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 the 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.
=======================================
Footnotes:
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 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..
Richard Swinburne is one famous philosopher of religion who takes this approach to arguments for theism[1]. He uses a formula from the 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.
=======================================
Footnotes:
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 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..