In his 1993 book titled Warrant and Proper Function, Alfred Plantinga proposes one of the most interesting arguments for the belief in God yet; the “Evolutionary Argument Against Naturalism” uses Bayesian probability to argue that combining naturalism and evolutionary biology simultaneously is self-defeating.
In this argument, R stands for “our cognitive faculties are generally reliable”, while N&E stands for “naturalism and evolution”. Plantinga realizes that evolutionary naturalism cannot specifically prioritize the intrinsic truth value of a belief; it is only able to prioritize the course of action incited by that belief based on how it contributes to an organism’s fitness in the context of survival. Therefore, he argues, evolutionary naturalism is self-defeating and cannot be rationally affirmed.
1. Pr (R | N&E) is low.
The probability that our cognitive faculties are reliable, given naturalism and evolution, is low.
2. Anyone who accepts (believes) N&E and sees that Pr (R | N&E) is low has a defeater for R.
This means that anyone who accepts naturalism and evolution acquires a defeater for the reliability of his/her cognitive faculties. A defeater is anything that undercuts the justifications for R being true.
3. Anyone who has a defeater for R has a defeater for any other belief she thinks she has, including N&E itself.
R is inclusive of all beliefs, as it’s the idea that our cognitive faculties are reliable; naturalism and evolution are beliefs, therefore, you have a universal defeater that applies to naturalism and evolution itself.
4. If one who accepts N&E thereby acquires a defeater for N&E, N&E is self-defeating and can’t rationally be accepted.
Believing in naturalism and evolution destroys all justifications to believe in naturalism and evolution, so it is self-defeating.
Conclusion: N&E can’t be rationally accepted.
Can you use your own reason to prove that your reason is unreliable? I’d argue not.
Plantinga’s argument is structured around a Bayesian probability framework, leaving room for probability-oriented refutations. In order to access his argument, Pr(R), equating to ‘the probability that our cognitive faculties are generally reliable’, must be set to 1 or close to 1—we’ll see why this is the case in a second.
Operationalizing Bayes’ Theorem, we can derive this equation; this is the first necessary step that Plantinga has to use to prove E&N is self-defeating.
Pr(E&N | R) = [Pr(R | E&N) * Pr(E&N)] / Pr(R)
An observation we’ll call O confirms hypothesis H if and only if the probability of H, given O, is higher than the probability of H by itself. In order to confirm the hypothesis, the ratio on the right-hand side of the equation involving O given H and O must be greater than 1.
Pr(H | O) / Pr(H) = Pr(O | H) / Pr(O)
If we already assigned the observation ‘our cognitive faculties are generally reliable’ a value close to or equal to 1, it becomes impossible for Pr(O | H) to exceed 1. If the maximum probability is 1, you would need to divide something by a decimal to make a probability exceed 1; Plantinga already assigned observation Pr(R), the divisor, a probability of close to or equal to 1.
If a sidewalk is wet, it usually confirms the hypothesis that it’s raining due to the fact that Pr(Wet) is usually substantially less than 1. But Pr(Wet | Raining) can significantly exceed Pr(Wet) as the probability of a wet sidewalk, given it’s raining, is high. When you divide a likely probability, say 0.9, by an unlikely one, say 0.1, you get a confirmation value greater than 1—in this case, 9. When it’s divided by a numerical value near 1, you can’t prove a hypothesis.
What if Plantinga simply shifted Pr(R) to a lower value? Then Pr(E&N | R) increases the more Pr(R) decreases, since a lower value in the denominator will keep raising the value present in the numerator; this makes it so the defeater derived from a low R value becomes inaccessible.
The most intuitive way to refute the EAAN is to point out that our cognitive faculties are probabilistically reliable, even granted that evolution and naturalism are true. According to Plantinga, evolution doesn’t select for truth—it merely keeps beliefs that are advantageous for survival, and as long as a false belief can produce the same responses as a true belief, naturalism doesn’t care.
That is most certainly true in a vacuum, but when presented with a network of millions of underlying beliefs interacting with each other to acquire knowledge, the chance of (R | E&N) is not low. Realize that in order for evolution and naturalism to select a belief, it can either be false (f) with what we’ll call a correct (C) response, or true (t) with a true (C) response. There are two important underlying assumptions with this model: if any false belief interacts with a true one, it is unlikely to create a true response.
∀t(t → C) - For all true beliefs, it implies a correct response, but there exist false beliefs that imply correct responses - Ǝ f(f → C). This means that Pr(C | t) is extremely close to 1, as having a correct action given a true belief is extraordinarily likely; Pr( C | f) is <<1, as it’s unlikely—but possible—that false beliefs create correct actions.
Let’s assume we have a system of beliefs that are all true. The probability of Pr(C | all t) = 1n = 1, where n denotes the number of beliefs.
Let’s assume we have Plantinga’s hypothetical system of beliefs, constituted by a mix of true and false ones. The probability of Pr(C | k false beliefs among n) = ek, where e is small as we’ve just proved. When we have an e-value significantly smaller than 1, that represents an exponential decay function that lowers the chance of an entirely false action dramatically for every belief in the system exponentially.
Now, the only thing left to do is to calculate the overall probability of a correct response across a belief network of size n.
You don’t need to memorize that equation, just know that the expression approaches 1 only if p → 1—i.e., the vast majority of beliefs are true. Applying this to Plantinga’s initial Bayesian equation, you can apply a likelihood constraint onto it, namely, if E&N were true and our beliefs were mostly false, the probability of observing coherent and successful action would be near 0.
Pr(observed behavioral success | E&N ∩ ¬R) ≈ 0, while
Pr(observed behavioral success | E&N ∩ R ) ≈ 1
The observed successes of human cognition, technology, and reasoning point overwhelmingly to the second scenario, where you would have to uphold a stupendous majority of true beliefs to advance any understanding of fields like STEM or cosmology.
What if false belief systems can still be coherent?
A belief has two parts—neurophysiological properties constituted by the brain’s chemical signals, and semantic properties which dictate the meaning of a belief; evolution only selects for neurophysiological properties. Paul can not only have the false belief of “tigers are friendly, and I can be friends with tigers by running away”, he can also have a whole belief system where running achieves any positive goals and predators are all friendly.
Note that such a network is not even theoretically possible. For a brain to be “wired” to respond to certain stimuli, it must represent those stimuli in some way. Paul’s brain needs to accurately track the tiger’s size, color, speed, and lethality in order to trigger the action of running when a tiger appears. If some neural structure is constantly triggered by tigers or predators for the mental representation “I love playing with my friends”, the link between syntax and semantics is broken.
Plantinga’s argument provides no premise connecting low probability to total epistemic defeat. Transitioning from “Pr(R | E&N) is low” to “E&N is self-defeating” requires that evolutionary naturalists have no grounds for believing R beyond E&N itself. Is that hidden assumption defended? No.
Someone who believes in evolutionary naturalism can justify the reliability of their cognitive faculties with the introspection of their own reasoning; anyone can cite examples from a laundry list of scientific accomplishments that could’ve only been performed with successful inquiry and reliable reasoning. Naturalists actually hold the inverse of what Plantinga assumes—they don’t believe R to be derived from E&N, they believe that E&N is derived from R.
Even if you charitably grant Plantinga’s assertion here, R is stating that our cognitive faculties are generally reliable, or that ‘the great bulk’ of our beliefs are true. If you defeat the claim that “at least 90% of our beliefs are true”, you don’t defeat the claim that “at least 75% of our beliefs are true”. Plantinga’s argument doesn’t give you a basis for universal skepticism here.
What if Pr(R | E&N) is just inscrutable, so you don’t have to prove that it’s low?
If a theist can prove that the evolutionary naturalist can’t give justification for E&N being reliable without already presupposing those faculties are reliable, it’s impossible to confirm R without collapsing into epistemic circularity. Suppose someone who believes E&N wants to evaluate whether or not E&N can support R. Any of their evaluations or reasoning remains contingent on the reliability of their cognitive faculties—asserted by R.
The theist here has an edge in escaping Agrippan skepticism; one could simply make the claim that God’s existence provides a non-circular explanation of why cognitive faculties are reliable. An omnipotent, omniscient, omnibenevolent creator wouldn’t design creatures whose faculties fail to discern between truths and lies.
The theistic solution can only escape circularity if a theist has independent grounds for believing in God that don’t hinge on already asserting R—theological arguments are all proofs based on reasoning, and hence assume the reliability of our cognition. If Pr(R | E&N) is inscrutable, you also can’t assert that Pr(R | TT) is high with confidence; the faculties that create such probability assessments are operating under ‘inscrutable’ conditions.
Does the EAAN succeed at defeating naturalism? No. Plantinga’s Bayesian framework is in a double-bind where either he fails to utilize R to prove anything by setting it too high, or fails to defeat evolutionary naturalism by setting R too low. By simply looking outside of a probabilistic framework, you’ll realize that the chance of R, even given E&N, is absurdly high—humanity has colonized an entire planet, traveled to the moon, eradicated smallpox, and can genetically engineer almost any species. None of these would’ve been possible in the slightest if we couldn’t rely on our own reason to get us there.
Plantinga does present a really interesting argument for God, albeit one with numerous structural pitfalls… It is definitely one of the most promising contemporary arguments for God, and I do expect that many of the responses I bring up can be thoroughly debunked by those smarter than me. In a few years, all the responses I’ve given may become completely obsolete, given we keep discussing these arguments thoughtfully! 🙂
If I got something wrong, I’m open to corrections and discussions in the comments!
Send this to someone who disagrees (or agrees) with you on theism!
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