Creationist Math

A common misconception is that evolution relies entirely on chance. For example, I once read part of a science textbook intended for homeschooling parents that included this analogy:

Imagine a yard containing all of the parts of a working computer that has been disassembled and the parts have been strewn all over the yard. How likely does it seem that a tornado could blow through the yard and randomly reassemble the parts to once again form a working computer?

This is an attempt to update the old Boeing 747 analogy from Fred Hoyle. He was attempting to illustrate the improbability of certain elements of life originating by chance.

Since such abuses of probability estimation seem to thrive still today, particularly in forums that are dominated by amateur commentators (I’m talking about you, Facebook), I thought it might be worthwhile to discuss a one of the many problems with analogies like this.

The modern theory of evolution—or you may hear it referred to as the modern synthesis—does not suggest that evolutionary events are the products of mere chance. While chance is a factor, such as in random mutations, it is not the only one. Consider 10 types of birds living on an island with 10 different beak shapes. Let’s suppose the available food source for these birds is only reachable by one of the beak shapes (perhaps it’s in a narrow hole or something). A naïve treatment of the probability of survival here would assign equal weight to every type of bird. However, we should easily recognize that survival is not random here. It will specifically favor the bird type that is able to reach the food source. So, there is a non-random factor at work. Specifically, reaching the food is needed for reproduction and survival and not all bird types can reach the food. An entirely natural process is performing selection.

Let’s also look at an example that does not involve living things. If you’re on a rocky beach, you might notice the distribution of rocks and pebbles has a specific pattern. Rocks will be sorted according to their size. There will be fairly uniform layers running parallel to the water. Let’s approach the problem like a creationist and see how we incorrectly determine the probability by thinking it’s random. To keep it simple, we’ll assume a small sample space of 16 rocks. Each letter group means the rocks are roughly the same size.

If I were to randomly pull rocks out of a bag and place them into the 16 squares, I calculate the chance as only 0.0000000159 that this pattern would appear. This is being pretty generous in that we have only 16 squares to fill and any of the A rocks can be in the first row, B rocks in the second row, etc. Even given these concessions, random chance is an unlikely explanation. So, should we conclude that there must have been intelligent involvement? Of course not. We know there are natural processes selecting for rock placement just as natural processes select for survival.

Any argument that calculates a probability based on random chance alone ignores this known feature, thus, is arguing against a straw man.

Extraordinary Claims Really Do Require Extraordinary Evidence

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) ]

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.

• P = 0.01 x .9 / (0.01 x .9) + (0.99 x .75) = 1.2%

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.

• P = 0.01 x .9 / (0.01 x .9) + (0.99 x .50) = 1.8%
• P = 0.01 x .9 / (0.01 x .9) + (0.99 x .25) = 3.5%
• P = 0.01 x .9 / (0.01 x .9) + (0.99 x .10) = 8.3%
• P = 0.01 x .9 / (0.01 x .9) + (0.99 x .01) = 48%

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.

The Lazy Person’s Guide to Dismantling the Moral Argument

I once was part of a comment thread where theists were asked what their favorite arguments in favor of God’s existence were[i]. The argument that seemed to stand above the rest by my informal count was the so-called Moral Argument. If you’re not familiar with this argument, it goes as follows:

1. If God does not exist, then objective moral values do not exist.

2. Objective moral values do exist.

3. Therefore, God exists.

Many are inclined to object to (1) on the basis of some secular theory providing an objective grounding for morality. I have done this in the past by appealing to contractualism. However, this turns complex very quickly and it’s notoriously difficult to gain agreement. I think there is a better way to dismiss the argument. By disputing (2), we can show that the argument does not actually give us reason to conclude anything. In fact, we can do this very simply as follows:

4. The justification for (2) is that everyone has an experience of morality.

5. Either this experience can be explained in natural terms or it cannot.

6. This experience can be explained in natural terms.

7. Therefore, natural explanations are sufficient to account for (2).

Basically, we are left with these possible scenarios, if a successful natural explanation can be given:

S1: The natural explanation is true and is sufficient to ground objective moral values

S2: The natural explanation is true, but is describing something that does not ground objective moral values

Under the first scenario, we affirm (2) and reject (1). Under the second scenario, we reject (2). Either way, the premises of the initial moral argument fail to support its conclusion. Since either scenario accomplishes this, we can forget about (1) altogether! All you have to do is support (6) by saying that our experience of morality can be explained naturally. This sidesteps the very thorny issues of metaethics[ii].

So, is (6) well supported by scientific literature? I think so. Two popular-level examples that come to mind are Marc Hauser’s Moral Minds: The Nature of Right and Wrong (P.S.) and Michael Shermer’s The Science of Good and Evil: Why People Cheat, Gossip, Care, Share, and Follow the Golden Rule. These tell an evolutionary story about morality, which I think is probably on the right track. You might even prefer a simpler argument that our experience is just a ‘gut’ reaction to things we find pleasurable, distasteful, etc. I can see a compelling argument being made with that approach too.

Thus, we have a very simple dismissal of many theists’ favorite argument.

Free Will and a Hidden God

One of my favorite arguments in favor of reasonable non-belief is called the argument from divine hiddenness. It goes roughly as follows:

1. There is a personal (relationship-seeking) and perfectly loving God.

2. There are people capable of having a relationship with this God.

3. A perfectly loving God would not act to hinder this relationship.

4. Belief in God is a necessary condition for a person to enter into this relationship.

5. Creatures capable of this relationship that do not resist God will always have this belief.

6. Yet, there exists reasonable non-belief.

Basically, if there are reasonable non-believers, then there is not sufficient evidence for belief. If there is not sufficient evidence for belief, then there is not a relationship-seeking, perfectly loving God.

The most popular response I’ve heard is that God presenting obvious evidence that he exists would restrict our ability to make morally significant free choices. Somehow if I knew God were real, then I would basically be forced to do good.

This quickly results in absurdity. Many Christians, for example, claim to have great confidence in God’s existence and yet apparently don’t think their freedom is hindered. The disciples were with God every day performing wonderous deeds and they are revered - certainly we wouldn’t say they didn’t make morally significant choices. Adam and Eve walked with God in the garden and still made a free choice. Or how about Moses, Noah, David, and even Satan? Did none of these people make free choices?

If these people were able to make morally significant free choices, despite having immediate knowledge of God’s existence and power, then the objection fails.

The Problem of Heaven

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.

Atheism and Evil: Part 2

In Part 1, you hopefully saw that atheism does not need to have an account of objective morality in order to present the problem of evil. But we were still left with a major question of whether secular morality even makes sense. To counter this claim, we will want to ensure a solution that provides the following, at a minimum:

• Internal coherence
• Moral realism
• Objectivity

Can secular morality be coherent?

To say that a worldview is coherent is to say that it agrees with itself internally. For example, imagine an atheist who prays every night. Those two things (being an atheist and praying) would not form a coherent worldview. So, what we want to do here is discover whether it’s coherent for an atheist to say something is really wrong without presupposing a god or co-opting theistic morality.

What is moral realism?

Moral realism simply means that you think moral claims describe objectively true or false propositions about the world. Morality is about reasons for intentional action. For the theist, their reason for acting a certain way is because it is commanded or desired by God. So their form of realism says that moral claims can accurately describe true propositions about what God commands. For the atheist, we will see that we can also provide reasons for action, which can be described as objectively true or false propositions.

What is objective?

You will find many uses of the term objective. William Lane Craig often describes objective as meaning: it’s true whether or not anyone believes that it’s true. In other words, if Germany had won WWII and brainwashed everyone to forget what happened, their actions would still be wrong.

Some will say objective means necessary, but this has never been demonstrated to my satisfaction and it is not entailed by Craig’s description. I think we can avoid, then, reference to absolutes or necessity. For example, there is an objective answer to this question: “How far is the tip of the Empire State Building from the tip of Olympus Mons at time t?” This relationship between the points is contingent (not necessary), but also has an objectively true answer. Whether or not anyone knows the distance between the two points, there is a fact of the matter. Similarly, I see no reason to tie objective morality with absolutes. It may be the case that every time you have two related things you will have the same outcome, but there is no requirement for it. If we can show that our moral statements can be tied to facts, like the example above, then I’d say we have something objective and we can form propositions to describe, as required by moral realism.

Continue reading…

Atheism and Evil: Part 1

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…