Does the Evidential Argument for Naturalism Succeed?

Evaluating Draper/Lowder’s evidential argument from evolution

Photo by Blake Verdoorn on Unsplash

The motivation for this article comes from a discussion on Twitter with Jeffery Jay Lowder. It was clear we were looking at the issue in very different ways. How is it possible not to talk past each other? The only way is to attempt to see the world as others do.

This article first sets out Draper/Lowder’s argument as accurately as I can. Any strawmen are unintentional! I will then explore these assumptions in more detail.

Draper/Lowder argument

Jeffery Jay Lowder points out: “Many conservative Christians and lay atheists alike claim that if biological evolution is true, then God does not exist.” But few think through the logic of this inference.

Paul Draper sets out this argument formally:

1) Evolution much more probable if naturalism is true than if theism is true

2) Pain and pleasure related to reproductive success much more probable if naturalism is true than if theism is true

3) 1 and 2 together very much more probable if naturalism is true that if theism is true

4) Naturalism is at least as probable as theism

5) Naturalism is very much more probable than theism (all other evidence held equal)

6) Naturalism entails theism is false

7) Highly probable theism is false

Can Bayesian networks help us untangle philosophical arguments?

I’ve found Bayesian networks (BN) to be a helpful tool for viewing the world through others’ eyes. BNs are graphical models representing complex relationships between variables. They consist of:

• network of nodes (represented by boxes or bubbles), with arrows representing probabilistic relationships.
• I will use GeNIe Modeler (Bayes Fusion) to construct the BNs.

Where possible, these probabilities are based on estimates from proponents like Draper or Lowder. Where these aren’t available, I’ve tried to make justifiable estimates.

Probabilities included in the BN are reasonably arbitrary. The primary value of these analyses are in exploring assumptions of the argument.

(1) Evolution much more probable given naturalism

Draper makes two main assumption:

• evolution is at least twice as probable on naturalism in comparison with theism.
• probability of evolution, given theism, is below 0.5.

Therefore, I’ve used the following probabilities in the BN:

• Probability of evolution, if theism is true=0.45
• Probability of evolution, if naturalism is true=0.90

(2) Pleasure, pain, and reproductive success

Draper/Lowder argue based on O1-O3 (see below), naturalism is much more likely to be true:

(O1) moral agents experiencing pain or pleasure that we know to be biologically useful.

(O2) sentient beings that are not moral agents experiencing pain or pleasure that we know to be biologically useful.

(O3) sentient beings experiencing pain or pleasure that we do not know to be biologically useful.

Draper uses the same description (“much more probable”) as argument (1). Therefore, to be consistent, I’ve used the same probabilities as above.

(3 and 4) Probability of naturalism and theism

Argument (4) assumes no preference for naturalism and theism before looking at the evidence (prior probability).This assumption allows the probabilities in (3) to be based purely on arguments in (1) and (2).

Argument (3) assumes that evolution (1); pain, pleasure, and reproductive success (2) are both much more likely under naturalism. So taken together are very much more likely under naturalism. Figure 1 supports this assumption that (3) logically follows from (1) and (2).

Figure 1. Bayesian Network Diagram of Draper/Lowder model

(5) All other evidence held equal

Draper/Lowder focus on the likelihood of naturalism and theism if evolution is true. So this assumption helps prevent us from getting side-tracked. However, it’s important to make the assumptions of (5) explicit.

Mathematically, we know that estimates of association are a combination of:

• the true magnitude of that association (for example, ‘evolution’ and ‘worldview’ nodes in Figure 2) and
• confounders (for example, ‘y’ node in Figure 2) associated with both variables.

Argument (5) assumes:

• x (all known confounders) does not influence the association between pleasure, pain, reproductive success and worldview
• y (all known confounders) does not influence the association between evolution and worldview

If these assumptions are not valid, then arguments (3), (5), and (7) are not valid.

Figure 2 Illustration of assumption 5: x and y have no impact on association between naturalism and theism

Evaluating sensitivity of assumptions

Arguments (3) and (4) are non-controversial so will not be considered further. However, arguments (1), (2), and (5) are highly uncertain.

Argument (1): evolution at least twice as likely under naturalism

Daniel Howard-Snyder questions this assumption. Why would we think God is more likely to engage in special creationism?

So a universe populated only with things whose properties and powers suffice to render it unnecessary for God to tinker with it later is a world that is maximally “grand, beautiful, and artful,” manifesting the gloriousness of its creator, his power and his wisdom. (Howard-Snyder, Evolutionary Argument for Atheism).

He proposes a Leibnizian argument (based on the above assumption):

1. Necessarily, if God exists, then, at creation, God has the power and wisdom to create a Leibnizian natural world.

2. Necessarily, if, at creation, God has the power and wisdom to create a Leibnizian natural world, then he will exercise his power and wisdom toward that end, provided that he has good enough reason to do so.

3. Necessarily, God has good enough reason to do so (if he exists).

4. So, necessarily, if God exists, then, at creation, he will exercise his power and wisdom to create a Leibnizian natural world.

Howard-Snyder doesn’t necessarily argue for the truth of the ‘Leibnizian argument’. His point is that we have no basis to judge whether special creationism or a Leibnizian natural world is more likely under theism.

So we have three possibilities for the model:

• evolution twice as likely under naturalism
• evolution more than twice as likely under naturalism
• evolution as likely under naturalism and theism

Argument (2) pain, pleasure, and reproductive success much more likely under naturalism

Peter van Iwagen, challenges argument (2). Similar to Howard-Snyder above, he argues we do not have enough information to determine whether O1–03 are less likely given theism.

For example, it is not possible to evaluate whether Draper’s conclusion is any more valid than the following argument:

(1) Every possible world that contains higher-level sentient creatures either contains patterns of suffering morally equivalent to those recorded by S [a certain distribution of suffering], or else is massively irregular.

(2) Some important intrinsic or extrinsic good depends on the existence of higher-level sentient creatures; this good is of sufficient magnitude that it outweighs the patterns of suffering recorded by S.

(3) Being massively irregular is a defect in a world, a defect at least as great as the defect of containing patterns of suffering morally equivalent to those recorded by S.

(Peter van Iwagen, The Problem of Evil, the Problem of Air, and the Problem of Silence)

Modifying probability assumptions for arguments (1) and (2)

We can see below (Table 1), the likelihood of naturalism and theism varies widely depending on how we weight our assumptions for arguments (1) and (2). The likelihood varies from naturalism and theism being equally likely to naturalism being just over 6 times more likely. This means arguments (1), (2), and (3) are inconclusive.

Table 1. Compares probability of naturalism and theism after variations in probability assumptions

Argument (5)

Assumption 5 can be acceptable in some experimental contexts — where randomization methods can cancel out (or minimize) the effects of confounding.

However, outside experimental settings, this assumption is very unlikely to be valid. The presence of x and y in Figure 2, if not explicitly taken into account, are likely to lead to a flawed assessment of the probability of naturalism and theism.

Alvin Plantinga proposed several options that need to be taken into account. I’ve included some of these below, and some additional nodes, in the Bayesian network (Figure 3):

• consciousness (C )
• intelligibility of evolution (I)
• existence of moral beings (M)
• association between religion, mental health, and physical health (R)

Each of these nodes are worthy of an article in itself. But to keep to a manageable length I will provide only brief justification below.

If there is sufficient interest I will follow up with more detailed justifications. I’m also very open to suggestions for where I could be wrong!

Consciousness

• Consciousness forms part of Draper/Lowder’s justification for argument (1).
• Assumption: Probability of consciousness is twice as likely under theism as naturalism.
• Lowder acknowledges consciousness is more likely under theism: “So the existence of human consciousness, while not entailed by theism, isn’t surprising on theism in the way it is on naturalism.”
• I’ve reflected this with the following probabilities: consciousness given naturalism=0.45 and consciousness given theism=0.90.

Intelligibility of evolution

• An evidential argument from evolution — assumes we can reliably discern the truth of evolution. Which in turn assumes the reliability of our cognitive systems.
• Assumption: probability of intelligibility of evolution is 1.8 times as likely under theism as naturalism.
• This reflects Draper’s argument that the likelihood of the reliability of our cognitive systems is inscrutable under naturalism.
• Whilst Plantinga has argued, under theism, the probability is high that our cognitive faculties are reliable.
• Humans created in the image of God implies “ we resemble God more particularly in being able to know and understand something of ourselves, our world, and God himself.” (Where the Conflict Really Lies)
• These arguments are reflected in the BN with the following probabilities: intelligibility of evolution given naturalism=0.5, intelligibility of evolution given theism=0.9.

Existence of moral beings

• Existence of moral beings forms part of Draper/Lowder’s argument (2)
• Assumption: probability of moral beings in our universe is twice as likely under theism as naturalism.
• Existence of moral beings is very likely, if not certain if theism is true.
• It’s not necessarily impossible under naturalism. For example, there are well developed arguments for the survival benefits of altruism.
• However, it is still surprising under naturalism for the existence of moral beings who judge actions that have survival benefits such as neonaticide and violence against step children as immoral.
• These arguments are reflected in the BN with the following probabilities: moral beings given naturalism=0.4 and moral beings given theism=0.8.

Association between religion, mental health and physical health

• Draper/Lowder’s argument (2) is informed by reflection on suffering including physical health and mental health.
• Assumption: probability of association between religious belief/activity and mental health and physical health is twice as likely under theism as naturalism.
• I’ve summarised the evidence elsewhere on the association between religion and health and addressed questions regarding whether this can be explained by confounding or additional factors unrelated to theism.
• This association is expected under theism and unlikely if naturalism is true.
• However, it is not impossible under naturalism — as could be accounted for by residual confounding (studies not being able to fully adjust for confounders) or some other unknown factor unrelated to theism.
• These arguments are reflected in the BN with the following probabilities: religion and health associated given naturalism=0.45 and moral beings given theism=0.9.

Removing assumption (5)

Table 2. Compares probability of naturalism and theism after taking into account potential confounders

Assumption (5) has a huge impact on probability estimates. I think this indicates Draper/Lowder’s argument from evolution may be accounted for by confounding.

When we take a more realistic approach, that addresses wider factors relevant to the argument, theism is more likely to be true in all scenarios considered.

However, an important caveat, this is a starting point. A work in progress. It is important to test further scenarios. But I think there are significant reasons to doubt the validity of Draper/Lowder’s conclusions that naturalism is very much more likely to be true than theism.

Bibliography

Paul Draper. The Distribution of Pain and Pleasure as Evidence for Atheism. In: The Problem of Evil: Selected readings (Ed. Michael Peterson).

Daniel Howard-Snyder. The Evolutionary Argument for Atheism.

Jeffery Jay Lowder. The Evidential Argument from Biological Evolution: Part 1.

Alvin Plantinga. Where the Conflict Really Lies: Science, Religion, and Naturalism.

Peter van Iwagen. The Problem of Evil, the Problem of Air, and the Problem of Silence. In: The Problem of Evil: Selected readings (Ed. Michael Peterson).