bookmark_borderAn F-Inductive Argument from Consciousness for Theism, Revisited

Edited on 15-Feb-20
While some theistic arguments are “God of the gaps” arguments, many, including those defended by Christian philosophers, are not “God of the gaps” arguments. Before accusing a theist of trotting out another “God-of-the-gaps” argument, atheists should first verify that the argument actually is a “God-of-the-gaps” argument.
Here is the basic structure of a “God-of-the-gaps” argument:

  1. Some odd or puzzling thing, E, occurs or exists.
  2. Science is unable to offer a plausible, God-free explanation for E.
  3. Therefore, God is the best explanation for E.
  4. Therefore, God exists.

There are many, well-known problems with such arguments. I’ve written on this topic elsewhere, so I won’t repeat those points here. Instead, I want to sketch how a theistic argument can avoid appealing to a gap in scientific knowledge. Here is the structure of an F-inductive argument from consciousness:
Let E=consciousness exists; N=naturalism; T=theism; B=background information; Pr(|H|)=the intrinsic probability of H; and Pr(x|y)=the epistemic probability of x conditional upon y

  1. E is known to be true, i.e., Pr(E) is close to 1.
  2. N is not intrinsically much more probable than T, i.e., Pr(|N|) is not much greater than Pr(|T|).
  3. Pr(E| T & B) > Pr(E | N & B).
  4. Therefore, other evidence held equal, N is probably false, i.e., Pr(T | B & E) > 0.5.

Whatever problems may exist with that argument, being a “God of the gaps” argument isn’t one of them. The present inability of science to explain consciousness plays no role whatsoever in the argument. What’s doing the work in the argument is the fact that theism, as a version of supernaturalism, entails that consciousness exists, whereas naturalism has no such entailment.
Allow me to explain. “Naturalism” is really just short-hand for “source physicalism,” which says that the physical world exists and, if the mental world exists, the physical explains why the mental exists (or, to allow for eliminative materialists, appears to exist). “Supernaturalism” is really just short-hand for “source idealism,” which says that a mental world exists and, if a physical world exists, the mental explains why the physical exists (or, to allow for eliminative idealists, appears to exist). “Theism” is a specific version of supernaturalism; it says that the mental being or entity which explains why the physical exists is a perfect supernatural person.
N.B. While theism does not entail human consciousness exists, theism does entail consciousness exists because theism entails that God exists and God is conscious, by definition. In contrast, naturalism is compatible with the non-existence of consciousness. So the existence of human consciousness, while not entailed by theism, isn’t surprising on theism in the way it is on naturalism. In that sense, human consciousness is evidence favoring theism over naturalism.
Objections to the Argument
Objection to (1): “We have no idea what ‘consciousness’, ‘mental,’ and ‘physical’ mean. Science can’t explain some E if the E is poorly defined.”
Reply: By a “mental world,” I mean the existence of a private, subjective world. By a “physical world,” I mean the existence of a public, objective world. By “consciousness,” I mean sentience.
Objection to (2): “But intrinsic probabilities don’t appeal to the propositions included in our background knowledge, and so ignore prior probabilities.”
Reply: As we say in computer science, that’s a feature, not a bug. Intrinsic probabilities come before prior probabilities. As the name implies, intrinsic probabilities are probabilities determined solely by the intrinsic properties of a proposition. Draper has argued (convincingly, in my opinion) that intrinsic probabilities are determined by scope, modesty, and nothing else. In contrast, prior probabilities are determined by the propositions in our background knowledge, such as “A physical universe exists,” “The universe is life-permitting,” “So much of the physical world is intelligible without appeal to supernatural agency,” and so forth.
Objection to (3): “The claim that Pr(E | T & B) > Pr(E | N & B) is unfounded because generic or mere theism doesn’t contain enough information to predict or demystify E. One would have to appeal to a specific kind of theism to justify something like (3), but a more specific kind of theism would have a lower intrinsic probability than mere theism.”
Reply: This is false for the reason explained above. While theism does not entail human consciousness exists, theism does entail consciousness exists because theism entails that God exists and God is conscious, by definition. In contrast, naturalism is compatible with the non-existence of consciousness. So the existence of human consciousness, while not entailed by theism, isn’t surprising on theism in the way it is on naturalism. In that sense, human consciousness is evidence favoring theism over naturalism.
Objection to (4): “But consciousness depends upon a physical brain. That’s more probable on naturalism than on theism.”
Reply: Correct. We know much more about the mental than the fact that it exists. We also know that it is dependent upon the brain, a fact which is much more likely on naturalism than on theism. So, once the evidence about consciousness is fully stated, it’s clear that there is also evidence favoring naturalism over theism. That fact, however, does nothing to refute this argument, which contains an “other evidence held equal” clause in its conclusion.
Objection to (4): “But the naturalistic evidence of mind-brain dependence outweighs the theistic evidence from consciousness.”
Reply: I am not aware of anyone having offered a successful argument for that claim. It’s not clear to me how such an argument could be adequately defended.
Objection to (4): “But the history of science contains numerous examples of naturalistic explanations replacing supernatural ones and no examples of supernatural explanations replacing naturalistic ones. That gives us reason to expect that science will eventually explain consciousness without God.”
Reply: I agree that gives us some reason to expect that science will eventually explain consciousness without appealing to God. That doesn’t change the fact, pointed out by (3), that the content of “naturalism,” as I have defined it, gives us no antecedent reason to expect consciousness to exist if naturalism is true, whereas “theism,” as I have defined it, does give us an antecedent reason to expect consciousness. This promissory naturalistic ‘atheodicy’ has no logical relevance to the argument anyway.
Objection to (4): “But (4) must be false because theism is false.”
Reply: That would follow only if one assumes that there can never be true evidence for a false proposition, but why assume that? There can be circumstantial evidence that a defendant is innocent of murder, while at the same time there could be other evidence for the defendant’s guilt, such as DNA evidence, which completely outweighs the circumstantial evidence. Similarly, a theist might say, “Suffering, imperfection, poor design, and mind-brain dependence are evidence against God’s existence, but that evidence is completely outweighed by the evidence from the finite age of the universe, the life-permitting conditions of the universe, human consciousness, etc.” Similarly, even if one believes (as I do) that it’s extremely improbable that God exists, one can consistently allow that consciousness is evidence–even strong evidence–favoring theism over naturalism, while simultaneously believing that other evidence outweighs the theistic evidence. People in general need to stop taking a binary, “all-or-nothing” approach to evidence.

bookmark_borderHow to Think about Historical Evidence about Anything, Part 1: The Credibility of Testimony

Note: So far as I know, no one working in New Testament scholarship, apologetics, counter-apologetics, or ancient history is applying the concepts in this blog post. As will soon become obvious, most of the ideas in this blog post are not mine, but if other people find these techniques useful, I would appreciate being given credit for the idea to apply them outside of their source discipline.

1. Schumian Framework for Decomposition of the Credibility of Testimony

Suppose witness W testifies E* that event E occurred. We wish to determine whether E actually happened. Clearly, E* and E are not identical; we could have E* when E did not happen. E* would entail E only if W were perfectly credible; otherwise, E* is evidence of E to the degree that we consider W credible.[1] Following evidence scholar David Schum,[2] I shall analyze the credibility of testimony in terms of three major attributes: veracity, objectivity, and observational sensitivity.  These attributes can be assessed by asking three questions respectively:
(a) Does W believe what he testified? This question focuses on W’s veracity or truthfulness.  If it is doubtful that W even believed what he testified, then W is not truthful and E* does not probabilistically favor E.  On the other hand, even if W believes what he testified, it does not follow that E is true. W could be entirely honest in reporting E, but E might not have happened. This would be the case if W were unobjective or inaccurate.[3]
(b) Did W’s senses give evidence of what he believed? If not, we would say that W is not objective. This would be the case if, for example, W so strongly wished E to occur that he believed E regardless of what his senses told him.[4]
(c) Was the sensory evidence accurate? Even if W believed what he testified and W’s senses gave evidence of what he believes, it could still be the case that what W believes is false. In other words, sensory evidence is not conclusive unless we believe that W is perfectly observationally sensitive. Both W’s physical condition and the general circumstances of observation at the time of observation might have caused the sensory evidence to be inaccurate.[5]
Since there are three credibility attributes and each attribute has two possible values, it follows that there are 23=8 combinations of potential values.
1: W is honest, objective, and observationally accurate.
2: W is honest, objective, and not observationally accurate.
3: W is honest, not objective, and observationally accurate.
4: W is honest, not objective, and not observationally accurate.
5: W is not honest, objective, and observationally accurate.
6: W is not honest, objective, and not observationally accurate.
7: W is not honest, not objective, and observationally accurate.
8: W is not honest, not objective, and not observationally accurate.[6]
The decomposition of the credibility attributes of W’s testimony is illustrated in Figure 1.[7] From W’s testimony (E*) we first draw an inference about his veracity. If we conclude that W did believe what he testified (Eb), we next consider his objectivity. Again, if we conclude that W is objective (Es), we then assess his observational sensitivity. If we then conclude that his sensory evidence was accurate, we then infer that E did occur.  Each inference based upon a credibility attribute is an example of an inferential link or stage of reasoning in a chain of reasoning.
schumian-figure1

Figure 1 Stages of reasoning involving attributes of W’s credibility

As Schum correctly observes, each inferential link in a chain of reasoning must ultimately be justified on the basis of an inductive argument.[8] Typically, such justification appeals to a statistical generalization. For example, the inference from E* to Eb might appeal to the following statistical generalization concerning W’s veracity: “If an ancient author writes that an event occurred, then at the time the document was written the author probably believed that E occurred.” In support of W’s objectivity, one might argue: “If at the time of his alleged observation a person believed that an event occurred, then this person’s senses often give evidence that the event occurred.” In support of W’s observational sensitivity, one could claim: “If a person’s senses give evidence that an event occurred, then usually the event occurred.”[9]
Clearly, not just any statistical generalization can justify an inferential link in a chain of reasoning regarding the credibility a witness’s testimony. Those who have studied the formal structures of inductive arguments know that statistical generalizations are just one premise in the type of inductive argument known as the statistical syllogism.

Z percent of F are G.

x is F.

[Z% probable] Therefore, x is G.

But the Rule of Total Evidence requires that we must take into account the total relevant and available evidence when selecting F (the reference class). This makes it difficult, however, to apply statistical generalizations to unique or singular events. And W has offered a specific account (E*) about a singular event.[10] Any reference class that satisfies the Rule of Total Evidence will be so specific that there will be no frequency data available to justify the generalization.
Drawing upon the work of philosopher L.J. Cohen,[11] Schum describes a method for testing statistical generalizations about singular events that is roughly based upon eliminative induction.[12] In his words:

What we can do is to put this generalization to a variety of different relevant evidential tests, each one designed to invalidate this generalization as far as W and his present testimony are concerned. … The more of these tests that W passes, the more we are entitled to infer that this … generalization holds in the present instance of W and his testimony E*. … A generalization is supported to the extent that this generalization survives our best attempts to show that it is invalid in the particular instance of concern.[13]

The results obtained from this testing constitute ancillary evidence (i.e., “evidence about evidence”) regarding the strength or weakness of the statistical generalization’s relevance to the link in question. If ancillary evidence is not provided in support of a statistical generalization, then the generalization is unsupported and may or may not be applicable to the inferential link.[14] In other words, the generalization that would justify the inferential link was “never put to the test.”[15] Therefore, any probabilistic inference made upon the basis of an unsupported generalization is weak.
Schum deduces, “a chain of reasoning cannot be any stronger than its weakest link.”[16]  It is an immediate consequence of this Schumian framework for witness credibility that the overall degree of credibility for a given piece of testimony (E*) is only as great as the weakest credibility attribute, regardless of how strong the other attributes may be. Accordingly, in order for E* to be credible, there must not be reasonable doubts about W’s veracity, objectivity, or observational sensitivity.

2. Nth Hand Evidence

For any piece of testimony (E*), a witness (W) may have obtained his or her information in one of three ways. First, the witness may have made a direct observation of the event she reports. Second, the witness may have received this information from another source, which I shall call nth hand evidence. I use the term “nth hand” to accommodate situations in which there are multiple sources in the chain. Third, the witness may have inferred the information, based upon information about other events.[17]
Let a source be a person or device who/that allegedly testified to the occurrence or nonoccurrence of some event of interest. A source is a primary source if it allegedly recorded the occurrence or nonoccurrence of that event. An immediate source is the source who/that informed you about this event. If an immediate source is not also a primary source, then the immediate source is either secondhand or nth hand evidence. Evidence is secondhand if there are no intermediate sources between the primary source and the immediate source. If there are intermediate sources, then the immediate source is nth hand evidence.[18]
Figure 2 depicts the chain of reasoning involved in a relatively simple appeal to secondhand evidence. In this example, we have a report (E*2,1) from an immediate source (S2) that a primary source (S1) reported (E*1) the occurrence of event E, which probabilistically favors hypothesis H.[19]
schumian-figure2

Figure 2 Secondhand Evidence

Thus, in order to determine the force of evidence E*2,1 upon hypothesis H in Figure 2, we must assess the credibility of two sources—immediate source S2 and primary source S1. If these two sources are people, we must consider the veracity, objectivity, and observational sensitivity of each witness. Figured 3 illustrates the stages of reasoning, when the credibility of each witness’s testimony is decomposed into those three credibility attributes.

{E, ¬E} S1’s Observational Sensitivity
{Es,1, ¬Es,1} S1’s Objectivity
{Eb,1, ¬Eb,1} S1’s Veracity
{E*1, ¬E*1} S2’s Observational Sensitivity
{Es,2, ¬Es,2} S2’s Objectivity
{Eb,2, ¬Eb,2} S2’s Veracity
E*2,1

Figure 3 Decomposed Credibility Attributes of Secondhand Evidence

It is an immediate consequence of this decomposition and the results of section 1 that the overall degree of credibility for a given piece of secondhand testimony (E*2,1) is only as great as the weakest credibility attribute of either witness (S1 or S2).
Moreover, due to the (alleged) dependence of our immediate source’s (S2’s)  testimony upon the primary source’s (S1’s) testimony, there is an interesting feature of the negations in the partitions for each of the credibility-related attributes. For example, the negation ¬Eb,2 means “Source S2 does not believe that event E happened (as allegedly reported by S1).”[20] Due to S2’s purported dependence upon S1, however, ¬Eb,2 can have two interpretations. First, ¬Eb,2 could mean that S2 believes E did not occur. Second, it could also mean that S2 has no belief about event E, which could be the case if S2 invented a story about S1 telling him that event E occurred.  In order to account for this possibility, then, ¬Es,2 includes the possibility that S2’s senses gave no evidence about what S1 said, ¬E*1 includes the possibility that S1 said nothing to S2; ¬Eb,1 includes the possibility that S1 has no belief about event E; and ¬Es,1 could mean that S1 made no sensory observations of event E. As Schum writes, “If we have to rely entirely upon S2, we have to consider the possibility that S1 said nothing at all about event E to S2 and perhaps never even made a relevant observation.”[21]
We are now in a position to fully appreciate the full significance of the fact that the overall degree of credibility for a given piece of secondhand testimony (E*2,1) is only as great as the weakest credibility attribute of either witness (S1 or S2). The strength of secondhand evidence, unlike that of firsthand evidence, may depend upon a witness whose credibility is unknown. (Indeed, in cases of ancient secondhand evidence, it is not uncommon for hearsay testimony to involve a putative primary witness whose very existence is otherwise unknown!) As Schum writes, “Absent evidence about the veracity, objectivity, and observational sensitivity of all sources in a chain of hearsay, we could hardly form any settled judgment of the inferential force of this species of evidence.”[22]  Any inference based upon such hearsay could not be regarded as a strong inductive argument, viz., such hearsay would not make E more probable than not. In plain English, such hearsay is worthless as evidence for E.
This same observation also applies to information for which we cannot identify a primary or intermediate source, which Schum labels rumor or gossip.[23] If information has come to us through a chain of sources and we cannot identify the primary source, then we do not know where or how they obtained this information.[24] In other words, we have information with an unknown primary source and therefore unknown credibility. Therefore, any inductive or probabilistic inferences based upon rumor or gossip must be regarded as weak.

3. Nth Hand Evidence and Observed vs. Inferred Sources

Although Wigmorean methods are appropriate for analyzing historical evidence, most discussions of these methods focus on how to apply them in legal contexts.  Thus, for example, when describing secondhand evidence, Schum provides the example of testimony (E*2,1) from an immediate source (S2) that a primary source (S1) reported (E*1) the occurrence of event E, which probabilistically favors hypothesis H.[25] While such an example is surely representative of hearsay testimony in modern courtrooms, it is not representative of nth hand evidence in the writings of ancient historians. As contemporary historian Michael Grant writes:

We nowadays like our historiography to be supported by documents. This did not function in the ancient world, for two reasons. First, the documents and archives, whether public or private, were hopelessly inadequate and without meaning, even if relatively numerous (and in some cases of early date). Second, the Greek and Roman historians did not care very much about these documents and rarely quoted or even paraphrased them.[26]

Nevertheless, there are other sources of evidence for the existence of a primary source besides an explicit reference from the immediate source; there are ways in which we may sometimes confidently detect the existence of a prior source, even if our immediate source fails to mention it. For example, it may be possible to infer the existence of a prior source based upon such factors as the proximity of the immediate source to the event(s) described or textual clues (grammar, vocabulary, etc.).
Since I have been unable to locate any discussion of an inferred prior source in the writings of the new evidence scholars, I shall attempt to advance the discussion by formulating the concept and its implications for the credibility of evidence.
Let us distinguish implicit and explicit forms of nth hand evidence. An immediate source is explicit nth hand evidence if it makes explicit reference to a prior source. For example, suppose we have a report (E*2,1) from an immediate source (S2) that a primary source (S1) reported (E*1) the occurrence of event E. S1 is an observed source because it was explicitly mentioned by an immediate source (S2).
Not all primary sources are explicitly mentioned by the immediate sources that use them, however. As we’ve seen, ancient writers often failed to satisfy modern expectations concerning the identification of the sources of their information. Let us define, therefore, implicit nth hand evidence as an immediate source that is based upon, but does not explicitly mention, a prior source. Thus, we may have a report (E*2,1) from an immediate source (S2) that is based upon, but does not explicitly mention, a primary source (S1) that reported (E*1), the occurrence of event E. S1 is an inferred source because it was not explicitly referenced by an (extant) immediate source.
By the very nature of the case, the credibility of an inferred source may often be unknown. This may be because the information is gossip (and hence the identity of the primary source is unknown) or, even if the identity of the source is inferred, nothing else is known about the identity of the source and hence the credibility of the inferred source is also unknown. If the credibility of the inferred source is unknown, then any inductive inferences based upon the inferred source must be regarded as weak.
Notes
[1] Joseph B. Kadane and David A. Schum, A Probabilistic Analysis of the Sacco and Vanzetti Evidence, (New York: Wiley, 1996), 46, 53.
[2] David A. Schum, The Evidential Foundations of Probabilistic Reasoning (New York: Wiley, 1992), 105.
[3] Schum 1992, 102.
[4] Schum 1992, 102.
[5] Schum 1992, 103-104.
[6] Schum 1992, 229.
[7] Cf. Kadane and Schum 1996, 56.
[8] Schum states that inferential links must always be justified on the basis of a statistical syllogism (in his words, “inductive generalizations”). While Schum is undoubtedly correct that links in a chain of reasoning are in practice usually justified by generalizations, especially in law, I see no reason to believe that inferential links must always be justified in this way. It seems at least possible that an inferential link in a chain of reasoning could also be justified by an explanatory argument.  See Kadane and Schum 1996, pp. 45-46, 51.
[9] Cf. Kadane and Schum 1996, 51.
[10] Schum 1992, 251.
[11] Especially his The Probable and the Provable (Clarendon: Oxford, 1977).
[12] Schum 1992, 243-251.
[13] Schum 1992, 249-251.
[14] Kadane and Schum 1996, 87, 152.
[15] Kadane and Schum 1996, 152.
[16] Schum 1992, 302.
[17] Schum 1992, 94-95.
[18] Schum 1992, 344.
[19] Schum 1992, 346-347.
[20] Schum 1992, 348.
[21] Schum 1992, 349.
[22] Schum 1992, 350.
[23] Schum 1996, 113.
[24] Cf. Kadane and Schum 1996, 113.
[25] Schum 1992, 346-347.
[26] Michael Grant, Greek and Roman Historians: Information and Misinformation (New York: Routledge, 1995), 34.

bookmark_borderWeighing Theistic Evidence Against Naturalistic Evidence

In the next-to-last paragraph of his book, C.S. Lewis’ Dangerous Idea: In Defense of the Argument from Reason, Victor Reppert makes a very interesting statement:

However, I contend that the arguments from reason do provide some substantial reasons for preferring theism to naturalism. The “problem of reason” is a huge problem for reason, as serious or, I would say, more serious, than the problem of evil is for theists. (emphasis mine)

I think this is a very interesting statement for two reasons. First, Reppert acknowledges that the so-called “problem of evil” — which is probably misnamed (see here) — is an evidential problem for theism. All by itself, that is a significant concession that is all too rare among theistic philosophers. But second (and more important), Reppert claims that naturalism’s ‘problem of reason’ is as big of a problem, if not a bigger problem, for naturalism as the ‘problem of evil’ is for theism. I want to focus on this second feature of interest about Reppert’s statement.
I recently asked, “Why Do So Many People Have a “Winner Takes All” Approach to Evidence about Gods?” Suppose you agree with my conclusion that there can be evidence for false propositions, so there can be evidence for atheism if God exists, and so there can be evidence for theism if God does not exist.
As soon as you admit that possibility, you have to be prepared to confront another possibility. How do you weigh competing items of evidence, especially when we don’t have numerical probability values (or likelihoods or Bayes’ factors) to work with? Here are two versions of this problem.
(1) Weighing Two Individual Items of Evidence
Suppose you have two items of evidence, E1 and E2, and two rival hypotheses, H1 and H2. E1 is evidence favoring H1 over H2, i.e., Pr(E1 | H1)  > Pr(E1 | H2). Let B1 the “Bayes’ factor” for E1 , i.e., the ratio of Pr(E1 | H1)  to Pr(E1 | H2). E2 is evidence favoring H2 over H1, i.e. Pr(E2 | H2) > Pr(E2 | H1). Let B2 be the Bayes’ factor for E2, i.e., the ratio of Pr(E2 | H1) to Pr(E2 | H2). If E1 is stronger evidence for H1 than E2 is evidence for H2, then B1 > 1/B2. Likewise, if E2 is stronger evidence for H2 than E1 is evidence for H1, then 1/B2 > B1. But how do you show that?
In some cases, it may be possible to show this is true by definition. For example, in my F-inductive argument from consciousness, I argue that Pr(consciousness | theism) =1 because theism entails the existence of consciousness. Now compare that result to a very weak argument against theism, the argument from scale. I have argued before that, as an argument against mere theism, the evidence of scale provides very weak evidence favoring naturalism over theism. So it seems obvious that if Pr(consciousness | theism) = 1, then consciousness is much stronger evidence for theism than scale is against it.
Or consider Paul Draper’s evidential argument from biological evolution. The key insight to understanding that argument is this. It is really an argument against special creationism, combined with a rigorous argument that special creationism is a viable auxiliary hypothesis to theism. In other words, theism provides a significant antecedent reason to expect that special creationism is true conditional upon the assumption that theism is true, where “antecedent” emphasizes the idea that we are abstracting away all of our evidence from biology. Draper’s evidential argument from biological evolution argues that Pr(special creationism | naturalism) = 0, whereas Pr(special creationism | theism) >= 1/2. Now suppose you have some extremely weak argument for theism, such as the argument from beauty. I don’t think beauty provides any evidence for theism, but for the sake of argument let’s pretend that it does. In that case, it would be obvious that the falsity of creationism is much stronger evidence against theism than beauty is evidence for it.
Not all comparisons of evidence will involve cases where at least one hypothesis entails neither the evidence to be explained nor the denial of the evidence to be explained. In those cases, it seems to me it will be more difficult, possibly impossible, to justify an objective comparison of evidential strength. (Whether it is impossible or merely difficult will have to be determined on a case-by-case basis.)
(2) Weighing Cumulative Cases Against One Another
Suppose now you have two “real” cumulative cases done the right way. In favor of H1, you have items of evidence E1 through E5. In favor of H2, you have items of evidence E6-E10. For example, let H1 be theism and H2 be naturalism. Then let our items of evidence be:
E1: the contingency of the universe
E2: the beginning of the universe
E3: the life-permitting conditions of the universe
E4: consciousness
E5: intentionality
E6: the hostility of the universe to life
E7: biological role of pain and pleasure
E8: falsity of special creationism
E9: mind-brain dependence
E10: psychopathy
You believe that E1-E5 are individually and collectively evidence favoring theism over naturalism. Likewise, you believe that E6-E10 are individually and collectively evidence favoring naturalism over theism.
As before, we’ll use “B” to represent the Bayes’ factor. Let B1-5 represent the ratio of Pr(E1 & E2 & E3 & E4 & E5 |T) to Pr(E1 & E2 & E3 & E4 & E5 |N). Let B6-10 represent the ratio of Pr(E6 & E7 & E8 & E9 & E10 | T) to Pr(E6 & E7 & E8 & E9 & E10 | N).
How in the world are you supposed to show that B1-5 > 1/B6-10?
(3) Is Naturalism’s ‘Problem of Reason’ as Big or Bigger than Theism’s ‘Problem of Evil’?
Let us now return to Reppert’s statement I quoted at the beginning of this post:

However, I contend that the arguments from reason do provide some substantial reasons for preferring theism to naturalism. The “problem of reason” is a huge problem for reason, as serious or, I would say, more serious, than the problem of evil is for theists. (emphasis mine)

Reppert does not attempt to defend this claim in his book, but in fairness we should note the argument from reason is a neglected topic in the philosophy of religion. It seems reasonable to devote an entire book just to (re-?)introducing the argument and defending it. But it would be a major accomplishment in the philosophy of religion, I think, if Reppert were able to successfully defend this claim. Perhaps he can devote his considerable philosophical talents to this task in a future book.

bookmark_borderDoes God Exist? Part 1

The overarching question for my ten-year plan is:
Is Christianity true or false?
After I clarify this overarching question, the first major question to investigate is this:
Does God exist?
I will, of course, at some point need to address the traditional arguments for the existence of God (ontological, cosmological, teleological, and moral arguments).  But I want my investigation to be systematic, and to avoid the problem of BIAS in the selection of arguments and evidence to be considered, especially to avoid the problem of CONFIRMATION BIAS (which is a common problem with Christian apologetics, including Richard Swinburne’s otherwise very careful case for God).
Here are some thoughts on how to approach this investigation:
FIRST, I will need to analyze the meaning of the sentence “God exists”.  I will probably follow Swinburne and analyze this sentence in terms of criteria, but then advocate, as Swinburne did, using a necessary and sufficient conditions definition instead of the criterial definition.
SECOND, following Swinburne, I will determine whether the sentence “God exists” is used to make a coherent statement.
If I determine that the statement “God exists” is incoherent, then that settles the issue:
One should reject the assertion that “God exists” because this sentence does NOT make a coherent statement.
Coherence is connected to logical possibility, so one way of analyzing the question “Does God exist?” is in terms of logical possibility and logical necessity and certainty and probability (click on image below for a clearer view of the diagram) :
Does God Exist - 1
 
 
 
 
 
 
 
 
 
I believe, however, that the sentence “God exists” can be used to assert a coherent statement, if one makes a few significant revisions to the concept of “God”, along the lines that Swinburne has suggested, with a couple of other revisions.  So, I expect that I will determine that some traditional conceptions of God make the sentence “God exists” incoherent, while with a few significant changes, a concept of God that is similar to the traditional conceptions will allow the investigation to continue beyond this initial question of coherence.
THIRD, there are various alleged ways of knowing or having a justified belief that “God exists”, which need to be considered:
1. Innate Knowledge
2. Religious Experience/Internal Witness of the Holy Spirit
3. Deductive Arguments for (and against) the existence of God
4. Non-Deductive Arguments for (and against) the existence of God
In terms of deductive arguments, I initially thought that it is possible that the issue could potentially be settled at that stage, if there were sound deductive arguments for the existence of God or against the existence of God.  But on reflection, I don’t think that is correct.
First of all, it is possible that there will SEEM to be sound arguments for the existence of God AND sound arguments against the existence of God.  If I identify any such arguments, then I would, obviously, focus some time and effort on trying to weed out one or more of these arguments as merely SEEMING to be sound, but not actually being sound.  But it is possible that I will end up with what SEEM to be sound arguments on both sides, in which case deductive arguments will NOT resolve the question at issue.
Furthermore, even if I find sound deductive arguments only for one position, say for the existence of God, and do not find sound arguments for the opposite position (say, for the non-existence of God), this still probably will NOT settle the issue.  The problem is that one or more premises in the sound argument(s) is likely to be less than absolutely certain.
Philosophical arguments for and against God usually involve some abstract principles, like the Principle of Sufficient Reason.  While some such premise might seem to be true, it is unlikley that a reasonable and objective thinker will arrive at the conclusion that such a premise is certain.  Because there is likely to be a degree of uncertainty about the truth of one or more premises in any deductive argument for or against the existence of God, the identification of one or more apparently sound deductive arguments will probably not settle the issue, even if all of the sound arguments support one side (theism or atheism).
So, it seems very unlikely that one can avoid examining evidence for and against the existence of God, evidence which only makes the existence of God probable to some degree or improbable to some degreee.  Furthermore, non-deductive arguments or cases can be quite strong.  If you have enough evidence of the right kinds, you can persuade a jury to send a person to his or her death for the crime of murder.  Sometimes, if the evidence is plentiful and the case is strong, a jury will return a verdict of “guilty” for first-degree murder in short order, without any significant wrangling or hesitation by the jurors.  Evidence can sometimes justify certainty or something very close to certainty.
If sound deductive arguments can fall short of making their conclusions certain, and if non-deductive reasoning from evidence can sometimes make a conclusion certain or nearly certain, then it would be foolish to fail to consider both sorts of arguments for and against the existence of God, even if we find some sound deductive arguments only for one side of this issue, and no sound deductive arguments for the other side.  Evidence and relevant non-deductive arguments/cases would still need to be considered.
Another possible way to analyze the question “Does God exist?” is in terms of the traditional roles that God plays:
Q1.  Is there a creator of the universe?
Q2.  Is there a ruler of the universe?
Q3. Assuming there is a creator of the universe and a ruler of the universe, are these the same person?
Q4. Has this person revealed himself/herself to humans through miracles, prophets, and inspired writings?
The first three questions are sufficient to determine whether “God exists” is true, so the fourth question is a bonus question that allows for a distinction between what I call “religious theism” and “philosophical theism”.
It seems to me that a very basic and important question to ask about God’s character is whether God has attempted to reveal himself/herself to humans.  Judaism, Christianity, and Islam all agree that God has attempted to reveal himself through miracles, prophets, and inspired writings, and this is a very basic and important belief in these western theistic religions.  So, this traditional view of God can be called “religious theism”.  But one could believe in the existence of God without buying into the idea that God has revealed himself through miracles, prophets, and inspired writings.  I call such a stripped-down version of theism”philosophical theism”.
Here is a diagram that spells out this way of approaching the question “Does God exist?” (click on the image to see a clearer version of the chart):
Does God Exist - 2
 
 
 
 
 
 
 
 
 
I have in mind, by the way,  time frames for each of the above questions:
Q1*.  Did a bodiless person create the universe about 14 billion years ago?
Q2*.  Has an omnipotent, omniscient, and perfectly good person been in control of every event in the universe for the past 10 billion years (or more)?
Q3*.  Did a bodiless person who is omnipotent, omniscient, and perfectly good, create the universe about 14 billion years ago, and then procede to control every event in the universe for the past 10 billion years (or more)?
Q4*.  Did a bodiless person who is omnipotent, omniscient, and perfectly good, create the universe about 14 billion years ago, and then procede to control every event in the universe for the past 10 billion years (or more), and then in the past 10,000 years reveal himself/herself to humans through miracles, prophets, and inspired writings?
I believe that Jeff Lowder’s approach to the question “Does God exist?” involves general categories of evidence, which he then examines for both evidence that supports the existence of God and evidence that goes against the existence of God.  This is somewhat similar to Swinburne’s approach, which starts out looking at evidence concerning the physical universe, then looks at evidence concerning evolution of human bodies, then evidence concerning human minds and morality, then evidence concerning human history, then religious experience.  But Jeff is more systematic in covering broad categories of evidence and more objective in looking for evidence supporting either side of the issue.
If you have another systematic approach to answering the question “Does God exist?”  I would be interested to hear about it.

bookmark_borderWhy Do So Many People Have a “Winner Takes All” Approach to Evidence about Gods?

If you’ve a regular reader of this blog — or any other blog or website devoted to the existence of God — you’ve probably noticed how often partisans for one side or the other have a “winner takes all” approach to the evidence. In the past, even I was guilty of making statements like, “There is no evidence for God’s existence.”
It now seems to me that one should be very cautious before making such statements (or the theistic equivalent, “There is no evidence against God’s existence.”) The more I study the nature of evidence in the abstract, the more hesitant I am to make the blanket statement “there is no evidence at all for God.” Yes, you read that correct.
Why on earth would an outspoken atheist such as myself say that? Three reasons. First, I think it’s very hard to defend such a statement. I cannot think of a successful “in principle” argument for that conclusion, which means you would have to give an empirical argument for it instead. But that, in turn, would require showing that every argument for (or against) God’s existence fails. That’s a time-consuming task at best.
Second, I think way too many people talk about evidence without really thinking deeply about what it means for a piece of data to be evidence. Once a person thinks long and hard about what it means for something to be evidence, they will learn that there is evidence and then there is evidence. Some piece of evidence, e, can be weak evidence for a hypothesis h, strong evidence for h, or somewhere in between. This is why in real life there are many cases where there is weak evidence for H1 but stronger evidence for H2. It may even be the case that most empirical questions are like that, rather than a situation where there is zero evidence for H1 and all of the evidence supports H2. This leads to my third point.
Third, the “winner takes all” assumes there are only two options: (1) ALL of the evidence supports theism, or (2) ALL of the evidence supports atheism (or naturalism). But why are those the only two choices? Why can’t a theist say this:

“I’ll admit that the arguments from evil and divine hiddenness are some evidence for theism, but I think they are outweighed by the evidence from the beginning of the universe, the cosmic fine-tuning of the universe, consciousness, morality, etc.”

Likewise, why can’t a naturalist say this:

“I’ll admit that fine-tuning, libertarian free will, and consciousness are some evidence for theism, but I think they are outweighed by the evidence from the course-tuning of the universe / hostility of the universe to life, biological role (and moral randomness) of pain and pleasure, evolution, mind-brain, dependence, and divine hiddenness.”

Finally, why can’t an agnostic say this:

“I’m an agnostic, but not because I believe there is no good evidence for or against God’s existence. Rather, I’m an agnostic because I think there is good evidence both for and against God’s existence. I think fine-tuning, libertarian free will, and consciousness are some evidence for theism. I also think the coarse-tuning of the universe / hostility of the universe to life, biological role (and moral randomness) of pain and pleasure, evolution, mind-brain, dependence, and divine hiddenness are evidence against God’s existence. And I don’t know how to weigh the former against the latter.”

My own view is that so-called the fully stated evidence about ‘fine-tuning’ isn’t evidence for God’s existence; I haven’t decided (pun intended) if I believe libertarian free will exists; and I think consciousness is evidence favoring theism over naturalism. But I believe that evidence is outweighed by all of the naturalistic evidence.

bookmark_borderOn Admitting There Might Be Some Evidence for the Other Side

Note: I thought I had blogged this before, but a quick search didn’t turn anything up.
Have you ever noticed how rare it is for a person to admit there might be any evidence against their position, at least (or especially) when it comes to religion? I think this should make people suspicious about whether their cognitive biases are playing a larger role than they might like to admit.
People can mean different things by “evidence.” Solely for the sake of discussion, I’m going to define “evidence” in this post to mean “some fact which is more probable on the assumption that one hypothesis is true than it is on the assumption that another hypothesis is true.” In mathematical symbols, where E is evidence, H1 is one hypothesis , and H2 is a contradictory hypothesis, this means that E is evidence for H1 just in case Pr(E|H1) is greater than Pr(E|H2).
Let’s conduct a thought experiment. Without knowing what H1 and H2 are, assume that both are coherent (i.e., they don’t contradict themselves in the way “There are married bachelors” would) and that H1 is true.
Now ask yourself this question.

Q: “Assuming H1 is true, why does it follows that there is no (zero) evidence against H1 and for H2?”

Using the definition of “evidence” I’ve provided in this post, the correct answer is this.

A: “It doesn’t follow at all. It’s possible that there is some evidence, however small, against H1 and for H2 and that evidence is outweighed by other evidence, evidence which more strongly favors H1 over H2.”

Now let’s apply this insight to competing worldviews like theism and naturalism. Based upon the answer I just provided, it should be obvious that

(1) If theism is true, there could be evidence against theism and for naturalism.

and:

(2) If naturalism is true, there could be evidence naturalism and for theism.

I think it’s no small coincidence that Christian philosopher Richard Swinburne, who takes a similar Bayesian approach to evidence, thinks the total evidence favors God’s existence, but evil and suffering provides evidence against God’s existence.

“So, given both of these additional hypotheses, and conscious of the very short temporal span of human and animal life (and to a lesser extent of the limits of pain and suffering within that life that can be experienced), my own final verdict is that a God would not need to be less than perfectly good if he were to bring it about or allow to occur that amount of suffering that exists for the sake of the greater good that results. Still, the need for additional hypotheses in order to save theism makes the resulting theistic theory more complicated than theism on its own (bare theism), and so reduces the probability of bare theism. Put another way, bare theism makes it less probable that we would find evil of as great a degree as we do than it would be on background evidence alone, because theism is compatible with the evidence only if we add to theism a further hypothesis or hypotheses. Hence, evil provides a good C-inductive  argument against the existence of God. But it does not provide a very strong one, for the reason that providing life after death for many humans (not merely those who need compensation) and becoming incarnate to share their suffering are the kinds of acts that a good God might well do anyway–for they are good acts (and perhaps good acts of different kinds from the other acts of God that we have been discussing, and maybe even acts of best kinds), whether or not required in order for God justifiably to allow the amount of evil that occurs. … So, with e as the occurrence of the moral and natural evils known to us, h as the hypothesis of theism, and k as the background evidence considered in previous chapters, P(h|e&k) < P(h|k), but the former is not less than the latter by very much.”
Richard Swinburne, The Existence of God (second ed., New York: Oxford University Press, 2004), 265-66.

I happen to disagree with Swinburne’s assessment of the strength of the evidence from evil, but that really doesn’t matter. With a clear (and rigorous) use of probability theory, Swinburne agrees that evil provides objective evidence against God’s existence.
Swinburne isn’t the only theist who admits this. Off the top of my head, I think I remember reading that philosophers Gregory E. Ganssle and Victor Reppert do as well. There are probably others.
Similarly, on the naturalist side, I’ve defended an argument from consciousness which says that consciousness is more probable on theism than on naturalism.
The moral here, I think, is that we should be skeptical whenever someone claims there is no (zero) evidence for something. Perhaps that is why the great philosopher Bertrand Russell, when asked what he would say to God after he dies if it turns Russell was wrong and God exists, is reported to have answered, “Not enough evidence, God! Not enough evidence!” He didn’t say, “No evidence, God! No evidence!” Instead, he said, “Not enough evidence.”

bookmark_borderA Key Difference between Science and Religion

In science, we ask, “What’s the evidence?”, before believing. Only religion* asks us to believe first and consider the evidence later, if ever.
Two clarifications:
1. I am not claiming that all religions do this. Rather, I’m claiming that if/when this happens, it only seems to happen in the context of religion. (If I’ve missed any non-religious examples of this, please let me know and I will issue a correction!)
2. Nor am I making the scientistic claim that the only way to know something is the scientific method. For the record, I think that claim is self-defeating. (If the only way to know something is the scientific method, do we know “the only way to know something is with the scientific method” through the scientific method? Of course not. The claim undermines belief in itself.)  Rather, I’m comparing scientific claims, such as:

X: Drug A works better than Drug B

to religiously significant empirical claims, such as:

Y: Jesus rose from the dead.

Nobody in the scientific community would say it’s okay to believe X before looking at the scientific evidence. In contrast, some religious philosophers do defend the idea that it’s okay to believe Y before looking at the historical evidence. In fact, William Lane Craig goes even further. He says it’s okay to believe Y without ever looking at the evidence. Furthermore, even if the historical evidence made it highly likely that Y is false, he’s gone on record saying that he would continue to believe Y anyway.

bookmark_borderJesus on Faith – Part 6

Here is the “Doubting Thomas” story from Chapter 20 of the Gospel of John:
24 But Thomas, one of the twelve, called Didymus, was not with them when Jesus came.
25 So the other disciples were saying to him, “We have seen the Lord!” But he said to them, “Unless I see in His hands the imprint of the nails, and put my finger into the place of the nails, and put my hand into His side, I will not believe.”
26 After eight days His disciples were again inside, and Thomas with them. Jesus *came, the doors having been shut, and stood in their midst and said, “Peace be with you.”
27 Then He *said to Thomas, “Reach here with your finger, and see My hands; and reach here your hand and put it into My side; and do not be unbelieving, but believing.”
28 Thomas answered and said to Him, “My Lord and my God!”
29 Jesus *said to him, “Because you have seen Me, have you believed? Blessed are they who did not see, and yet believed.”
This story does NOT show that either the author of the Gospel of John or Jesus (as portrayed in this Gospel) understood “faith” to mean “belief that is based on no evidence”, nor does it show that the author of John or Jesus (as portrayed in this Gospel)  understood “faith” to mean “belief that is based on insufficient evidence”.  It does show that the author of John and Jesus (as portrayed in John) would clearly REJECT both of these definitions of “faith”.
1. Thomas “was not with them when Jesus came.” (verse 24)
Jesus had already shown himself in his resurrected body to the other disciples and had talked with them (20:19-23). If “faith” meant “believing on the basis of no evidence”, then Jesus had thereby made it IMPOSSIBLE for his other disciples to have “faith” in him. Since “faith” is a requirement for salvation, that means that Jesus had made it IMPOSSIBLE for any of the other disciples to be saved from eternal damnation. But this is absurd! Clearly, neither the author of this Gospel nor Jesus (as portrayed in this Gospel) think that “faith” means “believing on the basis of no evidence.”
Furthermore, according to the Gospel of John, Jesus’ inner circle of disciples had already been eyewitnesses to many amazing miracles, such as Jesus turning water into wine (2:1-11), walking on water (6:16-21), feeding thousands of people with a few loaves of bread (6:1-14), and raising Lazarus from the dead (11:38-48). So, in appearing to the disciples in his resurrected body, Jesus was not only presenting them with evidence of his resurrection and divinity, Jesus was providing them with OVERWHELMING evidence of his resurrection and divinity (by the combination of the previous amazing miracles plus his appearances to them in his resurrected body).
Thus, if “faith” was understdood to mean “believing on the basis of insufficient evience”, then Jesus was making it IMPOSSIBLE for his disciples to have faith in him, by presenting them with OVERWHELMING evidence of his resurrection and divinity. Since faith is a requirment for salvation, Jesus would have made it IMPOSSIBLE for his disciples to be saved from eternal damnation, if this is how Jesus understood the word “faith”. But this is absurd. Therefore, it is clearly the case that neither the author of the Gospel of John nor Jesus (as portrayed in that Gospel) took the word “faith” to mean “believing on the basis of insufficient evidence”.
2. “Unless I see in His hands the imprint of the nail…” (verse 25)
Thomas has previously seen Jesus perform a number of amazing miracles. Now the other disciples of Jesus tell him that they have seen and talked with the risen Jesus, yet Thomas remains unconvinced. He demands direct first-hand evidence, to see and even touch the risen Jesus for himself.
3. “Reach here your finger…” (verse 27)
When Jesus appears a second time to his gathered disciples, this time with Thomas present, he does not scold Thomas for demaning first-hand evidence; rather Jesus immediately offers the exact direct evidence that Thomas had required. So, now not only does Thomas have evidence for the resurrection and divinity of Jesus, but in view of the previous amazing miracles that Jesus performed and that Thomas witnessed, in view of the testimony of Thomas’ fellow disciples to the resurrection, and in view of the visible presence of the resurrected Jesus who is speaking directly to him, Thomas is also given OVERWHELMING evidence of the resurrection and divinity of Jesus (according to the Gospel of John).
So, if “faith” means “believing on the basis of no evidence” or “believing on the basis of insufficient evidence”, then Jesus has made it IMPOSSIBLE for Thomas to have faith in him. Since faith is a requirement for salvation, Jesus has made it IMPOSSIBLE for Thomas to be saved from eternal damnation. But this is absurd. So, clearly neither the author of the Gospel of John nor Jesus (as portrayed in that Gospel) understood “faith” to mean “believing on the basis of no evidence” or “believing on the basis of insufficient evidence”.
Jesus provides Thomas and his other disciples with OVERWHELMING evidence of his resurrection and divinity precisely in order to get them to “believe”, to have faith in him, to firmly believe that Jesus is the Son of God, sent by God to be the savior of humankind. Jesus sees no conflict between faith and strong evidence: “…do not be unbelieving, but believing.” (verse 27)
4. “Blessed are they who did not see, and yet believed.” (verse 29)
It has been clearly established that Jesus does NOT understand “faith” to mean “believing on the basis of no evidence” and that Jesus does NOT understand “faith” to mean “believing on the basis of insufficient evidence”. It is clear that Jesus (as portrayed in the Gospel of John) views faith as being compatible with having OVERWHELMING evidence in support of the belief in question. But verse 29 appears to suggest that “faith” might also be compatible with belief that is based on insufficient evidence.
But having something less than OVERWHELMING evidence for a belief is not the same thing as having insufficient evidence for that belief. Obviously, Christians who have not personally witnessed miracles being performed by Jesus and who have not personally seen and talked with the risen Jesus will not have the same high level and degree of evidence for their belief in Jesus as resurrected Son of God as the original disciples of Jesus. Christians who lived in the second century and following centuries do not (at least in general) have the OVERWHELMING evidence for this belief that the original disciples had (or are reported to have had by the Gospels). But this does not mean that the evidence such Christians have is insufficient evidence.
At least, it is not obvious that OVERWHELMING evidence is the only sort of evidence that will be sufficient to justify their belief. If a skeptic wishes to argue that only OVERWHELMING evidence will be sufficient evidence in the case of the belief that Jesus rose from the dead, that is fine by me, but a clear and strong argument is required for this view, because it is not obvious or self-evident that anything less than such powerful evidence must constitute insufficient evidence.
Because it is NOT obvious or self-evident that only OVERWHELMING evidence will be sufficient evidence for the resurrection and divinity of Jesus, we cannot reasonably assume that the author of the Gospel of John believed that only such evidence would be sufficient evidence. We must allow for the very real possibility that the author of this Gospel and Jesus (as portrayed in this Gospel) thought that the faith of later generations of Christians could be based on sufficient evidence which was, however, something less than OVERWHELMING evidence.
The author of the Gospel of John may reasonably be presumed to have viewed the “testimony” presented in this Gospel to provide sufficient evidence (but not overwhelming evidence) for the resurrection and divinity of Jesus, as indicated by the verses that immediately follow the “Doubting Thomas” story:
30 Many other signs therefore Jesus also performed in the presence of his disciples, which are not written in this book;
31 but these have been written that you may believe that Jesus is the Christ, the Son of God; and that believing you may have life in his name.
Although the author of John and Jesus (as portrayed in that Gospel) appear to think that “faith” is compatible with both having OVERWHELMING evidence for a belief and also with having something less than OVERWHELMING evidence for the belief, it is not at all clear that “faith” is viewed as being compatible with belief on the basis of insufficient evidence.
In any case, it is clear that neither the author of John nor Jesus (as portrayed in that Gospel) undstand “faith” to mean “belief on the basis of insufficient evidence”. Therefore, the claim that sincere and devout Christian believers (who regularly read and study the Gospels) think that “faith” means “belief on the basis of insufficient evidence” is highly questionable. (Perhaps there are many Christians who are not sincere or not devout and who don’t bother to carefully read and study the Gospels, and such Christians might well have an understanding of “faith” that is different than what Jesus had or than what the author of the Gospel of John had.)

bookmark_borderEvidential Asymmetry, Scientific Confirmation of Prayer, and Horrific Evils

1. The General Case
One of the most important (and equally most often forgotten) lessons that Bayes’s Theorem can teach us about evidence is that the strength of evidence is a ratio. To be precise, let H1 and H2 be rival explanatory hypotheses, B be the relevant background information, and E be the evidence to be explained. Now consider the following ratio:

Pr(E | B & H1)
—————–
Pr(E | B & H2)

If Pr(E | B & H1) > Pr(E | B & H2), then this ratio is greater than one and the evidence favors H1 over H2. If Pr(E | B & H2) < Pr(E | B & H1), then this ratio is less than one and the evidence favors H2 over H1. And if Pr(E | B & H1) = Pr(E | B & H2), then this ratio is equal to one and the evidence favors neither H1 nor H2.
Paul Draper has taught me that this ratio has some interesting implications for topics that come up in debates between theists and naturalists. Suppose that Pr(E | B & H1) is really high and Pr(E | B & H2) is middling. In this case, there will be an evidential asymmetry: if E is true, E is not strong evidence for H1 over H2, but if E is false, then ~E is strong evidence for H2 over H1. This can be shown with a couple of examples.
First, suppose that E is true. If E is true, then E is not strong evidence for H1 over H2. This follows because the ratio of Pr(E | B & H1) to Pr(E | B & H2) is not high.
Second, suppose that E is false. This is where things get interesting. Because Pr(E | B & H1) is really high, the negation of E would strongly favor H2. Again, this follows from the ratio of the likelihoods: the ratio of Pr(~E | B & H1) to Pr(~E | B & H2) is high.
It is mathematically necessary that this evidential asymmetry will always be present when the evidence has a middling probability on one hypothesis and a very high (or very low) probability on the negation of that hypothesis. (The basic idea is that is the range of probabilities is zero to one, a high probability divided by a middle one must be relatively small while a middling probability divided by a low one must be relatively large.)
2. The Efficacy of Prayer and Scientific Confirmation
Let’s assume, as appears to be the case, that recent scientific studies have failed to confirm the efficacy of prayer. If facts about evil and divine hiddenness are included in our background knowledge, then those study results do not strongly favor naturalism over theism because the ratio of the likelihood of the evidence on naturalism to the likelihood of the evidence on theism is not really high. (This follows because the probability of such studies given theism and that background information is middling.) But now imagine the results had turned out differently and the studies had confirmed the efficacy of prayer. In that case, such results would strongly favor theism over naturalism.
This result shows that atheists are making a mistake when they accuse theists of using an unjustified double standard by dismissing the (negative) study results as evidentially insignifcant.  Rather, theists are correct that if the study results had confirmed prayer, then such positive results would have been strong evidence favoring theism over naturalism, but the absence of such results is only weak evidence favoring naturalism over theism.
3. Horrific Evils
The topic of horrific evils provides another example of evidential asymmetry. Horrific evils have a middling probability given naturalism but a very low probability given theism. So if horrific evils were absent, that fact wouldn’t strongly favor theism over naturalism, whereas the presence of horrific evils strongly favors naturalism over theism.
Acknowledgment
I owe the main point of this post, as well as both examples, to Paul Draper. Any errors in this post are, of course, mine.

bookmark_borderStan Stephens’s Categorical Misunderstandings of Atheism, Part 2

In my last post about Stan Stephens, I documented how he fundamentally misrepresents the purpose and nature of my evidential case for naturalism, in turn because he seems to fundamentally misunderstand inductive arguments.
Let’s continue reviewing Stan’s post on empirical evidence.

Now we can more readily see that not a single line item is a defeater for the question being asked, which again is this:

“where is the material, empirical, falsifiable but not falsified, replicable and replicated, open data, peer reviewed undeniable evidence that there cannot exist a deity?” And no matter how the questions are answered, they do not select or differentiate atheism as truth, necessary or even contingent.

If Stan knew as much about philosophy as he claims, he would know that questions don’t have defeaters. That massive category error–which lies at the heart of his statement that “not a single line item is a defeater for the question being asked”–simply reveals his ignorance of defeaters, not a problem with the evidence provided. But let that pass.
At the heart of Stan’s confused reply is the myth that atheists, naturalists, and materialists must believe that God cannot exist. That is a straw man of his own creation. The atheist qua atheist does not believe that God cannot exist; rather, he believes that God does not exist. The naturalist qua naturalist does not believe that the supernatural cannot exist; rather, he believes that the supernatural does not exist. The materialist qua materialist does not believe that the immaterial cannot exist; rather, he believes that the immaterial does not exist.
Because atheists, naturalists, and materialists aren’t required to believe that God, the supernatural, and the immaterial, respectively, cannot exist, there is no justifiable reason for Stan’s insistence that they prove as much.
If you’ll pardon an analogy between God and Sasquatch, here’s an analogy. I am an aSasquatchist because I think the existence of Sasquatch is extremely improbable. Stan’s requirement that atheists prove that God cannot exist is analogous to the demand that aSasquatchists prove that Sasquatch cannot exist. The proper response to both demands is, “Why? Why must I prove that such things cannot exist, when I don’t even believe that?”
Stan continues:

It is apparent that the concept of empirical evidence is different for JJ Lowder, in that it seems to refer to personal inferences which are taken from material situations, and even then not all of the claims even refer to actual material “things”. Perhaps this is a consequence of habitual inductive thinking; but the term “empirical” should ring a bell, one would think. Empiricism is the gold standard for material evidence. However, under mataphysical [sic] naturalism, who knows what the criteria might be, since they would likely be metaphysical? That renders them nonfalsifiable, empirically, though, and thus they can’t actually qualify as knowlege.

This is mostly a bunch of philosophical gibberish, but let me attempt to clarify what I think they key issues are. (1) As a Bayesian, I believe evidence is a term that describes a relationship between two or more propositions. One proposition (A) can be evidence for another proposition (B) insofar as A increases the probability of B.  (2) For “ultimate” metaphysical hypotheses like supernaturalism, naturalism, and theism, we can objectively compare the intrinsic probabilities of such hypotheses using such criteria as modesty and scope. 

The idea that subjective conclusions which are inferred from observations are conclusive, is incorrect.

Once again we see Stan attacking that stupid “atheists must believe conclusively / categorically / incorrigibly that God cannot exist” caricature of atheism. (What would Stan do without that idea?)
Stan then complains I did not respond to the following challenge.

Here’s the challenge to atheists: Rather than disproving disproof, as your approach has been, the more straightforward simple proof for atheism illuminates the problem for atheism:
When you can prove, conclusively, robustly, and incorrigibly that there positively is no deity in existence, cannot under any circumstance be a deity in existence, and have the material evidence for that, or even a disciplined, grouunded, [sic] deductive argument for that, then you have proven your case (atheism), and not until.
Further, when you can prove, conclusively, robustly, and incorrigibly that there positively is no non-material existence outside and beyond the capacity of material detection, and have the material evidence for that, or even a disciplined, grounded, deductive argument for that, then you have proven that case (materialism/physicalism as closed system), but not until.
Failure to provide these straightforward proofs would indicate that atheists and physicalists cannot have actual knowledge which supports their atheism and physicalism. Without that knowledge, atheism and physicalism are no more supported than mere fantasies.

At the risk of repeating myself, here is my response.
1. Atheists qua atheists don’t believe that there “cannot under any circumstance be a deity in existence,” so there is no justifiable reason for Stan’s demand that they provide such evidence.
2. Atheists qua atheists don’t believe that there “is no non-material existence outside and beyond the capacity of material detection.” Here Stan seems to be confusing atheists with materialists, and so his demand of atheists is misplaced.
3. Stan’s assertion–that the belief that God does not exist requires a deductive proof to be justified–is just that: an assertion or a claim which requires some sort of justification. I do not find such a reason anywhere in his post. On the contrary, it seems to me that there is good reason to think Stan’s assertion is false. Just as theism can be justified if the weight of the evidence makes God’s existence highly probable, atheism can be justified if the weight of the evidence makes God’s existence highly improbable.