If you haven’t caught sight of this video yet, it’s well worth the hour and a half: Stephen Colbert, out of character, interviewing Neil deGrasse Tyson with intelligent questions on the nature of science.
Neil deGrasse Tyson also gave An American Atheist the pleasure of an interview some months back as well.
Yes, it’s still true. The basic principles of mathematics and probability have not changed. Thus, it is surprising to read an article saying that requiring extraordinary evidence for extraordinary claims doesn’t make sense. At least, it’s surprising until you realize the person making the claim is probably an evangelical Christian with an extraordinary claim to promote. So, how should we respond? I’ll provide a short answer and a long answer.
The Short Answer
Bayes’ Theorem, which has been proven to be formally valid, tells us that extraordinary claims (things with very low prior probabilities) do indeed require extraordinary evidence. For example, imagine my friend tells me he won the World Series of Poker. I would first be struck by the improbability of such a claim considering the Main Event has over 6,000 entrants and this particular friend isn’t that good at poker. Even so, it’s not impossible and there is evidence which would overcome that initially low probability. Examples of significant probability-raising evidence would include if he had millions of dollars suddenly and if he had a WSOP bracelet. If you want to see this idea demonstrated mathematically, keep reading.
The Long Answer
This is Bayes’ Theorem:
P(h|e.b) = P(h|b) x P(e|h.b) / [ P(h|b) x P(e|h.b) ] + [ P(~h|b) x P(e|~h.b) ]
| Symbol | Meaning |
| P | Probability |
| H | Hypothesis |
| E | Evidence |
| B | Background Knowledge |
| | | Given |
| ~ | Not (or the negation of) |
| . | And |
In English, this says, “The probability that a hypothesis is true, given available evidence and background knowledge is equal to [and then you have the equation].” To understand the equation, let’s dig into the details just a bit.
The first term you’ll notice once you read past the = symbol is P(h|b); this is the prior probability. This term is concerned with the probability that a hypothesis is true given your background knowledge. So, when we say that the virgin birth has an incredibly low prior probability, that means that based on everything we know about the world through science, history, etc. this sort of thing doesn’t generally happen. Quite simply, we understand how babies are made, and this isn’t it. Further, in cases where parthenogenesis does actually occur in other animals, the resulting offspring are always female. So, if true, this would seem to be a one-time thing. I have no idea how many humans have ever existed, but let’s say there have been 100 billion. This would make the prior probability 1/100,000,000,000. Note that this is prior to considering any evidence for the case in question, hence the term prior probability.
The second term above is P(e|h.b), meaning the probability that you would have the available evidence given your hypothesis and background knowledge. In other words, would the available evidence be expected under the hypothesis? For example, say someone claims they’ve been to the beach for the past few hours. You notice they are sunburned and in their car is a beach towel. These things fit the claim well and would merit a high number. On the other hand, the lack of sun kissed skin and a movie ticket stub from two hours earlier would not be the sort of evidence you would expect.
This covers the numerator. It is the prior probability multiplied by the likelihood of the evidence.
Now, as you keep moving from left to right, you’ll notice that the first term in the denominator is the entire numerator repeated. That’s why the theorem is sometimes shortened to P = A / A + B. So, what is B? It is basically the same as discussed above, only for ~H, rather than H. It is the probability that your hypothesis is false and the likelihood of the available evidence given a false hypothesis. The number to plug in for ~H should be pretty simple, as it’s just 1 - H = ~H. For example, if we were talking about rolling a die, the probability of rolling a six in 1/6 and the probability of not rolling a six is 5/6. It just fills out the remaining possibilities. In every case, H + ~H should equal 1.
Let’s plug in some numbers using a very low prior probability and see the earlier claim in action.
Here we see a low probability event where the evidence is almost nearly as well explained by negating hypotheses and the probability is slightly raised, but remains very low. Now, let’s slowly decrease the likelihood that the evidence can be explained by alternative hypotheses and watch what happens to the outcome.
We don’t see a substantial increase in probability until we get into very low ranges of likelihood for the same evidence to be observed on alternative hypotheses. In the last example, there is only a 1% chance that the evidence can be explained by alternative hypotheses. In cases of low prior probability, the evidence must be such that it basically rules out alternative hypotheses to a very high degree.
In other words, extraordinary claims really do require extraordinary evidence.
Preface: The below post is inspired by a course on Nietzsche I am currently the teaching assistant for; however, Nietzsche has always been my favorite philosopher. The reasons why, however, are complex – no, I don’t agree with everything he says, far from it – and wonderfully, Nietzsche actually presents a great challenge to us in the atheist and skeptical movements; an opportunity to think in the most critical ways possible about why we care about these issues at all.
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God is dead, Nietzsche famously wrote. Based on these three words, one might assume that Nietzsche would be an atheist’s best friend. Think again.
Nietzsche was, of course, himself an atheist, if we are simply talking about whether or not he believed in God. But he harshly criticized the group of people he labeled “atheists,” along with scientists and rational skeptics. Why? If we are going to understand that, we first have to understand Nietzsche’s critique of Christianity.
Personally, my favorite picture of Friedrich. But I won't try to universalize that preference.
Nietzsche believed that Christianity grew out of the resentment, or ressentiment, of the weak in society – hence his famous phrase, “slave morality.” The genius of Christianity, according to Nietzsche, is its ability to take the will to power – which simply means the universal urge of man to express his spirit and impress himself upon the world – and turn it against itself. The values of Christianity, as captured in the Sermon on the Mount, celebrate humility and weakness – they argue, in other words, that the weak is good and the strong is bad. Moreover, Nietzsche argues, the priests of Christianity took the suffering of the masses and explained to them that they themselves were responsible for this suffering – the doctrine of original sin, obviously, clearly says as much. Moreover, not only does Christianity preach a worthlessness of human beings and consequently, the worthlessness of the earthly world itself, but it posits a self-sacrificing God (in the form of Jesus) that had to suffer and die for all these worthless human beings – thus, the doctrine of the crucifixion, rather than alleviating any guilt believers may suffer from, only increases it by adding to the heavy burden of debt we all owe to God. The consequence has been hundreds of years of scrupulous self-denial and the shaming of all our noble, passionate instincts – the will to power turned in wretched self-loathing against itself.
So this all sounds rather unpleasant, and I think it is in this highly psychological analysis of Christianity that some of the most brilliant (and accurate) insights of Nietzsche can be found. But why, then, would Nietzsche be critical towards atheists, scientists, and skeptics? Wouldn’t he see their focus on the physical, real world, and their rigorous skepticism of Christian theology as freeing, as liberating? Why in the world would he actually posit the opposite - that atheism and science, rather than being a way out of Christianity, are actually the product of Christian values - indeed, are Christian values in their most refined form?
Rank these possible ways to exist in order of preference:
1. People have free will and no evil exists
2. People have free will and some evil exists
3. People do not have free will and no evil exists
There is some debate about whether the second or third option is better, but clearly the vast majority of people would prefer the first option. It’s not even close, right? You have your cake (free will) and eat it too (eliminate evil). So, it seems fair to say that option (1) is objectively better than options (2) or (3).
According to most forms of Christianity, our world is best described by (2), but option (1) actually exists too—it’s called Heaven. Ironically, we’ll see that the existence of Heaven actually entails some serious problems for traditional Christian theism. Let’s explore these problems by asking a question.
What would the greatest possible being do?
God is often called the greatest possible being, dating back to St. Anselm of Canterbury. Whatever we take this to mean, I think one assumption is clearly justified: When given two or more options, the greatest possible being will necessarily take the best option available. Imagine a being that has two options. She can either cure every form of cancer or put a band-aid on a child’s skinned knee, but not both. Which action will be taken by the greatest possible being? Obviously she would cure cancer. This is a no brainer, right? Even though both actions would result in some amount of good, there is a clear candidate for which is the better action.
Now let’s consider the choices God had when creating the world. Does our own world represent the best choice among available options? If you’ve ever suggested to a theist that God could have eliminated evil when creating the world, you’ve probably heard something like, “Evil is a necessary byproduct of freedom.” This is a contrast between (2) and (3) and saying (2) is morally preferable. Notice the problem? They are ignoring (1), which they cannot deny is a realistic option because they actually believe it exists. So, the problem that God could have created a world with both free will and the absence of evil still stands. This means God did not perform the best action available.
Conclusion
If Heaven exists (or is a realistic option), then that means God is not the greatest possible being. We have reached a classic reductio ad absurdum where two commonly held Christian beliefs actually contradict each other, showing that either one or both is false.
Over the past weekend, an alliance of apologetics bloggers decided to tackle the problem of evil and suffering.
These were specifically timed to coincide with the anniversary of 9/11; you can find a list of these articles here. I had hoped this group would provide something other than the normal amateurish turnabout: “You can’t say something is evil, because you’re an atheist.” I was wrong.
In fairness, I didn’t read all of the articles, but those that I did read focused a considerable portion of their writing on this point.
As an atheist who deals quite a bit with ethical philosophy, statements like these are aggravating. So, I’d like to address two things about this attack on atheism. In my first post, I will show that the point is irrelevant to the problem of evil and suffering. In my second post, I hope to show the point is wrong, and atheists can use moral terms coherently. Continue reading…
Origin of Christianity is a French film released in 2003. Bringing together top Biblical scholars from all over the world, it explores the formation of Christianity from the time of Jesus to a few centuries after his death. Because it treats the birth of Christianity as a historical, rather than a theological event, it caused a decent amount of controversy even in fairly secular France. But it is without doubt the best documentary, on any topic, I have ever seen.
I should warn you that the things that make Origin of Christianity so great to a history nerd like me might make it mind-numbingly boring to you. It is not like most documentaries – there are no reenactments, and it lacks even the presentation of paintings and landscapes which, in most documentaries, the camera slowly zooms into or out of during narration. Rather, it consists of hours of listening to top scholars discuss chapters of early Christian history, all of them in front of a blank black background. The only visuals we get are of ancient church manuscripts, although these are coupled with the delightful background noises of libraries and archives. In other words, you need to be rather interested in early Christian history to find this film engaging. You have been warned.
But if you want to learn about the early church, watching all ten episodes of this film is probably the easiest way you could possibly do so. The topics selected are of central importance to Christian doctrine and the subsequent unfolding of Christian history. The scholars are engaging, articulate, and diverse in their opinions. Indeed one of the great things about the film is that it displays the process of historical inquiry and debate – while there is general consensus per episode on important points, there are some issues where conflicting viewpoints of various scholars are explicitly contrasted to one another. Thus Christianity is treated not only as a matter of historical – as opposed to theological – interpretation, but as a matter of historical interpretation which, on many points, allows no one to be completely, comfortably sure they have discerned the complete truth.[1]
Ok that might be stretching it a bit. But as I recently rewatched Kenneth Branagh’s Hamlet, I realized how rich this play is for contemplating the great unknowns – revelation, death, oh hell life itself – which atheism usually touches on. Indeed, Hamlet is more about asking questions than getting answers – and the play can therefore be a rich experience for someone inclined to lean more towards doubt than certainty.
First, let’s take Hamlet’s famous speech about suicide. In this monologue, Hamlet posits the possibility of hell as the primary reason to abstain from “self-slaughter”[1]– but that hell is considered as a possibility, rather than a certainty, is always clear. Furthermore, Hamlet muses that the possibility of eternal punishment, in preventing individuals from committing suicide, makes “cowards of us all.” This raises the question of free will and whether religion really contributes to free will – as Christians are fond of claiming these days – or obstructs it. And is suicide inherently immoral, or does this depend upon a deity that punishes humans for suicide? In any case, “To be or not to be” is indeed a question in this most famous of soliloquies, and not a dogma.
However Hamlet’s skeptical streak really comes out when he devises a test to ensure that his Uncle did indeed kill his father. The ghost of Hamlet’s father, of course, told Hamlet that he was poisoned by his brother – but Hamlet is worried that the ghost he saw might have been sent by the Devil to trick him into murdering an innocent man.
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