Abstract
In a recent article, David Kyle Johnson has claimed to have provided a ‘refutation’ of skeptical theism. Johnson’s refutation raises several interesting issues. But in this note, I focus on only one—an implicit principle Johnson uses in his refutation to update probabilities after receiving new evidence. I argue that this principle is false. Consequently, Johnson’s refutation, as it currently stands, is undermined.
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Notes
According to Johnson, skeptical theists are committed to this in virtue of being theists (429 fn. 18; cf. 427). While I am not entirely convinced this is a commitment of skeptical theism, I will not press the point.
(2013, p. 429) It is also not clear that this is a commitment of skeptical theism. Perhaps skeptical theism will not be refuted even if seemingly unjustified evils reduce the probability of theism some, but not by very much at all (cf. Wykstra 1996, pp. 145–6). Again, I will not press the point here.
Johnson’s use of ‘probabilistically relevant’ is curious. He writes as if ‘A is probabilistically relevant to B’ implies that the probability of B, given A, is higher than the probability of A by itself. This is curious because it seems to eliminate the possibility that A is probabilistically relevant to B by reducing the probability of B. However, this does not matter as long as we are clear about this usage.
In introducing these questions, Johnson does not clearly distinguish between questions of epistemic probability and ontology. His questions are clearly about epistemic probability. But the examples he provides (e.g., 2013, p. 430) are concerned with ontology, in particular, whether or not a justifying good would exist whether or not God did or whether or not a justifying good is detectable whether or not God exists. But questions about ontology and epistemic probability might differ—for instance, a justifying good of an evil may necessarily exist if the evil does (so, ontologically, God’s existence is not relevant to the existence of the justifying good), but supposing the justifying good is so great, God may desire to bring it about (so, epistemically, God’s existence is relevant to the existence of the justifying good). I return to this point at the end of ‘Equal Distribution Is False’ section.
The reason for this is to determine to what degree seemingly unjustified evils are evidence against the existence of God independently of arguments the theist might provide for theism.
The assumption is that the conditional probability of the justifying good being undetectable given that God does not exist is 1 (or very close to it). As we will see below, it is very important that this assumption is true, even though Johnson does not defend it.
One might object that G1 should not have a value of 0 but something very close to 0—even if the relevant good is detectable, sometimes we do not detect things we ought to because of fluky events. But Johnson could reformulate his argument—no better, no worse—with G1 having a value slightly higher than 0, so this would not be a significant objection.
We must redistribute the probability so as to not violate an axiom of probability that holds that the probability of mutually exclusive and exhaustive hypotheses should add up to 1. Since G1 has been eliminated, G2 and ~G are now mutually exclusive and exhaustive.
Equal Distribution applies only in a case where a hypothesis gets a new value of 0. This is a limit case. We can easily generalize the principle to apply to cases where a hypothesis deceases in value, even if it does not get a new value of 0 as follows:
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Generalized Equal Distribution—If there is a set of mutually exclusive and exhaustive hypotheses H1…H n , then if one of the hypotheses H x goes from a value a to a lower value b, then for any hypothesis that is not identical to H x , its new value is its previous value plus (a − b)/(n − 1).
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There are cases where Equal Distribution gets the right results—for instance, simple cases involving a fair dice, where one gradually learns more information as to what number did not come up. But Equal Distribution only gets the right results in these cases because (i) all of the hypotheses—e.g., that it came up a 1, or a 2, or a 3, etc.—begin with an equal value, and (ii) all of them equally predict the new information (e.g., it is not a 3) as it comes it—e.g., if it came up a 1, then the probability of it coming of a 3 is 0; if it came up a 2, then the probability of it coming of a 3 is 0, etc.
Strictly speaking, Bayes’ theorem is just a theorem in the logic of probability. This kind of application is to use Bayes’ theorem as a useful tool for determining epistemic probabilities (see Wykstra and Perrine 2012, pp. 384–6 for discussion of this use).
This is according to the total probability theorem.
Rounded off.
Thanks to an anonymous reviewer for raising versions of both of these worries.
For instance, if Johnson were to argue that, in these particular cases, Bayes’ theorem and Equal Distribution get the same result, then his use of Equal Distribution would be permissible. But to argue that they get the same result, he would have to provide the key conditional probabilities—which is exactly what I am urging is necessary!
Again (cf. fn. 7), we could permit this value to be slightly higher, but not much would hang on it.
I’ve omitted the calculations here, but the method is the same as the one used above.
Thanks to an anonymous reviewer for suggesting something like this line of reasoning to me.
References
Johnson, D. (2013). A refutation of skeptical theism. Sophia, 52(3), 425–45.
Wykstra, S. (1996). Rowe’s noseeum arguments from evil. In D. Howard-Snyder (Ed.), The evidential argument from evil (pp. 126–50). Bloomington and Indianapolis: Indiana University Press.
Wykstra, S., & Perrine, T. (2012). The foundations of skeptical theism: CORNEA, CORE, and conditional probabilities. Faith & Philosophy, 29(4), 375–99.
Acknowledgements
For helpful comments, I thank two anonymous reviewers.
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Perrine, T. A Note on Johnson’s ‘A Refutation of Skeptical Theism’. SOPHIA 54, 35–43 (2015). https://doi.org/10.1007/s11841-014-0437-x
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DOI: https://doi.org/10.1007/s11841-014-0437-x