SOPHIA DOI 10.1007/s11841-017-0599-4

Skeptical Theism Remains Refuted: a Reply to Perrine David Kyle Johnson 1

# Springer Science+Business Media Dordrecht 2017

Abstract 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. Keywords Skeptical theism . Atheism . Bayes Theorem 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. For simplicity, when figuring the relevant probabilities, I used a basic probability calculus that simply distributes the probability of falsified hypotheses equally. In his 2015 article ‘A note on Johnson’s Ba refutation of skeptical theism^,’ Timothy Perrine argued that, since ‘equal distribution’ (the assumption that the probability of falsified hypotheses should always be distributed equally) is false on Bayes Theorem (a superior method of determining probabilities), my argument is undermined unless I can show that my thesis also follows on a Bayesian analysis. It is the purpose of this paper to meet that burden. To do so, four Bayesian calculations are necessary. As I observed in 2013, when the skeptical theist says that there may be undetectable justifying reason to allow an evil (i.e., a JuffRE), there are two questions to ask: (1) Is God’s existence relevant to whether or not JuffREs exist? (2) Is God’s existence relevant to whether or not JuffREs are detectable? Consequently, there are four possibilities to consider when we observe a SUE. (Please note that, to keep the Bayesian calculations clear and concise, I have done the relevant work of justifying the values of the new conditional probabilities in footnotes.) * David Kyle Johnson [email protected]

1

King’s College, Wilkes-Barre, PA, USA

D.K. Johnson

1. God’s existence is relevant to both the existence and undetectability of JuffREs. The figures for the priors of the relevant hypotheses here are supplied in my original paper (Johnson p. 434)1 and by Perrine (2015: 42).2 PðG1 =kÞ ¼ :125

PðG2 =kÞ ¼ :375

Pð∼G=kÞ ¼ :5

When we observe an evil, the conditional probability of E (that we are unable to detect the JuffRE for the evil in question) on each of these hypotheses is:3 PðE=G1 &kÞ ¼ 0

PðE=G2 &kÞ ¼ 1 PðE=∼G&kÞ ¼ 1

Using Bayes to update our probabilities after observing that the evil in question has no detectable JuffRE produces this result: PðG1 =kÞ ¼ 0

PðG2 =kÞ ¼ :429

Pð∼G=kÞ ¼ :571

The probability of God’s non-existence jumps seven points, and the probability of God’s existence drops seven—a full 14-point shift. (Using equal distribution produced a shift of only 12 points.) My thesis remains intact. 2. God’s existence is relevant to the existence of JuffREs but not their undetectability. The priors in this case are different (see Johnson, p. 440). PðG1 =kÞ ¼ :25 PðG2 =kÞ ¼ :25 Pð∼G=kÞ ¼ :5

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. 1

Skeptical Theism Remains Refuted: a Reply to Perrine

The conditional probabilities however are the same.4 PðE=G1 & kÞ ¼ 0 PðE=G2 & kÞ ¼ 1

PðE=∼G & kÞ ¼ 1

And updating with Bayes we get: PðG1 =kÞ ¼ 0

PðG2 =kÞ ¼ :333

Pð∼G=kÞ ¼ :666

This time we have a full 32-point shift in favor of atheism whereas before, using equal distribution, we only had a 25-point swing. My thesis remains intact. 3. God’s existence is irrelevant to the existence of JuffREs but not to their detectability. In this case, we have six hypotheses to consider (see Johnson, p. 441–2).5 PðG1 =kÞ ¼ :0625 PðG2 =kÞ ¼ :1875 PðG3 =kÞ ¼ :25 PðA1 =kÞ ¼ :1875 PðA2 =kÞ ¼ :0625 PðA3 =kÞ ¼ :25 In this scenario, we must consider the occurrence of the evil (E1) and then the fact that its JuffRE is undetectable (E2) as two separate pieces of evidence. The relevant conditional probabilities for E1 are:6 PðE1 =G1 & kÞ ¼ 1 PðE1 =G2 & kÞ ¼ 1 PðE1 =A1 & kÞ ¼ 1 PðE1 =A2 & kÞ ¼ 1

4


P E1 =G3 & k
¼ 0 P E1 =A3 & k ¼ :6

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.

D.K. Johnson

When we update our priors given E1 we get: PðG1 =kÞ ¼ :096 P ðG2 =kÞ ¼ :29 P ðA1 =kÞ ¼ :29 PðA2 =kÞ ¼ :096

P ðG3 =kÞ ¼ 0 PðA3 =kÞ ¼ :23

The relevant conditional probabilities for E2 are:7 PðE2 =G1 & kÞ ¼ 0 PðE2 =A1 & kÞ ¼ 0

PðE2 =G2 & kÞ ¼ 1 PðE2 =A2 & kÞ ¼ 1


P E2 =A3 & k ¼ 1

Updating our probabilities given E2 yields: PðG1 =kÞ ¼ 0 PðA1 =k Þ ¼ 0

PðG2 =kÞ ¼ :468 PðA2 =kÞ ¼ :156 PðA3 =kÞ ¼ :375

This leaves atheism at 53.2%, which is 3.2% more likely than it was (50%), for a total shift of 6.4% in favor of atheism. Interestingly, under option 3, Bayes produces a result more friendly to theism than my previous ‘equal distribution calculations’ (which shifted the probability a full 37 points in favor of atheism). This is partially a result of the above conservative estimate (.6) I gave to P(E1/A3 & k); higher values for that figure would shift things even more in favor of atheism. In any event, however, my thesis still remains intact: SUEs reduce the probability of God’s existence. 4. God’s existence is irrelevant to both the existence of JuffREs and their detectability. The relevant priors (see Johnson, p. 443-4) are as follows: PðG1 =kÞ ¼ :125 PðG2 =kÞ ¼ :125 PðA1 =kÞ ¼ :125 PðA2 =kÞ ¼ :125

PðG3 =kÞ ¼ :25 PðA3 =kÞ ¼ :25

The conditional probabilities for E1 are the same as above (for the same reasons): PðE1 =G1 & kÞ ¼ 1 PðE1 =G2 & kÞ ¼ 1 PðE1 =A1 & kÞ ¼ 1 PðE1 =A2 & kÞ ¼ 1


P E1 =G3 & k
¼ 0 P E1 =A3 & k ¼ :6

Updating our priors given E1 we get: PðG1 =kÞ ¼ :19 PðG2 =kÞ ¼ :19 P ðG3 =kÞ ¼ 0 PðA1 =kÞ ¼ :19 PðA2 =kÞ ¼ :19 PðA3 =kÞ ¼ :23 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.

Skeptical Theism Remains Refuted: a Reply to Perrine

The conditional probabilities for E2 are also the same as above: PðE2 =G1 & kÞ ¼ 0 PðE2 =A1 & kÞ ¼ 0

PðE2 =G2 & kÞ ¼ 1 PðE2 =A2 & kÞ ¼ 1


P E2 =A3 & k ¼ 1

And updating the probabilities given E2 produces a similar result: PðG1 =kÞ ¼ :0 PðA1 =kÞ ¼ :0

PðG2 =kÞ ¼ :3125 PðA2 =kÞ ¼ :3125 PðA3 =kÞ ¼ :375

The probability of God’s existence drops (to 31.25%) making the overall shift in favor of atheism a full 37.5 percentage points. On equal distribution it was more (42 points), but my thesis remains intact.

Conclusion While it is true that equal distribution does not hold on Bayes, this undermines my original argument only if using Bayes to figure the relevant probabilities produces values that falsify my original thesis. It never does. Although in the last two cases it produces numbers slightly less friendly to my thesis, in the first two cases, Bayes produces figures even more friendly to my thesis. In every case, my thesis remains intact (seemingly unjustified evil reduces the probability of God’s existence) and thus skeptical theism remains refuted.

References Johnson, D. (2013). A refutation of skeptical theism. Sophia, 52(3), 425–445. Perrine, T. (2015). A note on Johnson’s ‘a refutation of skeptical theism’. Sophia, 54(1), 35–43.