Why Plantinga Needs a Math Lesson on Materialism

In a recent The New York Times interview, philosopher of religion Alvin Plantinga goes through an involved discussion about how evolution doesn't guarantee that our beliefs are true. This is absolutely a valid concern ... and, in fact, I know of no atheist who doesn't recognize the fallibility of our inherent beliefs and thought processes. In fact, some of the strongest arguments in favor of a rejection of theism is based on the psychological account of why people embrace theism. This YouTube series on the Psychology of Belief lays it out quite well.



So, we'll grant that we are not granted inherently true knowledge by evolution. His argument is that if you believe in both materialism (that is the viewpoint that there exists nothing that doesn't have a physical basis) and evolution, then you have to admit that you have no good reason for believing that any belief you hold is true. There's an extremely extensive dissection of the various flaws over on the Rationally Speaking blog, from Massimo Pigliucci, who has a deeper background in biology and philosophy both than I and quickly dissects the key conceptual problem with the argument.

But I'd like to take a different tactic, to really try to give Plantinga's argument enough rope to hang itself, because I just don't think it holds up on any level on its own merits. The problem is not that Plantinga misunderstands evolution, but rather that he appears to misunderstand how human beings (and materialists in particular) actually think!

Plantinga's Death Knell to Materialism

Let's consider his argument on its own merit, at least to the best of my ability. In his own words:

Evolution will select for belief-producing processes that produce beliefs with adaptive neurophysiological properties, but not for belief-producing processes that produce true beliefs. Given materialism and evolution, any particular belief is as likely to be false as true.

...

Here’s why. If a belief is as likely to be false as to be true, we’d have to say the probability that any particular belief is true is about 50 percent. Now suppose we had a total of 100 independent beliefs (of course, we have many more). Remember that the probability that all of a group of beliefs are true is the multiplication of all their individual probabilities. Even if we set a fairly low bar for reliability — say, that at least two-thirds (67 percent) of our beliefs are true — our overall reliability, given materialism and evolution, is exceedingly low: something like .0004. So if you accept both materialism and evolution, you have good reason to believe that your belief-producing faculties are not reliable.

But to believe that is to fall into a total skepticism, which leaves you with no reason to accept any of your beliefs (including your beliefs in materialism and evolution!). The only sensible course is to give up the claim leading to this conclusion: that both materialism and evolution are true. Maybe you can hold one or the other, but not both.

So if you’re an atheist simply because you accept materialism, maintaining your atheism means you have to give up your belief that evolution is true. Another way to put it: The belief that both materialism and evolution are true is self-refuting. It shoots itself in the foot. Therefore it can’t rationally be held.

The starting point is the valid recognition that evolution results in useful, adaptive traits rather than factually true beliefs. No argument there.

His next step is interesting. He is quite generous in assuming that perhaps 67% of our beliefs are, in fact, true, based on processes that were not optimized for truth-seeking. Using this, he then says if we have 100 beliefs (and we have many more), then we arrive at a very low overall probability of 0.004. The calculation is actually much worse than Plantinga suggests:

0.67¹⁰⁰ = 0.0000000000000000405%

That's 16 zeroes between the decimal point and the 4.

Now, what does this number actually mean?

It means that if a single individual has 100 beliefs, then the probability (based upon these parameters) is virtually certain that not all of these beliefs will be true.

(It should be noted that the probability that all of these beliefs are false is much worse ... you then end up with 47 zeroes instead of 16. Plantinga, of course, is not arguing that all beliefs are untrue, even assuming materialism and evolution, so let's get back to his argument.)

But for any individual belief, of course, the probability is much higher: 67% according to Plantinga's estimation.

Random Belief Analysis

So let's make an even less generous estimation. Let's assume that we have an exactly 50/50 split between a given belief being true or untrue.

First, let's note that, regardless of your worldview, it's kind of unlikely and troubling to evolution, human reason, or the very concept of truth to assume that there is an absolute lack of correlation between adaptive beliefs and truth. Even a religious fundamentalist would, I think, admit that believing a true thing is going to, on average, be more adaptive than believing a false thing. So this is by far an assumption that gives Plantinga's argument the widest berth that it possibly can to prove its validity.

Second, let's then consider how one can actually approach this problem of having false beliefs. Let's make some initial assumptions that we can start from:

Round One Assumptions:

• 50% of beliefs are true
• 50% of beliefs are false
• Random designation (no systemic biases in favor of or against truth)

A good first-order approach in this case is to check with other people. So we ask someone else, "Do you have this belief?" If they share this belief, there's now a 50% chance that you both have a true belief and a 50% chance that you have a false belief. And, in fact, you'll find in this situation that no amount of checking with other people will ever move the needle from a 50% probability.

Out of curiosity, what happens with Plantinga's model if we begin checking our beliefs with other people. There's a 33% chance that any given person is wrong, so if you check with 5 people, the probability that all 5 would find the same random belief to be wrong would reach the following:

Using Plantinga's model, there is a 0.391% chance that 5 people would hold the same false belief.

So, on this basis, we do see that some sort of internal cognitive bias would quickly multiply in a community to a growing factual consensus, based purely on the sort of crude mathematical argument that Plantinga offers.

But consensus by itself is not really how we check our beliefs, even at the most basic level. We check them against reality. Let's assume though that, since we're so bad at thinking in this scenario, that we are horrible at these checks. There is only a 1% chance that testing any given belief will accurately show a false belief to be false. (Ignoring any possible positive results for now, to make the math easier and also because it's easier to disprove something than to prove it.)

Again, I should note that there is also every reason to believe that this level of instinct is biologically ingrained in us through the process of evolution ... and, honestly, that it's ingrained in most animals on some level. An animal that cannot trust any "beliefs" about the world world with more than random correlation with reality would find themselves falling prey to all manner of natural selection effects. So this most basic level of analysis doesn't take much in the way of assumption beyond what we've already assumed to think that it would be implemented as a way of finding truth and falsehood.

So we implement this method. What happens then?

What we discover is that, if you check a given belief against reality a mere 10 times, and this process shows it to be false every time, then even this admittedly horrible method of distinguishing truth from falsehood results in the following:

Probability a False Belief will Survive Round One: 0.5 * (0.99)¹⁰ = 45%

And, of course, if you begin checking with other people who are also checking these beliefs in the same way, you reach the following:

Probability a False Belief will Survive Round One in a Community of 5 Checking Against Reality: 0.45⁵ = 1.8%

So in a community of 5 people, all of whom check a false belief against reality with a 1% accuracy, there is a 1.8% chance that the false belief would pass all of these checks and look equivalent to a true belief.

Congratulations. The neurologically challenged human race has developed some method of distinguishing true beliefs from false ones. On to round two...

Round Two Assumptions:

• 95% of beliefs are randomly assigned 50/50 between true/false
• 5% of beliefs are biased as follow:
• 10% are true things that we don't believe (false negatives)
• 30% are false things we do believe (false positives)
• 60% are true beliefs

We now move on to considering what happens if we give some credit to evolution to create even marginally reliable belief-forming pathways. Our first round analysis gives us a starting point and, again, I'll give the benefit of the doubt that we're a bit more flawed in our neuropsychology than we really have any excuse for being.

Let's again go with just checking with other people and see what we get:

Probability of Given Belief Being True: 0.95 * 0.5 + 0.05 * 0.6 = 50.5% 

Probability of 5 People Randomly Believing the Same False Thing: 0.495⁵ = 3%

We see that even in this rudimentary situation, there is a strong reason to go with the community consensus from a truth-generating point of view. The randomness and biases tend to get weeded out, even at this level.

Now that we have some cognitive neurology that actually works, we can assume that we're able to develop a plan for testing against reality that does a bit better than 1% at disproving a false belief. Let's assume that it is 10% effective at showing a false belief to be false. What do we then get when we conduct another 10 tests using our improved methodology?

Probability a False Belief will Survive Round Two: 0.495 * (0.90)¹⁰ = 17%

Probability a False Belief will Survive Round Two in a Community of 5 Checking Against Reality: 0.17⁵ = 0.014%

Ideally, we will respond rationally to the above evidence and stop believing these false beliefs. We are able to eliminate 83% of our initial false beliefs! We don't have to replace them with true beliefs, either, if we're okay with uncertainty. (Replacing them with true beliefs would favor the anti-Platinga argument, so this is again giving him the benefit of the doubt.) The result is the following:

Probability of a Given Belief Being True after Round Two (individual testing): 85.7% 

Probability of a Given Belief Being True after Round Two (group testing): 99.98%

I really don't need to go much further, I don't think, to show that the process of checking a belief against physical reality - the very belief that atheists actually demand as a methodological step for knowing anything! - does work at generating true beliefs, even granting it virtually every concession that we can realistically grant.

Conclusion

Plantinga's criticism of materialism/evolution just does not hold up. Recall that he gave an example of 100 beliefs and the probability it would take for them all to be true. Let's compare this to the results from Round Two's extremely crude falsification methods:

Probability 100 random beliefs True using Plantinga's assumptions (individual):
0.0000000000000000405% 

Probability 100 random beliefs True using Plantinga's assumptions (group):
99.8% 

Probability 100 random beliefs True using Round Two falsifiability rules (individual):
0.0000198647083%

Probability 100 random beliefs True using Round Two falsifiability rules (group):
98%

The "group" numbers represent what we get if we eliminate everything that 5 people agree are false, both in Plantinga's evidence-free assumptions and my own evidence-based ones from Round Two.

First of all, we see that testing against the evidence greatly increases the truth percentage of beliefs for an individual, way beyond what Plantinga would give credit for with his original assumptions.

Second, we see that both our overall level of truth greatly increases - in fact become nearly identical for both sets of assumptions - if we work in a group and just begin throwing out anything that we all agree are false beliefs. And this does, in general, match with empirical evidence, because even the most ardent atheist and most devout theist share far more beliefs than they disagree on (though neither might be willing to admit it). (I'll confess, the high value for the Plantinga's group number surprised me. I thought the reliance on evidence would play a more important role in the methodology. However, I did make every assumption overwhelmingly in Plantinga's favor, so I shouldn't be too surprised.)

Third, let me be clear: I think Plantinga is completely flawed in his approach and thinking about how beliefs are formed ... but my point is that even if he were absolutely correct, his argument would not hold up on its own merits. I am not presenting this trying to persuade anyone into materialism because nothing above actually supports materialism in and of itself, it merely supports our ability to gain true beliefs given false beliefs.

Therefore, there is every reason for a materialist evolutionist to, in fact, believe that they have a capacity to trust their beliefs, so long as they rely on evidence and are not trying to acquire knowledge and understanding entirely on their own.

There are extremely real negative neurophysical pathways built into the brain - for entirely adaptive reasons - which can kick in, of course, meaning that a group begins being pathological in its thinking, driving away from true beliefs and toward false ones. See the video posted above. This is precisely the reason to cultivate skepticism, as it helps to short-circuit these cognitive biases.

In conclusion, the materialist is well insulated from concern about Plantinga's criticisms of his rationality and his belief in the evidence for evolution can continue unabated ... at least until some kind of actual evidence to the contrary shows up.