alexander pruss

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Junia and Bayesian Epistemology: Philosophical probability trumping Biblical scholarship?

Alexander Pruss is one of the smartest people I’ve encountered. Though I don’t always agree with his conclusions, the sharpness of his intellect and his wit is always fascinating. His blog is frequently a place to flex mental muscles, as he offers small, one-off arguments to spur discussion. Recently, he wrote a post entitled “Junia/Junias and the base rate fallacy” Pruss argued that application of Bayesian analysis to biblical scholarship would help solve the question of whether Junia/Junias was an apostle. Apologies in advance for possible lack of care with terms like “factor,” “probability,” and “odds”; I tried to be careful but I’m tired.

The Argument

The preliminaries are explanations of Bayes’ Theorem and the meaning of the “base rate fallacy,” both of which are easily searched online, but I provided the links here (with all the caveats that a little bit of knowledge is a dangerous thing and Wikipedia articles don’t make anyone an expert). With that information in mind, we approach Pruss’s argument.

Pruss does fudge the numbers some, admitting he hasn’t explored the question on the actual numbers for some of these probabilities. So, for example, he begins by giving a 9:1 factor for Junia:Junias names in the early church. With that, and with the note that to avoid the base rate fallacy, we ought to assign a probability (he gives .9) to the question of whether this person was “among” the apostles, it yields a .19 rate of false positives for people who are not woman apostles to be assigned the notion of being a woman apostle. Moreover, if we say that there are 12 male apostles (the disciples) for every one female apostle (Junia), the probability of an apostle being a woman is now 1/13. Finally, because “not everyone Paul praises is an apostle” we have to assign a probability to whether Paul is praising an apostle here (Pruss gives it .3). This means that “the chance that a randomly chosen person that Paul praises is a female apostle even given the existence of female apostles is only about (1/13)×(1/3) or about three percent.”

Plugging in the .19 we got above for false positives and doing more math (read his post), we now discover that “even assuming that some apostles are female, the probability that Junia/s is a female apostle is at most about 14%, once one takes into account the low base rate of women among apostles and apostles among those mentioned by Paul.”

Pruss immediately notes the numbers are made up and could change the overall results.


There are some significant problems with Pruss’s argument here. First, the fact is that there is no extant name “Junias/Junianias” found anywhere in lexical evidence whatsoever. Thus, instead of .9 for Junia being a woman, it should be 1. One comment pointed this out and Pruss pressed the argument that even in this case, the math would still be “significantly less than 50%” for Junia to be a female apostle. Doing the math is too hard for my tired brain, but let’s just say he’s right. The question still remains of why the chances for Junia to be a female apostle would be so low.

Looking at his other percentages, it seems a large part of the argument, once we’ve established Junia is female, turns on whether it is the case that she may not be “among” the apostles. Pruss’s position here falls into the goalpost moving arguments that complementarians have engaged in since the lexical evidence turning her into a man came up dry. Typically, this is how it goes:

Junia was not a man => Okay, Junia was not an apostle => Okay, Junia was not the type of apostle that was authoritative

The third stage above is one that is essentially a theological fiction supported almost entirely by punting to the fallacious importation of the semantic range of a word into a foreign context. When Paul wrote to say that Junia was an apostle, according to this argument, but she was one only in the semantic meaning of the word apostle as witness/sent one/messenger. Never mind that the word is used for an office in the New Testament, including in the writings of Paul (1 Corinthians 12:28). No, because it does not serve the purpose of continuing to prevent women from holding pastoral office, the entire semantic range of meaning for the word “apostle” must be imported in order to reduce Junia in status once again. This fallacious importation of meaning is a demonstration of an ad hoc explanation. (Unfortunately, Pruss himself succumbs to this goalpost moving argument in the comments on this post when he questions whether Junia as an apostle would be an authoritative apostle or not.)

But it is the second stage that is at question initially, and here, once again, it seems that the importation of complementarian assumptions into the text has occurred, for this reading goes against the earlier known readings from church fathers (see here, for example) which saw Junia as an apostle and did not import the lexical range of the word into “among” either. So, again, the factor needs to be moved from .9 to 1.

The proportion of male:female apostles is made up, as Pruss acknowledges. It’s possible that the reality is 1:1 or 100:1. So it would be possible to move numbers around to make it either extraordinarily likely Junia was a woman apostle or unlikely. It also seems to me the 1/3 possibility that Paul is praising an apostle seems high. So again, this would potentially lower the probability for Junia as a woman apostle. It could raise it, though that seems unlikely given the biblical text. Nevertheless, significant gains were made with “Junia” being established as the name and being among the apostles. And, the question of just how likely something ought to be in order to be epistemically justified in believing it is itself a matter of very hot debate. If, say, the likelihood for Junia being a woman apostle were 33%, would someone be justified in holding that belief? The answer to that question is very messy indeed.

But the most relevant evidence, the most clear counter-point to Pruss wasn’t even considered. That is this: using prior probability to determine the likelihood of an event does not matter if the event has already occurred. That is, if it is the case that Paul does name a woman apostle, then whether or not this was likely or unlikely given any number of other prior probability considerations does not change what Paul does in Romans 16:7. And while Pruss tries to say that his use of Bayesian theorem ought to somehow guide biblical scholars in their reading of this text, what he doesn’t consider is that highly improbable events do occur and that if they do, whether or not the event is improbable does not impact the event’s actually having occurred. Indeed, it is unclear as to why a biblical scholar should take such prior probability into account to begin with (apart from, potentially, taking caution with offering interpretations that are particularly unlikely). Suppose that the name were not Junia but Rebecca and the Greek text were so clear as to make it impossible to take it as anything but “among the authoritative apostles” (despite their being no use of this term in the NT and it being a demand for evidence by complementarians that they cannot meet for people they themselves admit to being apostles). What then? Would a scholar be justified in dismissing the sentence written by Paul that “Rebecca was an authoritative office-holding apostle” simply because of prior probabilities? It seems obvious the answer is no. So then the question is why should the biblical scholar be beholden to prior probabilities in a supposedly less clear case (and again, I by no means grant that it is unclear)? Again, the answer seems to be that the scholar ought not to worry about that, given the relevant data is directly in front of them.


Bayesian reasoning is interesting. I’ve enjoyed reading about it and learning about it from time to time. Whether or not it is helpful to theological questions is a concern for a different time, though it is a fascinating question to ponder (related questions such as how can we fill in sometimes arbitrary probabilities for certain events/people/etc. and still think the theological reasoning is sound would be interesting to explore in depth). In this specific case, though, it seems clear that Pruss’s argument fails for several reasons. All of these center around the actual meaning of the text (the name Junia and the meaning of “among the apostles”) which no amount of external probabilities can alter. Pruss’s argument is a fun mental exercise that need not undermine confidence in the data of the text itself: Junia was a female apostle. Pruss’s claim that biblical theologians ought to use Bayesian reasoning in their exegesis does not seem to be sustained by this example.


A Brief Biblical Proof for Women Pastors– Read why 1 Corinthians 12:28 is an even bigger problem for complementarians, as it effectively guarantees women may hold the same or more authority than that of pastors.

On the Femnization of the Church– It is frequently alleged that the church is being “feminized” and that this is a bad thing. Check out this post, wherein I analyze this notion from a few different angles.

Women in the Ministry: The philosophy of equality and why complementarianism fails– I argue that the position in which women are excluded from church leadership entails inequality of being.



The preceding post is the property of J.W. Wartick (apart from quotations, which are the property of their respective owners, and works of art as credited; images are often freely available to the public and J.W. Wartick makes no claims of owning rights to the images unless he makes that explicit) and should not be reproduced in part or in whole without the expressed consent of the author. All content on this site is the property of J.W. Wartick and is made available for individual and personal usage. If you cite from these documents, whether for personal or professional purposes, please give appropriate citation with both the name of the author (J.W. Wartick) and a link to the original URL. If you’d like to repost a post, you may do so, provided you show less than half of the original post on your own site and link to the original post for the rest. You must also appropriately cite the post as noted above. This blog is protected by Creative Commons licensing. By viewing any part of this site, you are agreeing to this usage policy.

The Ontological Argument: Question Begging?

Is the ontological argument question begging? Short answer: some versions yes, others, no. For the long answer, read on:

Many versions of the ontological argument appear to beg the question. The Anselmian version of the argument seems invalid, but there are other formulations of it which avoid its invalidity (cf. Maydole’s chapter on the Ontological Argument in The Blackwell Companion to Natural Theology, eds. Craig + Moreland, 553ff). Then, Alvin Plantinga came along and introduced the modal ontological argument, which relies on S5 modal logic. I have discussed Plantinga’s argument elsewhere, as well as demonstrated its validity.

Therefore, we will focus on a new considerations. Consider the following very simple version of the modal ontological argument:

1) Possibly, God necessarily exists

2) Therefore, God necessarily exists

The argument seems, at first face, to be a very strange argument. However, the argument does not beg the question when viewed through modal logic. 1) does follow from 2) in a non-tautological way, but 1) must be established.

Symbolically, the argument is written as the following (Take “T” to be “God exists”):

1) ◊□T

2) □T

S5 modal logic is based upon this very axiom. Namely, ◊□x⊃□x or  ◊□x iff □x (Hughes & Cressewell, A New Introduction to Modal Logic, 58). For in modal logic:

3) that which is “possible” exists in “some possible world.”

4) That which is necessary exists in all possible worlds

Therefore, if something is possibly necessary, then it must obtain in some possible world (3). however, if it is necessary, then it exists in all possible worlds (4). Therefore, if something is possibly (exists in some possible world) necessary (exists in all possible worlds), then it exists in all possible worlds.

Is this argument question begging? If it is, then it is not obviously so. Alexander Pruss has argued out that the argument is question begging only if it is directed at one who does not understand that 1) entails 2) (Pruss, The Principle of Sufficient Reason, 232). I’m not convinced that this is correct. Soundness of arguments don’t depend upon whether people understand them–they depend on whether they are valid or true.  However, it seems Pruss has an intuitive point here, in that even if this argument isn’t question begging, it appears to be.

How might the theist respond? Well, Pruss argues that if the theist argues for the establishment of S5, then it is no longer question begging (232). Alvin Plantinga does just that in God, Freedom, and Evil, as Pruss points out. We’ve already established elsewhere that Plantinga’s argument doesn’t beg the question regardless (see here), but this symbolic proof is bolstered by providing an argument for S5.

Then, it seems to be the case that if S5 modality is valid, God necessarily exists.

Are there versions of the ontological argument that resist this reduction to the “simplistic” version offered here? Yes, there are.  For example, Stephen Parrish’s ontological argument:

5) The concept of the GPB (Greatest Possible Being) is coherent (and thus broadly logically possible)

6) Necessarily, a being who is the GPB is necessarily existent, and would have (at least) omnipotence, omniscience, and moral perfection essentially.

7) If the concept of the GPB is coherent, then it exists in all possible worlds.

8 ) But if it exists in all possible worlds, then it exists in the actual world.

9) The GPB exists (Parrish, God and Necessity, 82)

This argument may initially seem to be susceptible to the same reduction, but it can avoid this reduction by lengthening it to:

10) the GPB is coherent (and logically possible)

11) the GPB’s coherence entails modal possibility

12) the GPB is necessary

13) modally, if something is possibly necessary, then it is necessary

14) the GPB exists necessarily

The key premise here is 10), because if it is true, then the rest of the argument follows necessarily. What reasons do we have for thinking 10) is true? Such a debate is beyond the scope of this post (good discussions can be found throughout theistic philosophy of religion–see, in particular, Craig and Moreland, Philosophical Foundations for a Christian Worldview and Swinburne, The Coherence of Theism; see also my brief discussion in the post on the argument here); but it seems to me that there is no incoherence in the concept. If that is the case, then I am justified in holding 14).

Therefore, it seems the modal ontological argument is not question begging, particularly if one argues first for the validity of S5 modality. Furthermore, there are other modal arguments which don’t rely on a reduction to a simple modal argument. For example, Parrish’s ontological argument relies instead upon the coherence of the GPB. Such arguments are successful if arguments against the GPB’s coherence are shown to be unsuccessful. In either case, God exists.

Ergo deus est.



Maydole, Robert E. “The Ontological Argument.” The Blackwell Companion to Natural Theology. Edited William Lane Craig and J.P. Moreland. Blackwell, 2009.

Parrish, Stephen E. God and Necessity. University Press of America. 1997.

Pruss, Alexander. The Principle of Sufficient Reason. Cambridge. 2006.


The preceding post is the property of J.W. Wartick (apart from citations, which are the property of their respective owners) and should not be reproduced in part or in whole without the expressed consent of the author. All content on this site is the property of J.W. Wartick and is made available for individual and personal usage. If you cite from these documents, whether for personal or professional purposes, please give appropriate citation and provide a link to the original URL. By viewing any part of this site, you are agreeing to this usage policy.



Alexander Pruss on Open Theism

Open Theism is basically the view that God does not know the future. The Evangelical Philosophical society recently tweeted this post by Alexander Pruss on the topic. I found it very interesting. The argument he presents is (quoted word for word from his blog):

  1. (Premise) If p is overwhelmingly probable on the balance of God’s evidence, then God believes p.
  2. (Premise) If open theism is true, then some of the propositions that are overwhelmingly probable on the balance of God’s evidence are false.
  3. Therefore, if open theism is true, God believes some falsehoods.
  4. (Premise) God believes no falsehoods.
  5. Therefore, open theism is false.

I think that perhaps the best way for the open theist to avoid this argument may actually be to deny (4), for which Pruss does not argue. The open theist could hold that: (4`) Possibly, God believes falsehoods. I doubt that many open theists would be perturbed by accepting this premise, but I may be wrong. If I’m right, however, Pruss’s neat argument doesn’t work. Again, check it out.


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