INTRODUCTION
Paul Draper has developed an argument that theists, but not atheists, bear a burden of proof based on his theory of intrinsic probability. The purpose of this post will be to determine the soundness of this argument.
INTRINSIC PROBABILITY
The intrinsic probability of a hypothesis is the prior probability of a hypothesis independent of any data or background knowledge. It tells you the absolute prior probability of a hypothesis before we consider the evidence for that hypothesis, “If we abstract from all factors extrinsic to a hypothesis, then the only thing that could affect the epistemic probability of that hypothesis is how much it says and how well what it says fits together. No other factors affecting probability could be intrinsic to the hypothesis.”[1] There are two criteria for assessing the intrinsic probability of a hypothesis, coherence and modesty:
Paul Draper has developed an argument that theists, but not atheists, bear a burden of proof based on his theory of intrinsic probability. The purpose of this post will be to determine the soundness of this argument.
INTRINSIC PROBABILITY
The intrinsic probability of a hypothesis is the prior probability of a hypothesis independent of any data or background knowledge. It tells you the absolute prior probability of a hypothesis before we consider the evidence for that hypothesis, “If we abstract from all factors extrinsic to a hypothesis, then the only thing that could affect the epistemic probability of that hypothesis is how much it says and how well what it says fits together. No other factors affecting probability could be intrinsic to the hypothesis.”[1] There are two criteria for assessing the intrinsic probability of a hypothesis, coherence and modesty:
COHERENCE: “The coherence of a hypothesis depends on how well its components fit together.”[2] This will include the uniformity of a hypothesis.
MODESTY: “The modesty of a hypothesis is inversely proportional to its “content”—to how much it says. Hypotheses that say less—for example, because they make fewer claims or less specific claims or claims that are narrower in scope—are, other things being equal, more likely to be true than hypotheses that say more.”[3] This will include the scope, and specificity of a hypothesis.
NATURALISM, SUPERNATURALISM, AND OTHERISM
The definitions of naturalism, supernaturalism, and otherism are as follows:
Naturalism is the hypothesis that “…the physical world existed prior to any mental world and caused any mental world to come into existence.”
Supernaturalism is the hypothesis that “…the mental world existed prior to any physical world and caused any physical world to come into existence.”
“Otherism is the statement that both naturalism and supernaturalism are false.”[4]
When we apply the criteria of coherence and modesty to these three hypotheses the result is as follows:
“Naturalism and supernaturalism are equally probable intrinsically because they are equally modest and coherent. Since the intrinsic epistemic probability of otherism is greater than zero, naturalism and supernaturalism are each less probable intrinsically than their denials. So both naturalists and supernaturalists bear a burden of proof and that burden is equal.”[5]
THE INTRINSIC PROBABILITIES OF ATHEISM AND THEISM
The next move for Draper in showing that theists, but not atheists, bear a burden of proof is to argue that theism is many times less probable than supernaturalism because it adds several claims to the claims of supernaturalism while atheism is a less specific version of naturalism, and so, atheism is many times more probable than naturalism:
“a. Theism is a very specific version of supernaturalism and so is many times (i.e. at least 10 times) less probable intrinsically than supernaturalism.
b. Naturalism is a specific version of atheism and so is many times less probable than atheism.
c. Thus, since naturalism and supernaturalism are equally probable intrinsically, it follows that atheism is many times more probable intrinsically than theism, which entails that atheism has a high intrinsic probability (certainly higher than .9) while theism has a very low intrinsic probability (certainly lower than .1).”
d. Therefore, theists but not atheists bear the burden of proof.” [6]
ASSESSMENT OF DRAPER’S ARGUMENT
FIRST PART: As noted in the beginning, intrinsic probabilities are determined apart from, and independently of all data and background information. That is, before we look at any actual evidence in favor of theism, it has a lower intrinsic probability than naturalism, and especially atheism. While this is true on Draper’s theory of probability, there are three important facts to keep in mind:
There are three significant implications that follow from this concession. First, if there is evidence to think that a personal and absolutely perfect being exists necessarily, then theism has a high prior probability, while atheism and naturalism would have a prior probability that is virtually zero (because we are dealing in epistemic probabilities the probability wouldn’t necessarily be exactly zero). Second, if there is evidence that establishes either that a supernatural person exists necessarily, or that a supernatural perfect person exists necessarily, but not both, then naturalism would be necessarily false, while some version of supernaturalism would be necessarily true. Third, because it is impossible for either of these implications to be true on naturalism, it follows from probability theory that even weak evidence for the existence of a necessary being that exists in either one, or both ways above, is moderately strong evidence that naturalism is necessarily false.
Draper would object as he did in The Great Debate (On The Plausibility Of Naturalism And The Seriousness Of The Argument From Evil) to Plantinga : "...theism asserts that the natural world was created by an omnipotent, omniscient, and morally perfect person, which assumes, not only that there is a maximum possible degree of power, knowledge, and moral goodness, but also that these three attributes are compatible with each other and with the existence of natural entities. Even ignoring specific arguments, clearly it is much more likely that some hidden incoherence lurks in the assertion that there exists a creator of nature possessing the highest possible degree of several distinct scaling properties than in the simple assertion that no such creator exists. Therefore, if I am mistaken and theism really is a necessary proposition, then it is very probably a necessary falsehood, which means that my assumption in my opening case that it is a contingent proposition is not only dialectically appropriate (for the reasons given in the previous paragraph), but dialectically generous."
I have two responses. First, this objection commits the gambler's fallacy. Second, as Yujin Nagasawa has argued (A New Defense of Anselmian Theism), theism is committed to the notion of the greatest conceivable being. However, the notion of the greatest conceivable being doesn't entail an OMNI-God. Hence, if there are any arguments which show the logical impossibility of a single, or set of OMNI attributes, then all that would show is that we cannot conceive of an OMNI-God, not that theism is necessarily false.
SECOND PART: Another legitimate strategy to completely avoid Draper’s burden of proof argument would be to engage in theory building. Theory building involves explaining some phenomena where a specific theory or set of theories fall out naturally one after the other from a more general theory. New predictions are confirmed by new evidence at every transition from a more general theory to a more specific theory. For example:
“There is an astronomical object by the name of Cygnus X-1 that many astronomers think is a black hole. In fact, it is widely regarded as the most probable object to be identified as a black hole. Now the evidence that would establish the identity of Cygnus X-1 as a black hole can be analyzed in this same way. First, you have to assume the Copernican Hypothesis. The Copernican Hypothesis is that the same laws of nature that operate here on Earth operate in distant galaxies and in outer space. If there were totally different laws, then we could not make any inference. So you have got to start by assuming some sort of Copernican principle. Secondly, the General Theory of Relativity needs to be true. In order for black holes like this to exist, you would have to assume Einstein’s General Theory of Relativity. Thirdly, you need to think that it is probable that the x-ray eclipse of the companion body of Cygnus X-1 is caused by Cygnus X-1 itself. There is a kind of x-ray flux in and out that goes on in its companion body, and you have to say that there must be an invisible object that is causing this. Fourth, the orbit of this companion object indicates that the object is three to four times the mass of the sun – it is about three to four solar masses. And this is an inference based on its orbit – it is the evidence of the orbit that makes you think that Cygnus X-1 is about three to four times the mass of the sun. Fifth, the flickering x-ray output of the object gives it a size of about nine-miles in diameter. So you must infer that this is about the size of the object based on these flickering x-ray outputs. Sixth, no other object can be this small and yet this massive. For example, a neutron star might be an alternative to a black hole, but a neutron star cannot be so small and yet so massive. So, on the basis of these lines of inference, the inference is that Cygnus X-1 is most probably a black hole.”[10]
In the case of Draper’s argument, what we would do is start off with a general hypothesis that has a high absolute prior probability (e.g. supernaturalism), or one that is not so low when compared to naturalism and atheism that the burden of proof is one sided, and then build up to a more specific hypothesis (e.g. Christian theism) in evidential stages. So for example:
STEP 1: Start off with the hypothesis of supernaturalism, and argue that the existence of self-
consciousness, the beginning of the universe, and the contingency of the universe not only confirms supernaturalism over naturalism, but two of those arguments show that naturalism is necessarily false. Moreover, such arguments move us beyond mere supernaturalism by making it likely a powerful, personal, and unembodied mind exists. It is extremely important to note that virtually none of the arguments typically launched against theism by atheists and naturalists even apply to supernaturalism!
STEP 2: Add a further claim to this personal supernaturalism; something akin to axiarchism by saying that this powerful, personal unembodied mind is essentially good; and then argue that the existence of embodied moral agents, the beauty and simplicity of mathematics, the discoverability of the universe, the formational economy of the universe, the existence of objective moral facts, and the like confirm this more specific hypothesis. Here is where the typical arguments atheists and naturalists lodge against theism will come into play but notice that the absolute prior probability at this stage is many times higher than theism still, and the explanatory power of supernaturalism from stage 1 is very very many times more probable compared to naturalism and atheism! And of course any evidence in a later stage is evidence for an earlier stage as well.
STEP 3: Add a further claim to personal supernatural axiarchism which would be something like this being has revealed it’s will for us in the person of Jesus by raising him from the dead, and bring in the case for the resurrection.
STEP 4: Go back to Draper’s theory of intrinsic probability which says that theism has the greatest intrinsic probability of all the supernatural hypotheses if we weight coherence higher than modesty.
CONCLUSION: Theism only starts off with a low absolute prior probability if we start off with that hypothesis rather than arrive at it. More specific hypotheses can increase in probability rather than start off with a low prior probability when one engages in theory building which involves conditioning on new evidence each time a new claim or hypothesis is added to a more general hypothesis.
SUMMARY AND CONCLUSION
Draper’s theory of intrinsic probability is controversial, but even if we grant its validity and soundness, the key question becomes: Is there at least weak evidence that shows the necessity of some form of supernaturalism, and/or theism to be true? If the answer is yes to one or both of these questions, then naturalism is necessarily false, and/or theism is necessarily true. Since the answer is yes to both of these questions:
Kalam Cosmological Argument
http://www.apologeticsinthechurch.com/uploads/7/4/5/6/7456646/craig-and-sinclair-the-kalam-cosmological-argument.pdf
Leibnizian Cosmological Argument
http://www.apologeticsinthechurch.com/arguments-for-the-existence-of-god/the-leibnizian-cosmological-argument-by-alexander-pruss
Moral Argument From Necessary Moral Truths
http://www.apologeticsinthechurch.com/uploads/7/4/5/6/7456646/dealing_with_more_objections_to_the_moral_argument.pdf
this implies that naturalists and atheists have the burden of proof either to offer positive evidence for their hypotheses, or show that such arguments for theism are logically impossible because even weak evidence for a necessary being shifts the burden of proof back to the atheists and naturalists. Since it cannot be shown that such arguments are logically impossible, atheists and naturalists have the burden of proof to offer a positive case for their respective hypotheses. Thus, in this first sense, Draper's argument is correct, but the burden of proof is easy to shift. In another sense however, we saw that if we engage in theory building, or hypothesis building, Draper is placing an unnecessary burden of proof on theists, and Christian theists at that! Lastly, Draper’s theory of probability can actually assist the case for theism by showing that it has the highest intrinsic probability of all its supernatural rivals.
[1] Paul Draper, God and the Burden of Proof
[2] ibid
[3] ibid
[4] ibid
[5] ibid
[6] ibid
[7] I owe this point to Lydia McGrew
[8] Taken from Paul Draper’s talk at Purdue in honor of Richard Swinburne
[9] Paul Draper, Christian Faith and the Problem of Evil, ed. by Peter Van Inwagen, More Pain and Pleasure: A Reply to Otte, pg. 47
[10] William Lane Craig, http://www.reasonablefaith.org/defenders-2-podcast/transcript/s6- 23
MODESTY: “The modesty of a hypothesis is inversely proportional to its “content”—to how much it says. Hypotheses that say less—for example, because they make fewer claims or less specific claims or claims that are narrower in scope—are, other things being equal, more likely to be true than hypotheses that say more.”[3] This will include the scope, and specificity of a hypothesis.
NATURALISM, SUPERNATURALISM, AND OTHERISM
The definitions of naturalism, supernaturalism, and otherism are as follows:
Naturalism is the hypothesis that “…the physical world existed prior to any mental world and caused any mental world to come into existence.”
Supernaturalism is the hypothesis that “…the mental world existed prior to any physical world and caused any physical world to come into existence.”
“Otherism is the statement that both naturalism and supernaturalism are false.”[4]
When we apply the criteria of coherence and modesty to these three hypotheses the result is as follows:
“Naturalism and supernaturalism are equally probable intrinsically because they are equally modest and coherent. Since the intrinsic epistemic probability of otherism is greater than zero, naturalism and supernaturalism are each less probable intrinsically than their denials. So both naturalists and supernaturalists bear a burden of proof and that burden is equal.”[5]
THE INTRINSIC PROBABILITIES OF ATHEISM AND THEISM
The next move for Draper in showing that theists, but not atheists, bear a burden of proof is to argue that theism is many times less probable than supernaturalism because it adds several claims to the claims of supernaturalism while atheism is a less specific version of naturalism, and so, atheism is many times more probable than naturalism:
“a. Theism is a very specific version of supernaturalism and so is many times (i.e. at least 10 times) less probable intrinsically than supernaturalism.
b. Naturalism is a specific version of atheism and so is many times less probable than atheism.
c. Thus, since naturalism and supernaturalism are equally probable intrinsically, it follows that atheism is many times more probable intrinsically than theism, which entails that atheism has a high intrinsic probability (certainly higher than .9) while theism has a very low intrinsic probability (certainly lower than .1).”
d. Therefore, theists but not atheists bear the burden of proof.” [6]
ASSESSMENT OF DRAPER’S ARGUMENT
FIRST PART: As noted in the beginning, intrinsic probabilities are determined apart from, and independently of all data and background information. That is, before we look at any actual evidence in favor of theism, it has a lower intrinsic probability than naturalism, and especially atheism. While this is true on Draper’s theory of probability, there are three important facts to keep in mind:
- In our day to day lives, hypotheses with lower intrinsic probabilities are confirmed with a high degree of confidence. Just start thinking about the proposition that the Holocaust took place, that the Civil War took place, that your mother exists (complete with all the stuff you know about your mother), and a million other "complex" propositions that are obviously well-justified. The entire idea of looking at things and not fretting because they have such a huge hurdle of low prior probability to overcome is epistemologically commonplace.[7]
- Draper’s theory can be used to show that theism has a greater intrinsic probability than its supernatural rivals. If coherence (uniformity) is given more weight than modesty in determining intrinsic probability then theism can be shown to have a higher intrinsic probability than its supernatural rivals:
- Polytheistic explanations for example postulate many gods and hence a variety that theism doesn’t.
- Quasi-theism postulates a finite god that is not Omni which exhibits much less uniformity than the theistic gods. An OMNI-God (omniscient, omnipotent, everlasting, and the like) is more coherent than forms of quasi-theism because to postulate that God can bring about some contingent future states but not others is less coherent than an omnipotent God because the ability to bring about some such states is evidence to bring about other states. Moreover, omniscience is intrinsically more likely than limited knowledge. Postulating a being that is everlasting and uniformly lacks all non-rational desires is more coherent than a supernatural being that has a variety of non-rational desires as well (e.g. process theism).
- Non-personal forms of supernaturalism are strongly incoherent because any mind that can act must have abilities, powers, knowledge, desires and a duration of existence which means this mind cannot be anything other than a mind that has a variety of non-rational desires, finite powers, and finite knowledge which is all less coherent than theism.[8]
There are three significant implications that follow from this concession. First, if there is evidence to think that a personal and absolutely perfect being exists necessarily, then theism has a high prior probability, while atheism and naturalism would have a prior probability that is virtually zero (because we are dealing in epistemic probabilities the probability wouldn’t necessarily be exactly zero). Second, if there is evidence that establishes either that a supernatural person exists necessarily, or that a supernatural perfect person exists necessarily, but not both, then naturalism would be necessarily false, while some version of supernaturalism would be necessarily true. Third, because it is impossible for either of these implications to be true on naturalism, it follows from probability theory that even weak evidence for the existence of a necessary being that exists in either one, or both ways above, is moderately strong evidence that naturalism is necessarily false.
Draper would object as he did in The Great Debate (On The Plausibility Of Naturalism And The Seriousness Of The Argument From Evil) to Plantinga : "...theism asserts that the natural world was created by an omnipotent, omniscient, and morally perfect person, which assumes, not only that there is a maximum possible degree of power, knowledge, and moral goodness, but also that these three attributes are compatible with each other and with the existence of natural entities. Even ignoring specific arguments, clearly it is much more likely that some hidden incoherence lurks in the assertion that there exists a creator of nature possessing the highest possible degree of several distinct scaling properties than in the simple assertion that no such creator exists. Therefore, if I am mistaken and theism really is a necessary proposition, then it is very probably a necessary falsehood, which means that my assumption in my opening case that it is a contingent proposition is not only dialectically appropriate (for the reasons given in the previous paragraph), but dialectically generous."
I have two responses. First, this objection commits the gambler's fallacy. Second, as Yujin Nagasawa has argued (A New Defense of Anselmian Theism), theism is committed to the notion of the greatest conceivable being. However, the notion of the greatest conceivable being doesn't entail an OMNI-God. Hence, if there are any arguments which show the logical impossibility of a single, or set of OMNI attributes, then all that would show is that we cannot conceive of an OMNI-God, not that theism is necessarily false.
SECOND PART: Another legitimate strategy to completely avoid Draper’s burden of proof argument would be to engage in theory building. Theory building involves explaining some phenomena where a specific theory or set of theories fall out naturally one after the other from a more general theory. New predictions are confirmed by new evidence at every transition from a more general theory to a more specific theory. For example:
“There is an astronomical object by the name of Cygnus X-1 that many astronomers think is a black hole. In fact, it is widely regarded as the most probable object to be identified as a black hole. Now the evidence that would establish the identity of Cygnus X-1 as a black hole can be analyzed in this same way. First, you have to assume the Copernican Hypothesis. The Copernican Hypothesis is that the same laws of nature that operate here on Earth operate in distant galaxies and in outer space. If there were totally different laws, then we could not make any inference. So you have got to start by assuming some sort of Copernican principle. Secondly, the General Theory of Relativity needs to be true. In order for black holes like this to exist, you would have to assume Einstein’s General Theory of Relativity. Thirdly, you need to think that it is probable that the x-ray eclipse of the companion body of Cygnus X-1 is caused by Cygnus X-1 itself. There is a kind of x-ray flux in and out that goes on in its companion body, and you have to say that there must be an invisible object that is causing this. Fourth, the orbit of this companion object indicates that the object is three to four times the mass of the sun – it is about three to four solar masses. And this is an inference based on its orbit – it is the evidence of the orbit that makes you think that Cygnus X-1 is about three to four times the mass of the sun. Fifth, the flickering x-ray output of the object gives it a size of about nine-miles in diameter. So you must infer that this is about the size of the object based on these flickering x-ray outputs. Sixth, no other object can be this small and yet this massive. For example, a neutron star might be an alternative to a black hole, but a neutron star cannot be so small and yet so massive. So, on the basis of these lines of inference, the inference is that Cygnus X-1 is most probably a black hole.”[10]
In the case of Draper’s argument, what we would do is start off with a general hypothesis that has a high absolute prior probability (e.g. supernaturalism), or one that is not so low when compared to naturalism and atheism that the burden of proof is one sided, and then build up to a more specific hypothesis (e.g. Christian theism) in evidential stages. So for example:
STEP 1: Start off with the hypothesis of supernaturalism, and argue that the existence of self-
consciousness, the beginning of the universe, and the contingency of the universe not only confirms supernaturalism over naturalism, but two of those arguments show that naturalism is necessarily false. Moreover, such arguments move us beyond mere supernaturalism by making it likely a powerful, personal, and unembodied mind exists. It is extremely important to note that virtually none of the arguments typically launched against theism by atheists and naturalists even apply to supernaturalism!
STEP 2: Add a further claim to this personal supernaturalism; something akin to axiarchism by saying that this powerful, personal unembodied mind is essentially good; and then argue that the existence of embodied moral agents, the beauty and simplicity of mathematics, the discoverability of the universe, the formational economy of the universe, the existence of objective moral facts, and the like confirm this more specific hypothesis. Here is where the typical arguments atheists and naturalists lodge against theism will come into play but notice that the absolute prior probability at this stage is many times higher than theism still, and the explanatory power of supernaturalism from stage 1 is very very many times more probable compared to naturalism and atheism! And of course any evidence in a later stage is evidence for an earlier stage as well.
STEP 3: Add a further claim to personal supernatural axiarchism which would be something like this being has revealed it’s will for us in the person of Jesus by raising him from the dead, and bring in the case for the resurrection.
STEP 4: Go back to Draper’s theory of intrinsic probability which says that theism has the greatest intrinsic probability of all the supernatural hypotheses if we weight coherence higher than modesty.
CONCLUSION: Theism only starts off with a low absolute prior probability if we start off with that hypothesis rather than arrive at it. More specific hypotheses can increase in probability rather than start off with a low prior probability when one engages in theory building which involves conditioning on new evidence each time a new claim or hypothesis is added to a more general hypothesis.
SUMMARY AND CONCLUSION
Draper’s theory of intrinsic probability is controversial, but even if we grant its validity and soundness, the key question becomes: Is there at least weak evidence that shows the necessity of some form of supernaturalism, and/or theism to be true? If the answer is yes to one or both of these questions, then naturalism is necessarily false, and/or theism is necessarily true. Since the answer is yes to both of these questions:
- Necessarily, a personal and supernatural being exists:
Kalam Cosmological Argument
http://www.apologeticsinthechurch.com/uploads/7/4/5/6/7456646/craig-and-sinclair-the-kalam-cosmological-argument.pdf
Leibnizian Cosmological Argument
http://www.apologeticsinthechurch.com/arguments-for-the-existence-of-god/the-leibnizian-cosmological-argument-by-alexander-pruss
- Necessarily, a personal, supernatural, and essentially good being exists
Moral Argument From Necessary Moral Truths
http://www.apologeticsinthechurch.com/uploads/7/4/5/6/7456646/dealing_with_more_objections_to_the_moral_argument.pdf
this implies that naturalists and atheists have the burden of proof either to offer positive evidence for their hypotheses, or show that such arguments for theism are logically impossible because even weak evidence for a necessary being shifts the burden of proof back to the atheists and naturalists. Since it cannot be shown that such arguments are logically impossible, atheists and naturalists have the burden of proof to offer a positive case for their respective hypotheses. Thus, in this first sense, Draper's argument is correct, but the burden of proof is easy to shift. In another sense however, we saw that if we engage in theory building, or hypothesis building, Draper is placing an unnecessary burden of proof on theists, and Christian theists at that! Lastly, Draper’s theory of probability can actually assist the case for theism by showing that it has the highest intrinsic probability of all its supernatural rivals.
[1] Paul Draper, God and the Burden of Proof
[2] ibid
[3] ibid
[4] ibid
[5] ibid
[6] ibid
[7] I owe this point to Lydia McGrew
[8] Taken from Paul Draper’s talk at Purdue in honor of Richard Swinburne
[9] Paul Draper, Christian Faith and the Problem of Evil, ed. by Peter Van Inwagen, More Pain and Pleasure: A Reply to Otte, pg. 47
[10] William Lane Craig, http://www.reasonablefaith.org/defenders-2-podcast/transcript/s6- 23
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