Philosophical Gerrymandering and Cumulative Case Arguments For Theism

I've argued that no argument for God, taken by itself, demonstrates theism -- or even makes theism more probable than not. However, this leaves open the possibility that, when taken together, these arguments do demonstrate the truth of theism, or at least make theism more probable than not.

Richard Swinburne is one famous philosopher of religion who takes this approach to arguments for theism[1]. He uses a formula from probability calculus known as Bayes' Theorem to argue in this way. He calls an argument that raises the probability of a hypothesis a good C-inductive argument, and he calls an argument that makes a hypothesis more probable than not a good P-inductive argument. He then considers a large variety of arguments for theism, and admits that none of them, when construed as a deductive argument, constitutes a sound argument for God's existence. However, he argues that a number of them, when reformulated as inductive arguments, each raise the probability of theism at least a little bit. Thus, he thinks that a number of them are good C-inductive arguments for theism. And when taken together, they make theism at least a little bit more probable than not, making the set of arguments taken together a good P-inductive argument for theism.[2]

To illustrate Swinburne's ideas about C-inductive arguments, P-inductive arguments, and cumulative case arguments, consider a simpler example. Suppose we're detectives investigating a murder, and that we know that either Smith committed the murder or that Jones did it. Then we have two hypotheses:

H1: Smith committed the murder
H2: Jones committed the murder

Suppose further that the following constitutes all our evidence, or data:

D1: Smith's fingerprints are on the murder weapon (a gun)
D2: Jones's fingerprints are on the murder weapon
D3: Smith had a strong grudge against the victim for sleeping with his wife
D4: Jones disliked the victim
D5: Jones is a terrible shot
D6: A somewhat reliable acquaintance of Jones said they talked to Jones at his house at 8pm, which was only 10 minutes before the time of the murder.
D7: Jones lives about 15 minutes from the victim's house.
D8: Smith lives 5 minutes away from the victim's house.

Notice that no single piece of evidence makes either hypothesis even slightly more probable than not -- i.e., not one of D1-D8, when considered individually, is a good P-inductive argument for either hypothesis as to who killed the victim. However, each one (or at least most of them), when taken individually, raises the probability of the relevant hypothesis at least a little bit, in which case each one (or at least most of each one) is a good C-inductive argument. And when taken together, they do make H1 a bit more probable than H2. In fact, D1-D8, taken together, constitutes a good P-inductive argument for H1. Similarly, even if none of the arguments for God establish the truth or the probability of theism, perhaps they do when taken together. Well, do they?

I've already mentioned that Swinburne thinks they do. Some other examples include J.P., Moreland[3], WIlliam Lane Craig, and Basil MItchell.

So, for example, suppose our hypotheses are:

H1: theism
H2: naturalism

And suppose our data are:

D1: the apparent contingency of the universe
D2: the apparent fine-tuning of the universe
D3: the apparent irreducibility of consciousness to the physical
D4: religious experiences of various sorts
D5: the existence of morality[4]

What's the probability of H1 on D1-D5? Of course, as everyone in this debate admits, there's probably no way to assign precise numerical values to the pieces of evidence here, whether taken individually or collectively[5]. To be charitable, though, let's say that each of D1-D5 raises the probability of theism at least a bit, and thus each is a good C-inductive argument for theism. Furthermore, let's be charitable and say that, when taken together, the probability of H1 on D1-D5 is a very strong P-inductive argument, raising the probability of H1 to .9 (i.e. 90%)[6]. Do we now have a cumulative case argument based on D1-D5 that makes the posterior probability of H1 higher than that of H2?

No, we don't. For to truly assess the posterior probability of a hypothesis, one has to include in the data pool *all* of the evidence that has a bearing on the hypotheses in question; to ignore the other evidence is tantamount to philosophical gerrymandering: artificially limiting the range of relevant evidence in order to ensure the conclusion you want. It would be analogous to arguing above that Jones probably committed the murder by just presenting D2, D4, and D6 of the data presented there, and suppressing all the rest.

But it turns out that there is a lot of data that appears to conflict with theism that needs to be added to the data pool before we can properly assess the hypotheses. Some of this evidence includes:

D6: massive amounts of apparently random and pointless suffering
D7: massive religious diversity
D8: empirical studies on the ineffectiveness of prayer
D9: the apparent hiddenness of God
D10: evolution

But once we throw in this data, it's no longer clear whether H1 (i.e., theism) is more probable than H2 (i.e., naturalism): even if the probability of H1 was about .9 on D1-D5, it sinks down to about .5 (i.e., 50%) when we evaluate it on D1-D10. At worst, H1 is lower than .5 on the total evidence.

So it seems to me that cumulative case arguments for theism fare no better than the same arguments taken singly.

1. See especially his classic book, The Existence of God (Oxford: Clarendon Press, 1979). In this post, I refer to the revised edition (1991). An extensively revised edition was released in 2004. A popular-level presentation of the main ideas in that book can be found in his book, Is there a God? (Oxford: OUP, 1996).

2. While this is roughly correct, technically it isn't quite right. In at least the original edition, Swinburne argues for the weaker claim that, taken together, the arguments for theism he endorses give theism a probability of at least .5 (50%), or thereabouts. He then argues that (what he dubs) the Principle of Credulity applies to religious experience -- i.e., like ordinary perceptual and memory experience, religious experience enjoys prima facie justification (it's "innocent until proven guilty"). But since he thinks he's shown that theism isn't improbable on the evidence (i.e., it's not less than 50% probable), then the prima facie justification of religious experience isn't undercut, and thus religious experience of God justifies theism. In an appendix in the 1991 version of the book, he considers the new "fine-tuning" version of the design argument, and concludes that with this new piece of data, theism is indeed more probable than not, in which case there is a decent P-inductive, cumulative case argument for theism. I haven't read the newest edition of Swinburne's book, but I believe he is even more optimistic about the cumulative case for theism is if anything even stronger than he thought in his 1991 version.

3. Moreland's views here are a bit more optimistic than Swinburne's. He thinks that there are a lot of sound deductive arguments for theism, and that several versions of the design argument are good P-inductive arguments all by themselves. Thus, the function of a cumulative case for theism isn't primarily to make theism more probable than not, but rather to (i) provide a finer-grained conception of the identity of the God established by the arguments (e.g., to rule out deism), and (ii) to strengthen a theistic case already made strong by most of the arguments taken by themselves. See his "rope" analogy of theistic arguments in his debate with Kai Neilsen (Does God Exist? The Great Debate), as well as his remarks in Philosophical Foundations for a Christian Worldview (co-authored with William Lane Craig). William Lane Craig seems to endorse this view as well. This comes out especially in his discussion of the arguments of natural theology in his popular-level debates, as well as the co-edited book on the Christian Worldview just mentioned.

4. It should be pointed out that although at least some theists take moral arguments to support theism, Swinburne does not -- indeed, he doesn't even think they make good C-inductive arguments for theism. For he takes moral truths to be necessary truths, akin to mathematical truths (e.g., 1+1=2), in which case they would exist even if God did not. See his discussion of this in his chapter on moral arguments in his The Existence of God (1991).

5. For example, Swinburne says this explicitly in the final chapter (not the appendix) of The Existence of God (1991). Plantinga says this in Warranted Christian Belief (Oxford: OUP, 2000).

6. This is of course extremely generous. For not even Swinburne thinks the probability is this high even when you add more theism-friendly pieces of data (see footnote 2, where I mention that Swinburne thinks the data give theism a posterior probability of around .5). Plantinga more-or-less agrees with Swinburne's assessment. See Plantinga's section on the Problem of Dwindling Probabilities in Warranted Christian Belief, where he argues that inductive arguments for theism aren't sufficiently strong to render religious belief epistemically appropriate.


Rayndeon said...

Excellent comments, exapologist. I think, though, it's worth pointing out that there are very good responses to show that the contingency of the universe, the fine-tuning of the universe, the existence of consciousness, and moral ontology provide *no* support for the theistic hypothesis at all. That is what most detractors of the cosmological, fine-tuning, moral, and noological arguments charge after all. And I'm strongly convinced that they are correct on that charge.

However, I'm not sure about religious experience, because that largely needs to be taken on a case by case basis, but there are certainly some general comments in order. For instance, religious experience is largely amorphous, but perhaps that problem can be solved by switching to John Hick's religious universalism, although that's *clearly* unpalatable to most Christian and Muslim philosophers.

Your point about suffering and the hiddenness of God (i.e. religious diversity, ineffective prayer, etc) is spot on, I think. Not only that, but I'm fairly convinced that the problem is not merely empirical, but *analytic*, guaranteeing a zero posterior probability on theism, via successful logical problems of evil.



exapologist said...

Hi Rayndeon,

Thanks for raising the nice points you mention. However, my point in granting the evidential force of the various pieces of data is purely for the sake of argument. The intended bite of my post is to show that the best cumulative case arguments are resounding failures even if you give them virtually the most charitable reading possible (although, as you point out, they *don't* deserve that).

Best, and happy holidays!


Anonymous said...

So it seems to me that cumulative case arguments for theism fare no better than the same arguments taken singly.

Agreed. We really don't know why there is this existence, until we ask an additional question: "why don't we know"? Asking that question sent me over to atheism.

Tim said...

Swinburne and others have explicitly responded to Plantinga's principle of dwindling probabilities. In the recent exchange with the McGrews in Phil Christi, Plantinga admits (albeit with an ill grace) that he's been caught in an error in the modeling of the historical argument.

exapologist said...

Hi Tim,

Thanks for your nice points about the subsequent responses to Plantinga's Dwindling Probabilities argument. However, the point in the footnote I mention isn't essentially tied to Plantinga's Dwindling Probabilities Argument per se. In a portion of the passage in WCB I have in mind (273ff., in the same passage as his Dwindling Probabilities Argument), he's using Swinburne's cumulative case argument as an example. He seems to agree with Swinburne's assessment, at the very end of The Existence of God, that the probability of theism on such a case isn't considerably above 1/2. He then points out that if Swinburne is right, then this isn't nearly enough to make belief in God reasonable. In other words, the cumulative case isn't sufficient to justify theistic belief even *prior to* consideration of Plantinga's Dwindling Probabilities argument.

(for completeness sake: Plantinga then gives the cumulative case the strongest possible defense, in order to knock it down. He argues that even if it *did*, contrary to reasonable guesstimates, render theism very probable -- say around .9 -- it would nonetheless get whittled down to about .5 or below, in light of the Problem of Dwindling Probabilities. But as you nicely point out, this latter argument has been knocked down in subsequent discussion).

Aside from this point, though, I'd be interested to learn whether you agree with me about my main point in this post, viz, that cumulative case arguments don't make theism more probable than not.



Anonymous said...

Ex, while I agreed with you earlier and still do, cumulative case type arguments are all one has. That's how I approach the matter in my book from the opposite perspective, dwindiling probabilities or not. There is no other alternative.

William Abraham: “It should be clear that evaluating world-views will never be based on probabilistic arguments, since one cannot simply isolate one presupposition for evaluation. The case must be cumulative--a case must be built slowly.” It is based upon cumulative case type arguments like “jurisprudence, literary exegesis, history, philosophy, and science.” “One must be well educated in the relevant moral, aesthetic, or spiritual possibilities.” But, “mastering all the relevant data and warrants needed to exercise the required personal judgment seems remote and impractical…This is surely beyond the capabilities of most ordinary mortals.” “One simply has to proceed, often in an ad hoc fashion, and work through the issues as honestly and rigorously as possible.” William J. Abraham, An Introduction to the Philosophy of Religion, (Prentice-Hall, 1985).

Anonymous said...

From my book (see what you think):

As a Thomist, Norman Geisler’s arguments start “from below.” His apologetic includes twelve successive steps: 1) Truth about reality is knowable; 2) Opposites cannot both be true; 3) The theistic God exists; 4) Miracles are possible; 5) Miracles performed in connection with a truth claim are acts of God to confirm the truth of God through a messenger of God; 6) The New Testament documents are reliable; 7) As witnessed in the New Testament, Jesus claimed to be God; 8) Jesus’ claim to divinity was proven by an unique convergence of miracles; 9) Therefore, Jesus was God in human flesh; 10) Whatever Jesus (who is God) affirmed as true, is true; 11) Jesus affirmed that the Bible is the Word of God; 12) Therefore, it is true that the Bible is the Word of God and whatever is opposed to any biblical truth is false.” The thing about these twelve apologetical steps is that his whole case will fall to the ground if any one step if shown faulty. I will argue against several of these steps in this book. I’m not even so sure of his first step!

Furthermore, Alvin Plantinga has proposed something he calls the “Principle of Dwindling Probabilities” against cumulative case type arguments in general, using Richard Swinburne’s case for theism in specific. If we take Norman Geisler’s twelve step apologetics as our example we see that each successive step is built on the probability of the previous step. If, for instance, the probability of step six is 75%, and if each successive step through to number twelve is also 75% (being very generous), then the result is a probability of about 13% for his whole case. That’s because we simply multiply the percentages to find the probability of the final conclusion.

So even though I’ll present a cumulative case against Christianity, I don’t have any successive steps for my control beliefs which are built on any previous one. Unlike Dr. Geisler, when I start “from below” I begin with several epistemological issues to see which set of control beliefs I should adopt when coming to the Christian faith, and rather than being built on each previous step they are separate arguments that reinforce each other.

Tim said...


Thanks for the response.

Swinburne doesn't think the probability of theism is barely over .5 on all of the public evidence; he merely thinks the considerations he has given so far -- broadly, the arguments of natural theology -- do the job of getting it to that point. So you should not represent Swinburne as concurring with Plantinga that the probability of theism overall is barely (if at all) over .5.

Swinburne's argument is stratified, and for good reason; if you try to do the teleological argument first, for example, then you have a problem estimating the additional force of the cosmological argument independently since some of the data have already been presupposed. His full argument is built across several works. The Existence of God merely presents the first steps. Check out Revelation: From Metaphor to Analogy and The Resurrection of God Incarnate.

I think your post does not bring out very clearly the structure of cumulative case arguments. A cumulative case is, to start with, a case: it is a presentation of favorable evidence, including (if the context warrants and space permits) a consideration of some of the most salient pieces of counter-evidence. When the topic is very broad -- and theism certainly qualifies -- it is particularly difficult to give full consideration both to the positive evidence and to the negative considerations. Good, sober, serious work on the topic could fill a library.

There is always, in any empirical case of this sort, the theoretical possibility that at the last minute we will discover some piece of evidence that scotches the entire argument. But this holds good for any cumulative argument, including (say) the argument for the age of the earth or the antiquity of man or the death of Julius Caesar. The bare possibility should not, and in practice does not, paralyze us; as long as the case is founded on a reasonably broad base of evidence and there are no glaring problems, it may do its job well.

It belongs to the advocate for the other side to bring forward objections, and you raise five of them:

D6: massive amounts of apparently random and pointless suffering
D7: massive religious diversity
D8: empirical studies on the ineffectiveness of prayer
D9: the apparent hiddenness of God
D10: evolution

To evaluate the weight of these considerations against the cumulative case mounted, we would have to get into details across a wide range of disciplines including history, theology, science, metaphysics, and epistemology. Much depends also on the version of theism one has in view. D6 cuts through Precious Moments Theism like a Damascus blade through a silk cushion; it is not so effective against sophisticated versions of Judaism, Christianity, and Islam. D7 has always seemed to me to be a weak consideration; I do not even know whether there is any organized theistic group that would have a problem coping with it as a piece of evidence. D8 is effective only given a considerable number of assumptions not shared by all thoughtful theists; I wouldn't use this as an argument unless I were contesting a specific form of fundamentalism or charismatic evangelicalism. D9 needs to be fleshed out more; if it is not to collaspe into D6 (i.e. into the silence of God), then it does not seem to me to be a strong consideration against major monotheisms. D10 is susceptible of a number of interpretations. If evolution is interpreted fairly broadly, it is compatible with plausible versions of each of the major monotheistic religions, though not with the fundamentalist versions of them. As Michael Roberts has pointed out recently, the majority of Christian scholars even in the late 1700s accepted an old earth, well before Lyell and Darwin.

If evolution is interpreted more narrowly (as entailing atheism), then of course it cannot be absorbed into any version of theism. But it's also much harder to make the case that, taken that way, it's true.

So though I agree that some of the considerations you raise are pertinent to the overall case for theism, I do not think you have succeeded in showing that a cumulative case does not succeed. And it is another thing altogether to suggest that the assembly of the components of a cumulative case "fare no better" than they do taken singly. This is too strong a claim even if, on the total evidence we have at present, theism is less probable than not. For it may be that the cumulative case shows that the evidence is nearly balanced, where taking only one line of argument into account it might favor atheism heavily. And of course, mutatis mutandis, presentation of only one of the lines of argument against theism without others might leave us with an inflated conception of the strength of the case for theism.

exapologist said...

Hi John,

No, I agree with you -- a cumulative case is all we've got. I agree with Tim that Plantinga's Dwindling Probabilities argument doesn't work. My own view is that the evidence isn't amenable to fine-grained probability assignments, but if I were to ball-park it, I would say that the evidence is, at best, roughly 1/2 (but probably a bit lower), in which case agnosticism is the most reasonable position to take.

Anonymous said...

Ex, I do believe Plantinga's PDP applies to Geisler's approach, that's why I used it against him.

Doesn't it make sense to ask why it is we cannot figure it out (i.e. agnosticism)? I argue that agnosticism is the default position everyone must share when approaching these issues, at least initially. Anyone moving off the default position has the burden of proof, for that person is making a knowledge claim. I argue it's a small step and a small knowledge claim to move in the direction of atheism, especially when compared to a full blown Christian faith.

I argue that chance events cannot be figured out hindsight. There can be no explanation for such an event. Since we cannot figure out why there is something rather than nothing, therefore there is no God. That's my knowledge claim.

What are your thoughts about this?

evangelical said...

I guess I am more in line with Moreland than Swinburne for I would say that a cumulative argument, at least a good one, would make the certainty of theism even more strongly certain. To more clearly see this, it shall behoove us to start by examining the apparentness of many of the Ds in the simplified version of the argument in this post of exapologist's.

D1:apparent universal contingency-Is the natural order, taken as a whole, merely apparently contingent? I think it is necessarily (in a non-logical sense) contigent but I deal with this point under the deductive argument from contingency so shall move on now to

D2:Apparent universal fine tuning-The natural order, taken as a whole, is fine-tuned. There is nothing apparent about it. I deal with this elsewhere too so shall immediately proceed to

D3: Apparent irreducibility of human consciousness-The only objections to its actuality that I can think of are a. a priori materialism (which begs the question) or b. brain damage affecting consciousness (which is easily explained by supposing the immaterial mind flows through the brain like radio waves through a radio. In other words, if the radio is broken, that says nothing to the 'health' of the radio waves themselves.) Finally, how could love, for example, arise naturally? Love is centered in the heart which is an aspect of the mind. The naturalist says the mind is the brain but if the brain is natural (and it is) then how could it give birth to the immaterial (i.e. love)? It could not.

D6: Apparently gratuitous evil-If you admit it is only apparent then it may not be actual, that is, it may not really be gratuitous. In any case, the problem of evil as a whole is not logically sound. If the Bible is true, then apparently gratuitous evil is not so gratuitous after all. Instead it is at least an indirect result of free-human sin.

D9: Apparent hiddenness of God-God is not hidden at all if 'hiddenness' is defined too strongly. God is clearly present from my point of view. But to speak of the hiddenness of God, prior to the conclusion of a cumulative case for the existence (or nonexistence) of God, seems to be begging the quesion. If it is not, then we may appeal to the many ways in which God has made His existence clear.

So we see that 'apparent' in D1-5 should be 'actual' and in D6-10 it ('apparent') should be 'actually not'.

This leaves us only a few Ds to look at.

D4: multitudinous religious experience-It is hard to argue that there is such. If one wants to use this as negative evidence, that comes under D7. But D7 can be easily answered by supposing that the various religions are misinterpreting their experiences.

D5:ethical grounding-I see no way to ground ethics objectively if their is no God. Consider a syllogism made famous by Craig:
1. If objective moral values don't exist, God does not exist.
2. Objective moral values do exist.
3. Therefore, God exists.
No morals = no God. Morals = God. How could anyone argue with this?

D8: Fulfilled prayer statistically insignificant-How is this relevant data? God does not promise, at least in my own tradition, to answer every prayer in the affirmative. Or, it is possible that God answers less prayer just during studies because He wants to answer prayers of the believers (and a scientist testing prayer is, at least methodologically, a non-believer).

D10:Evolution-I guess you've never heard of theistic evolution.

Now let's restate the simplified argument with our new insights.

D1: The universe is contingent.
D2: The universe is fine-tuned.
D3: The human consciousness is not irreducible to the physical.
D4: There are religious experiences of various sorts. These require some sort of explanation.
D5: There is morality which could only come from a God.
D6: Since there is could be freedom there is the possibility of sin. There is sin which brings with it, according to theists, consequences of suffering that is, apparently, otherwise gratiutous.
D7:There is a massive diversity of religious doctrinal systems though all may be, to some extent, true or at least they may easily point to the truth of theistic being which may exist.
D8:There is no reason to suppose prayer is empirically testable.
D9:God is not as plain as He could be but He is plain enough to be known to exist beyond any doubt. Philosophical theology, for example, tells us this.
D10:Apparently God, if He exists, created through evolution.

Now, in these ten Ds, taken individually or collectively, I see nothing which makes the nonexistence of God probable (>50%) at all. So H1 is certainly at least more certain that H2. I personally would go farther and say it is absolutely certain.


exapologist said...

Hi Evangelical.

Thanks for your comment. I sympathize with your ambitiousness, but I think discussing a comprehensive assessent of theism vis-a-vis naturalism is beyond the scope of a comment thread. However, a more managable way to discuss such a topic would be to reduce it to its parts. Thus, we can discuss the arguments taken individually under the heading of the respective posts discussing each line of evidence. As such, I would defer you to those posts.

I see that you've started to do just this. I promise I'll address them as time permits. For now, I would suggest that we finish our discussion of Behe's argument, and then we can move on to other posts.



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