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Skeptical Theism Remains Refuted: a Reply to Perrine


In my 2013 article ‘A Refutation of Skeptical Theism,’ I argued that observing seemingly unjustified evils (SUEs) always reduces the probability of God’s existence. When figuring the relevant probabilities, I used a basic probability calculus that simply distributes the probability of falsified hypotheses equally. In 2015, Timothy Perrine argued that, since Bayes Theorem doesn’t always equally distribute the probability of falsified hypotheses, my argument is undermined unless I can also show that my thesis follows on a Bayesian analysis. It is the purpose of this paper to meet that burden.

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  1. G1 is my original hypothesis (D) ‘God exists, so does the relevant JuffRE, and it is detectable.’ G2 is (E) ‘God exists, so does the relevant JuffRE, but it is not detectable,’ and ∼G is (F) ‘God does not exist (and neither does the relevant JuffRE).’

  2. One might wonder why the probability of P(G1/k) is not 0 given that G1 stands for ‘God does exist, so does the justifying good, but it is detectable’ and we are considering an option where God’s existence is relevant to whether the justifying good in question is undetectable. But when asking whether God’s existence is relevant in this way, we are asking whether God ever makes JuffREs exist and makes them undetectable (or, alternately, whether JuffREs always exist ‘naturally’ and are always ‘naturally undetectable’). If God ever does such a thing, it does not follow that he does so in every case (and we are, after all, considering one case (one SUE) at a time). Now, if he ever does such a thing, for any given evil it would seem to follow that God doing such a thing is more likely than not; this is why I assumed here that P(G2/k) has a higher value than P(G1/k) (and this is also what I mean by saying that God’s existence is also probabilistically relevant to the existence and detectability of JuffREs in this scenario). But it does not follow in this scenario that P(G1/k) is 0. After all, no theist is going to think that God always makes JuffREs undetectable—some of them actually are detectable. (It’s also worth noting that if P(G2/k) were equal or lower than P(G1/k), SUEs would lower the probability of God even more—so my assumption that P(G2/k) > P(G1/k) in this scenario is generous.)

  3. It’s important to note that Perrine (2015) claims (on p. 42) that P(E/∼G & k) cannot be assigned a value. He is incorrect. Although some clumsy wording on my part (statement (1) on p. 431) may have obscured this, in this scenario God’s existence is not merely probabilistically relevant to whether there is a JuffRE. The question is whether (when it comes to this particular evil) God causes the JuffRE or it happens on its own. In this scenario, the theist is claiming that (regarding the evil in question) God causes it. Consequently, God’s existence is necessary if there is to be a JuffRE for the evil in question. (I do make this clear in footnote 30 of my original paper.) It follows that P(E/∼G & k) = 1. If God does not exist then the evil in question does not have a JuffRE and thus it is guaranteed that one is not detectable.

  4. If God would be responsible for the existence of this particular evil’s JuffRE then, if God exists it must have one (and in this scenario, it would be naturally undetectable). If God does not exist, however, then it does not have a JuffRE (and thus it obviously goes undetected).

  5. The hypotheses are as follows:

    G1: God exists, so does a justifying good, and it is undetectable.

    G2: God exists, so does a justifying good, and it is detectable.

    G3: God exists but the justifying good does not.

    A1: God does not exist, but the justifying good does, and it is detectable.

    A2: God does not exist, but the justifying good does, and it is undetectable.

    A3: God does not exist and neither does the justifying good.

  6. Based on the principle of indifference, and to be fair, I am assuming that the probability of the evil itself (E1) is just as likely as not: P(E1) = .5. But to figure these conditional probabilities, we must consider how likely the evil is on the given hypotheses. On G3, the evil in question would not occur (because God would not allow the evil unless it was justified). On G1, G2, A1, and A2, the evil is guaranteed to occur because on each of those hypotheses, the JuffRE for the evil exists. Since in order for the JuffRE to justify the evil in question, the evil in question would have to be the only way to bring about the JuffRE (see Johnson (2013: 427)), if the JuffRE does justify the evil in question then the evil is a necessary condition for the JuffRE’s existence (and the JuffRE in turn would entail the evil’s existence). Consequently, the probability that the evil exists given that the JuffRE exists would be 1. The other hand, on A3, God does not exist and the evil would have no justification. Given that, as theists often claim, a Godless universe would be cold and indifferent and thus unjustified evil would be common, it would seem that A3 would raise the probability of E1 beyond .5. Conservatively, I have merely raised it a point (to .6) but as long as it is raised to some degree (as it obviously should be), the results of the calculation will still be friendly to my thesis.

  7. Since both G1 and A1 state that the JuffRE would be detectable, they do not predict E2 (that the JuffRE would be undetected). G2, A2, and A3 all predict E2 since they state that the JuffRE is undetectable.


  • Johnson, D. (2013). A refutation of skeptical theism. Sophia, 52(3), 425–445.

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  • Perrine, T. (2015). A note on Johnson’s ‘a refutation of skeptical theism’. Sophia, 54(1), 35–43.

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Correspondence to David Kyle Johnson.

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Johnson, D.K. Skeptical Theism Remains Refuted: a Reply to Perrine. SOPHIA 56, 367–371 (2017).

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  • Skeptical theism
  • Atheism
  • Bayes Theorem