Swinburne’s Case for God – Part 7


The first premise of Swinburne’s case for God makes a fairly modest claim:
1. Based on evidence other than religious experience, the existence of God is not very improbable.
Because the expression “not very improbable” is a bit vague, I argued for the following clarification of premise (1), in my last post:
1b. Where e is the specific evidence (considered by Swinburne in EOG) for and against the existence of God, excluding the evidence of religious experience, and where h is the hypothesis that God exists, and where k is our background knowledge: P (h I e & k) > .20

In Swinburne’s estimation, the relevant evidence (other than the evidence from religious experience) makes the probability of God’s existence significantly
…all that my conclusion so far amounts to is that it is something like as probable as not that theism is true, on the evidence so far considered. However, so far in this chapter I have ignored one crucial piece of evidence, the evidence from religious experience. (EOG, 2nd ed., p.341)
In other words, according to Swinburne:
P(h I e & k) ≈ .50
This is where e is the relevant evidence other than religious experience.
Since this is only an approximation, we could consider Swinburne to be correct if the actual probability were somewhere from .40 to .60:
(4) Where e is the specific evidence (considered by Swinburne in EOG) for and against the existence of God, excluding the evidence of religious experience, and where h is the hypothesis that God exists, and where k is our background knowledge: .40 ≤ P(h I e & k) ≤ .60
Clearly, (4) implies (1b), becuase if the probability of h is between .40 and .60, then the probability of h is greater than .20.
In EOG, Swinburne considers eleven arguments on the question of the existence of God. The first premise of Swinburne’s case for God is concerned with ten of the arguments, and excludes the final argument that is based on religious experience. Two of the ten arguments are set aside as having no significant force, leaving eight arguments to use as the basis for showing that the probability of God’s existence is between .40 and .60.
Seven of the eight remaining arguments are supposed to provide some confirmation of the existence of God, while one argument (the problem of evil) is supposed to provide some disconfirmation of the existence of God. Since each of the arguments that confirm the existence of God is supposed to bump up the probability a bit, so that the cumulative force of the arguments is greater than that of any one particular argument, the claim that Swinburne has to make for each of the confirming arguments is very modest.
Suppose that the problem of evil is only strong enough to cancel out the weight of one of the seven confirming arguments. That would leave six confirming arguments to support the cumulative probability of between .40 and .60.
If we assume that the prior probability of the existence of God was equal to one chance in a hundred, i.e. P(h I k) = .01, and if we assume that each of the six remaining confirming arguments bumps up the probability by the same amount (on average), then the probability of h would seven times .01:
P (h I e & k) = 7 x .01 = .07
On this scenario, Swinburne’s claim that the probability of h (given the relevant evidence other than religious experience) was between .40 and .60 would clearly be false, as would the weaker claim made in premise (1b), namely that h was greater than (or equal to) .20.
However, suppose that the prior probability of the existence of God was a bit higher: .05, and suppose that each of the six confirming arguments (remaining after cancelling out one of the confirming arguments with the problem of evil) added .05 to the probability (on average). In that case, the probability of h would be seven times .05:
P (h I e & k) = 7 x .05 = .35
On this scenario, Swinburne’s stronger claim (4) would be false, but this would still be enough to establish his first premise (1b), because a probability of .35 is greater than a probability of .20.
If we were to assume that the prior probability of h was .06, and that each of the six confirming arguments (remaining after the problem of evil cancelled out one confirming argument) bumped up the probability by .06, then not only would premise (1b) be true, but so would Swinburne’s stronger claim:
P (h I e & k) = 7 x .06 = .42
These different scenarios make two important points. First, Swinburne only needs to establish fairly weak claims about the force of his confirming arguments. If each confirming argument bumps up the probability of the existence of God just a bit (say .04 or .05) that may well be sufficient to establish the first premise of his case for God (if force of the problem of evil is only about the same as one of the confirming arguments, and if there is at least a tiny prior probability of the existence of God).
Second, the difference between success and failure is small, now that we have clarified the probability required to make the first premise true. If the average bump up of probability by the confirming arguments (and the prior probability of God’s existence) is .02 (i.e., two chances in a hundred), then premise (1b) is likely to be false, but if the average bump up of probability by the confirming arguments (and the prior probability of God’s existence) is .03 (i.e. three chances in a hundred), then premise (1b) is likely to be true (depending on the force of the problem of evil in disconfirming God’s existence).
greater than .20:

About Bradley Bowen
  • http://www.blogger.com/profile/03125711244980154445 Bradley C.

    I really appreciate your blog posts. You take a very respectful and rational approach to looking at theistic arguments, and lay them out in a clear and comprehensive way.

    Thank you for taking the effort to engage in discussion with these arguments, and laying them out in a way that is so accessible. I look forward to watching this all play out.

  • http://www.blogger.com/profile/05770427187548083625 Havok

    Does Swinburne take into account arguments other than the problem of evil, and if not would they be relevant?

  • http://www.blogger.com/profile/05713099591321368658 JJ Anderson

    It surprises me that someone as intelligent as you might believe that your quantitative analysis has any meaning. How would you begin to assign actual probabilities? Your equations look sciency and sophisticated, but nothing plus nothing still equals nothing. It seems self-defeating to follow Swinburne down the rabbit hole to fantasyland!

    In your response to LadyAtheist's comment on Part 6, you said:
    Swinburne has spent a number of decades studying philosophy, theology, and science in order to be able to present a clear, modern, rigorous, and comprehensive case for the existence of God.

    How can you consider Swinburne “rigorous” if his numbers are made up, and not based on anything?

  • http://www.blogger.com/profile/05211466026535549638 Bradley Bowen

    Bradley C. said…
    I really appreciate your blog posts. You take a very respectful and rational approach to looking at theistic arguments, and lay them out in a clear and comprehensive way.
    ======
    Thank you for the kind words. I hope that this series of posts helps you to have a clear understanding of Swinburne's case for God.

    I don't believe in God myself, but I have great respect for Swinburne's effort to lay out a clear, modern, rigorous, and comprehensive case for the existence of God.

  • http://www.blogger.com/profile/05211466026535549638 Bradley Bowen

    Havok said…
    Does Swinburne take into account arguments other than the problem of evil, and if not would they be relevant?
    ============
    Response:
    In his book The Coherence of Theism, Swinburne deals with conceptual/linguistic objections to theism. He argues that the sentence "God exists" makes a factual statement that is coherent, i.e. that does not contain a self-contradiction.

    In The Existence of God, Swinburne only considers two arguments against the existence of God: the problem of evil and the argument from the hiddenness of God.

    You raise an important point. If Swinburne ignores some significant inductive evidence against God, then he could be involved in the fallacy of confirmation bias: looking hard for evidence that confirms a favored belief, while not looking hard for evidence that disconfirms the belief.

  • http://www.blogger.com/profile/05211466026535549638 Bradley Bowen

    JJ Anderson said…
    It surprises me that someone as intelligent as you might believe that your quantitative analysis has any meaning.
    How would you begin to assign actual probabilities?

    How can you consider Swinburne “rigorous” if his numbers are made up, and not based on anything?
    ====================
    Response:

    Swinburne provides reasons and arguments to support any probability estimates that he gives. So your claim that his "numbers are made up, and not based on anything" is false.

    One of the problems I have understanding Swinburne's argument is that he rarely gives specific
    probability estimates. Most of his points involving Bayes' Theorem have to do with vague
    quantifications and relative comparisons (e.g. This conditional probability is greater than that one).

    If you reject any of Swinburne's probability estimates, then you need to either (a) show that there is a problem with his reasons in support of the probability estimate that you reject, (b) provide a better/stronger case for some alternative probability estimate, or (c) give a clear argument for why no justifiable probability estimate can be produced for the particular hypothesis in question (given the specified evidence and background knowledge).

    If you have a specific objection to make(along the lines just mentioned), please do so.

  • http://www.blogger.com/profile/05348780254008374268 Tristan D. Vick

    Bradley Bowen

    This is an excellent series. You should collect them and publish them in a journal or as part of a philosophy of religion book. Excellent work all the way around.

    If you do have plans on publishing these articles, be sure to give me a heads up!

  • http://www.blogger.com/profile/10297638045257556827 mobathome

    Specific objection 1:

    When you multiply seven arguments's likelihoods with a prior, you're assuming those arguments are probabilistically independent of each other. Does Swinburne provide reasons for accepting this of the seven arguments he uses?

    Specific objection 2:

    I paraphrase: “If you put garbage in Bayes' Theorem nothing comes out but garbage. But this garbage, having passed through a Mathematical Theorem, is somehow enobled and none dare criticize it.'' So it is with whatever numbers Swinburne decided his arguments could appear to support.

    Specific objection 3:

    A Bayesian probability is a personal statement of the strength of one's belief in a statement. Anyone's numbers are acceptable. Swinburne's result reflects his personal beliefs, and are not necessarily compelling or meaningful for anyone else.

    Specific objection 4:

    Bayes's theorem calls for normalizing the result by dividing the product by the prior probability of the combined data. Does Swinburne do this?

    Specific objection 5:

    A Bayesian probabilist does not work with point estimates as you do here (and in later posts I see), but with distributions over all possibilities for all unknown quantities. Does Swinburne give distributions or state enough information for you to derive distributions for all unknown quantities?

    Specific objection 6:

    Specifying prior distributions allows a Bayesian probabilist to analyze the sensitivity of their posterior to their choices of prior probabilities. Sensitivity of the posterior to prior is critical. the more small changes in prior distributions result in large changes in the posterior distribution, as you show here, the less the conclusion should be reasonable. This is evidence against the reasonableness of Swinburne's argument.

    Specific objection 7:

    This is more about the assignment of likelihoods in later posts. That N possibilities are imagined as an outcome for a random variable does not automatically make their respective likelihoods 1/N. For example you quote Swinburne: “I argued [in Chapter 6] that it would be an equal best act to create or not to create such creatures … so we should suppose the logical probability that God would create such creatures to be 1/2.'' This is garbage in. That in Swinburne's estimation two possibilities are equal best acts does not make the probability of God doing them equally likely. Much more need be said before this can be accepted, including ruling out any other other possibilities (and no, I don't accept the law of excluded middle.)

  • http://www.blogger.com/profile/05211466026535549638 Bradley Bowen

    Mobathome said:

    Specific objection 1:

    When you multiply seven arguments's likelihoods with a prior, you're assuming those arguments are probabilistically independent of each other. Does Swinburne provide reasons for accepting this of the seven arguments he uses?
    =============
    Response:

    Thank you for all of the specific objections that you have stated above.

    I wish I had time to discuss each one at length, but right now I'm tied up with trying to write a general article on Swinburne's case for God.

    I will try to address your objections one at at time over the coming months, but it will probably take a while for me to respond to them all.

    Swinburne does not claim nor assume that the arguments are independent of each other. To the contrary, he points out that later arguments presuppose earlier ones. Rather, later evidences presuppose earlier evidences.

    He arranges the arguments into a logical order so that the force of the earlier arguments is not counted twice or multiple times.

    For example, the cosmological argument is the first one he considers. The background knowledge in this case is merely apriori or necessary truths; no empirical data is included in the background knowledge for that argument.

    The evidence used in this first argument is this:

    1. There exists a complex physical universe.

    According to Swinburne, the a priori probability of the existence of a complex physical universe is very low, but he argues that if God exists, there would be a significant chance that God would create a complex physical universe. He also argues that "if there is not God, the existence of a complex physical universe is not much to be expected; it is not a priori very probable at all…" (EOG, p.151)

    The second argument he considers is the Argument from Temporal Order. The evidence used in that argument is this:

    2. The (complex) physical universe is governed by "laws of nature sufficiently simple for rational beings to extrapolate from past to future with normal success." (EOG, p.164)

    Clearly (2) presupposes (1), and Swinburne points this out. But he does not count the weight of the first argument twice or multiple times, because the evidence of the first argument becomes the background knowledge for the second argument (i.e. claim (1) is the background knowledge for the probability calculation concerning the force of the second argument).

    As each new argument is considered, the evidence used in the previous arguments is rolled into the background knowledge used in the probability calculation for the evaluation of the latest argument.

    Does that make sense?

  • http://www.blogger.com/profile/10297638045257556827 mobathome

    I'm glad you've taken my seven objections seriously enough to respond, even though it will take you a while to consider each of them. Thank you.

    Whether Swinburne discounts each successive argument enough to account for their relationships to the previous ones is a matter of mathematics. The Wikipedia page on Bayes' Theorem shows briefly some extensions of the theorem to more than two events. When you have the time, I would appreciate your looking it over and say whether you think Swinburne is "playing by the rules."

  • http://www.blogger.com/profile/05211466026535549638 Bradley Bowen

    Further comment on mobathome's objection #1:

    Swinburne clearly sees some of his later arguments for God as having a logical dependency on his initial arguments. For example, the primary evidence he uses in his cosmological argument is admitted to be a necessary condition for the evidence he uses in his teleological argument from spatial order (the existence of simple laws of nature in a complex physical universe assumes the existence of a complex physical universe).

    However, other kinds of logical relationships/dependencies can occur besides 'A is a necessary condition of B'. So the issue that you raise cannot be set aside as easily as my previous response suggests.

    Another possible relationship is that 'A increases the probability of B' or 'A makes B probable' or 'A decreases the probability of B' or 'A makes B improbable'. There may well be such logical relationships between some of the bits of evidence that Swinburne puts forward as evidence for God, relationships that Swinburne fails to notice or point out.

    If there are such relationships, then that could impact the probability calculations that Swinburne uses in his proof for God. Also, I think such relationships may require imagination and/or philosophical skill to uncover.


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