by your thoughts you wander off the road getting into a minor accident. It just so happens that a mile down the road there is a huge pileup, one that you would have been invovled in had you not wandered off the road. “Aliens used space technology to invade my thoughts to prevent me from getting in the pileup!” you say.

Avoiding a pileup in this fashion is highly unlikely. So given that aliens did invade your thoughts, it would make sense of the evidence. Yet how much more unlikely is it that aliens would interfere in your life in this way? It’s got to be a few orders of magnitude more improbable than avoiding a pileup like this. Focusing on the conditional (i.e. given that X is true accounts for Y) while ignoring the low prior probability is a Prosecutor’s Fallacy (or Base Rate Fallacy).

Looking at the simple formula for Bayes’ P(E | H) * P(H) / P(E) you can see what happens if P(H) is zero or near zero. So it doesn’t matter how high P(E | H) is, and ignoring the prior in this case would be a Prosecutor’s Fallacy.

Something That Equally Explains Everything Explains Nothing

Let’s say you get diagnosed with some extremely deadly cancer. You go to the doctor and he says “Out of the 1 million people diagnosed with this cancer in the past 50 years, only one has lived past 6 months after diagnosis at this stage.”. You look on the Internet and find out that there are only 10 people on the entire planet right now with your cancer.

One year later you are still alive, the other 9 people are dead. “Praise the aliens!” you say. “They kept me alive even though those other people died. They are so benevolent, and my survival is evidence of their beneficience!”. You go to a friend of yours with your revelation, and she asks “But what about the other 9 people who died?”. You reply “That is also evidence of the aliens’ benevolence, because they ended their suffering!”

Barring the arrogance displayed, is there something wrong with this reasoning? Besides the previous fallacies? Sure, given that the aliens are good beings you would survive one year with the cancer. This would be P(Surviving Cancer | Good Aliens). But what about the compliment, P(Not Surviving Cancer | Good Aliens)? If one asserts a high probability of surviving cancer given the goodness of the aliens, and in turn then asserts a high probability of not surviving the cancer (i.e. 9 out of 10 people died in this scenario) given the goodness of the aliens, this leads to a contradiction in probability terms. Because P(Surviving Cancer | Good Aliens) + P(Not Surviving Cancer | Good Aliens) = 1.00. If P(Surviving Cancer | Good Aliens) is .99, this necessitates that P(Not Surviving Cancer | Good Aliens) is 1.00 – .99, or .01.

If the probability of both conditionals is equal, then one cannot be more than .5. And this is only with binary evidence. If there are multiple possible exclusive outcomes that all evidence the goodness of the aliens, then this further diminishes the conditional probability if you assert that they are all equally likely. If there are 1,000 mutually exclusive instances (i.e. “exclusive” meaning examples like you can’t both live and die at the same time, be married and a bachelor at the same time, be in NYC, Tokyo, Afhanistan, and London all at the same time, etc.) that all have the same conditional probability, the conditional probability can only be 1 / 1000.

Absence of Evidence is Evidence of Absence

According to the standard definition of “evidence”, this is any event or fact that supports some hypothesis. In Bayesian terms, this means any fact or event that increases the prior probability of some hypothesis, whether weak or strong. So if P(H | E) > P(H), this should mean that P(H | ~E) < P(H). So with the alien abduction example, if I had some super awesome alien weapon this would corroborate my alien abduction:

P(Alien Abduction | Alien Weapon) = P(Alien Weapon | Alien Abduction) * P(Alien Abduction) / P(Alien Weapon)
= .99 * .01 / .01
= .99

If I didn’t have some super awesome alien weapon, or absence of evidence, it would look like this:

P(Alien Abduction | No Alien Weapon) = P(No Alien Weapon | Alien Abduction) * P(Alien Abduction) / P(No Alien Weapon)
= .01 * .01 / .99
= .0001 / .99
= .000101

Remember the compliments: P(E) + P(~E) = 1.00. P(E | H) + P(~E | H) = 1.00.

Or, P(Alien Weapon) + P(No Alien Weapon) = 1.00.
P(Alien Weapon | Alien Abduction) + P(No Alien Weapon | Alien Abduction) = 1.00.

So if P(Alien Weapon | Alien Abduction) is .99, this means that P(No Alien Weapon | Alien Abduction) = 1.00 – .99. This then creates our Bayes’ Theorem for absense of evidence:


P(H | ~E) = P(~E | H) * P(H) / P(~E).

So if you want to prove that absense of evidence either does or does not mean evidence of absense, just use that formula. Absense of evidence only means evidence of absense if the presence of evidence is evidence of presence.

In this alien abduction example, the prior moved down from .01 to .000101 due to the absence of evidence.


But it looks like I’m already late to the game. People have already attempted to apply Bayes’ to logical arguments and fallacies: Fallacies as Weak Bayesian Evidence. Look at the Argument from Ignorance:

1. Prior beliefs influence whether or not the argument is accepted.

A) I’ve often drunk alcohol, and never gotten drunk. Therefore alcohol doesn’t cause intoxication.

B) I’ve often taken Acme Flu Medicine, and never gotten any side effects. Therefore Acme Flu Medicine doesn’t cause any side effects.

Both of these are examples of the argument from ignorance, and both seem fallacious. But B seems much more compelling than A, since we know that alcohol causes intoxication, while we also know that not all kinds of medicine have side effects.

2. The more evidence found that is compatible with the conclusions of these arguments, the more acceptable they seem to be.

C) Acme Flu Medicine is not toxic because no toxic effects were observed in 50 tests.

D) Acme Flu Medicine is not toxic because no toxic effects were observed in 1 test.

C seems more compelling than D.

3. Negative arguments are acceptable, but they are generally less acceptable than positive arguments.

E) Acme Flu Medicine is toxic because a toxic effect was observed (positive argument)

F) Acme Flu Medicine is not toxic because no toxic effect was observed (negative argument, the argument from ignorance)

Argument E seems more convincing than argument F, but F is somewhat convincing as well.

The Argument from Ignorance is just another version of the Absence of Evidence argument. Absence might be strong or weak evidence, but it’s still evidence if it moves the prior in any direction. This is different than “I don’t know how things work, therefore aliens” argument, which should be renamed to the Bill O’Reilly Fallacy.

So the Argument from Ignorance is weak evidence, since we aren’t taking into account both the success rate and the false positive rate. It’s incomplete Bayesian reasoning, but it’s not inherently fallacious. It might be fallacious or it might not be fallacious.

How about circular reasoning?

A. God exists because the Bible says so, and the Bible is the word of God.

B. Electrons exist because we can see 3-cm tracks in a cloud chamber, and 3-cm tracks in cloud chambers are signatures of electrons.


The “circular” claim reverses the direction of the inference. We have sense data, which we would expect to see if the ambiguous interpretation was correct, and we would expect the interpretation to be correct if the hypothesis were true. Therefore it’s more likely that the hypothesis is true. Is this allowed? Yes! Take for example the inference “if there are dark clouds in the sky, then it will rain, in which case the grass will be wet”. The reverse inference, “the grass is wet, therefore it has rained, therefore there have been dark clouds in the sky” is valid. However, the inference “the grass is wet, therefore the sprinkler has been on, thefore there is a sprinkler near this grass” may also be a valid inference. The grass being wet is evidence for both the presence of dark clouds and for a sprinkler having been on. Which hypothesis do we judge to be more likely? That depends on our prior beliefs about the hypotheses, as well as the strengths of the causal links (e.g. “if there are dark clouds, how likely is it that it rains?”, and vice versa).

Thus, the “circular” arguments given above are actually valid Bayesian inferences. But there is a reason that we consider A to be a fallacy, while B sounds valid. Since the intepretation (the Bible is the word of God, 3-cm tracks are signatures of electrons) logically requires the hypothesis, the probability of the interpretation cannot be higher than the probability of the hypothesis. If we assign the existence of God a very low prior belief, then we must also assign a very low prior belief to the interpretation of the Bible as the word of God. In that case, seeing the Bible will not do much to elevate our belief in the claim that God exists, if there are more likely hypotheses to be found.

So it looks like some fallacies might actually not be fallacies. It could be the amount of confidence we place in the logic that is the fallacious reasoning. So for absence of evidence being evidence of absence, it’s not necessarily a fallacy. It could be that the lack of evidence only diminishes the prior probability by .1%. The problem would come about by relying only on the absence to prove a point, when a difference of .1% isn’t much to write home about.

Since probability is a form of induction, it might be that all fallacies of induction could be expressed using Bayes’ theorem. Here is a longer version of the post.

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Disrupting Dinner Parties

Feminism is for everyone!

My ὑπομνήματα about religion

The New Oxonian

Religion and Culture for the Intellectually Impatient

The Musings of Thomas Verenna

A Biblioblog about imitation, the Biblical Narratives, and the figure of Jesus

The Syncretic Soubrette

Snarky musings from an everyday woman