The Argument from Scale (AS) Revisited, Part 3

In part 2 of my series on the evidential Argument from Scale (AS), I concluded that neither metaphysical naturalism nor theism explain the evidence regarding the scale of the universe, if we restrict our background knowledge to the two propositions I identified as B1 and B2. In this post, I want to explore the effect of adding a new statement (B3) to our background knowledge:

B3. God’s purpose(s) include the creation of embodied moral agents.

I want to emphasize that I don’t claim theism entails B3 or even (merely) makes B3 probable. Rather, I am treating it as an assumption, one which is necessary, I think, for (most?) fine-tuning arguments for God’s existence to get off the ground. If we don’t have any good antecedent reason on theism to think God wants embodied moral agents, it’s hard to see why we have any good antecedent reason on theism to think God would want to design a physical universe in such a way that it would support the existence of embodied moral agents, such as humans.[1] What I want to do is explore what happens if we include B3 in our background knowledge and then assess a Bayesian version of the AS.

Preliminaries

For convenience, allow me to state B3 as part of a review of the relevant background evidence, evidence to be explained, and rival explanatory hypotheses.

B: The Relevant Background Evidence

1. A physical universe, which operates according to natural laws and which supports the possibility of intelligent life, exists.

2. Human beings are a type of intelligent life and exist only on Earth. Furthermore, human beings are moral agents.

3. God’s purpose(s) include the creation of embodied moral agents. [assumption]

E: The Evidence to be Explained

1. Temporal Scale: Humans appeared in the universe long after the beginning of the universe. For more than 99.999% of the history of the universe, humans have been absent from it. Even if we only consider earth history, for more than 99.99% of the history of the earth, humans have been absent from the earth.

2. Spatial Scale: The total universe is many orders of magnitude greater than the size of the earth. The greater part of the universe is not accessible to human exploration.

H: Rival Explanatory Hypotheses

theism (T): the hypothesis that there exists an omnipotent, omniscient, and morally perfect person (God) who created the universe.

metaphysical naturalism (N): the hypothesis that the universe is a closed system, which means that nothing that is not part of the natural world affects it.

Bayesian Argument — Version 2

Again, I’m going to apply the relative odds form of Bayes’ Theorem to our rival explanatory hypotheses N and T:

Pr(N| B & E)   Pr(N | B)   Pr(E | N & B)
------------ = --------- X --------------
Pr(T| B & E) Pr(T | B) Pr(E | T & B)

My strategy will be to determine if there is a way to show that both of the ratios on the right-hand side of the equation are greater than one. I’m going to treat the first ratio on the right-hand side of the equation, the ratio of prior probabilities, as unchanged.  Let’s move directly to the second ratio on the right-hand side of the equation, the ratio of explanatory powers.

The Ratio of Explanatory Powers

If we assume that, if God exists, He would want to create embodied moral agents, then this makes the existence of embodied human moral agents slightly more probable on theism than on naturalism. In other words Pr(E | N & B) > Pr(E | T & B). While T & B does not entail that the universe would be created on a human scale, a human scale of the universe is slightly more likely on T than on N. This can be shown using a theorem of the probability calculus.

If O represents an observation, H is our explanatory hypothesis, and A is an auxiliary hypothesis, then we can measure the “effect” of combining H with A by using the Weighted Average Principle (WAP):

Pr(O|H) = Pr(A|H) x Pr(O|H&A;) + Pr(~A|H) x Pr(O|H&~A)

WAP tells us that as Pr(A|H) increases, the closer Pr(O|H) will be to Pr(O|A&H;). Similarly, as Pr(A|H) decreases, the closer Pr(O|H) will be to Pr(O|H &~A).[2]

Let M represent the hypothesis that God’s purpose(s) include the existence of embodied moral agents. Let S represent the auxiliary hypothesis–that is, auxiliary to B3–that God created the physical universe on a human scale, i.e. the temporal and spatial scale of the universe is favorable to human beings. According to WAP:

Pr(E|M) = Pr(S|M) x Pr(E|M&S;) + Pr(~S|M) x P(E|M&~S)

Pr(S|M) is slightly greater than Pr(~S|M) for two, related reasons. First, the truth of M represents one possible state of affairs in which S is also true, a state of affairs which would not obtain if M is false. Second, the falsity of M does not represent a different, extra state of affairs in which S could be true, in a way that is different from the one represented by the truth of M.

WAP tells us that if Pr(S|M) > Pr(~S|M), then Pr(E|M) will be closer to Pr(E|M&S;) than to Pr(Pr(E|M&~S). But that entails that Pr(E | N & B) > Pr(E | T & B).

Notice that the argument is not that N makes E probable , i.e., Pr(E | N&B;) > 0.5, or that T makes E improbable, i.e., Pr(E | T&B;) < 0.5. Rather, the argument simply compares the explanatory power of N to the explanatory power of T and states that the former is slightly greater than the latter. That claim is not in any way undermined by the fact that Pr(E | N&B;) < 0.5 and Pr(E | T&B;) < 0.5.

The Bayesian Version of AS Formulated

We are now in a position to formally state the Bayesian version of AS.

(1) E is known to be true.
(2) Pr(E/N&B;) > Pr(E/T&B;).
(3) Pr(N/B) > Pr(T/B).
(4) Therefore, Pr(N|E&B;) > Pr(T/E&B;). [From (2) and (3)]
(5) N entails that T is false.
(6) Therefore, other evidence held equal, Pr(T|E&B;) < 0.5. [From (4) and (5)]

Series on the Argument from Scale

Notes

[1] Cf. Richard Swinburne, The Existence of God (2nd ed.), who explicitly argues that Pr(B3 | T) > Pr(~B3 | T).
[2] Paul Draper, “Pain and Pleasure: An Evidential Problem for Theists.”

About Jeffery Jay Lowder

Jeffery Jay Lowder is President Emeritus of Internet Infidels, Inc., which he co-founded in 1995. He is also co-editor of the book, The Empty Tomb: Jesus Beyond the Grave.

  • http://www.blogger.com/profile/15227129983621069565 Paul

    Do you think the theist's theological (both Natural and proper) claim that creation in some way "points" to God affects this? So there's claims from the Psalmists on down to natural theologians that, say, the power of the ocean in some way points to the power of its creator, for example. Or, the beauty of the sunset somehow compels us to reflect on the beauty of the divine artist, etc. On this view (which turns the key premise on its head, since creation points to *God* and is not primarily about a habitat for humans), I could see the theist saying that the immense size of the universe is to be expected given the infinite God who made it. This affects size.

    What of the temporal point? What if God planned to come back at some point in human history, say, when humans, as a race, reached a certain level (perhaps in knowledge, immorality, or simply via the world-wide spread of the gospel through ordinary means; or maybe, as Anselm might want to say, when the saved humans equalled the number of fallen angels, so that we'd have a fitting relationship between the two), call this t. Moreover, suppose God would then destroy creation in some way, issuing in the final judgment, etc. Suppose further that the odds are high that God would do this via secondary causes, as is his usual M.O. Thus he let's the universe "collapse" on itself, or be swallowed by black holes, or our solar system be destroyed by a super nova, etc. Presumably this takes a long time—it's still here after 13 billion years! Now, if God started humanity when he started creation, we'd move past t. Thus, God has been "pre-heating the oven" for the 99.9999% of the time we've not been here. He then "puts us in" at just the right time so that we achieve t and then the universe is brought to an end.

    On both these views, which seem plausible to me (and the first seems to be standard Christian theism), the argument seems to not get off the ground.

    Thoughts?

  • http://www.blogger.com/profile/10289884295542007401 Jeffery Jay Lowder

    Paul — This is a great question. I think there is a relationship between the purported evidence of creation, fine-tuning, etc. and the AS. For example, one could consistently say that fine-tuning is evidence favoring theism over naturalism, but, given the fact of fine-tuning, the scale of the universe is evidence favoring naturalism over theism. In fact, the very way I've formulated my Bayesian version of the AS leaves this possibility open. While it says that the scale of the universe favors naturalism over theism, that argument works only granted certain items of background knowledge. And the AS, by itself, obviously says nothing about whether those individual items of background knowledge can be used to construct an evidential argument for theism and against naturalism.

    One of the reasons I am doubtful about the fine-tuning argument (FTA) is because I don't see any reason to believe that B3 is true. That also means I have to be doubtful about the AS. But, as a sort of reductio against the FTA which requires that B3 be true, I could use the AS as an undercutting defeater. Even then, however, I think the evidential force of the AS would be quite limited. I haven't seen a version of the FTA that works, but if I did, I would think the FTA is much stronger evidence for theism than the AS is evidence against it.

    Regarding the argument from beauty, I have never found that argument plausible. If beauty does provide evidence favoring theism over naturalism (and I am unable to see how), it seems to me that it would be extremely weak. Perhaps the argument from beauty is the theistic counterpart to the AS, in the sense that both provide at best very weak evidence for their conclusions?

    Regarding the temporal scale of the universe, you ask, "What if God planned to come back at some point in human history….?" I'm afraid I do not understand why you think that scenario undermines the (admittedly limited) evidential force of the AS, which is an argument against theism, not Christian theism. Since Christian theism logically entails theism, the probability of the former cannot exceed the probability of the latter (though it could be less).

    Following a similar strategy employed by Paul Draper regarding the evidential argument from evil, I would say that the evidential force of the scenario you describe needs to be measured using the Weighted Average Principle (WAP). If we apply WAP, what we will find is this. Given theism (as opposed to Christian theism), there is little antecedent reason to expect that scenario to be true. Therefore, Pr(E|T&B;) will be closer to Pr(E|T&B;&~scenario) than it will be to Pr(ET&B;&scenario;).

  • http://www.blogger.com/profile/15227129983621069565 Paul

    Hi Jeff, sorry if I was unclear.

    I'm interested in this argument employed against Christian theism. My complaints were not so much to defend any *argument* from natural theology (which can be distinguished as natural theology alpha and beta, as Michael Sudduth does, and I have in mind alpha here), but to wonder whether the view that creation "testifies" to its maker (as the Psalms, Proverbs, and Romans seems to suggest, as well as Christians throughout history) is either a rebutting defeater (or insulating defeater) against this kind of argument? So, take the view that creation testifies to God, declares his attributes, so that "Not only," writes Calvin has God, "sowed in men's minds that seed of religion of which we have spoken but revealed himself and daily discloses himself in the whole workmanship of the universe. As a consequence, men cannot open their eyes without being compelled to see him" (1. 5. 1.).

    On this view, what would we expect the size of God's creation to be given God's infinity? That we find an incomprehensibly large universe seems just what we'd expect. So what does the assumption that God created the world (partly) to point to him say about size?

    (I'll leave my remark about time scale alone for the time being).

  • http://www.blogger.com/profile/10289884295542007401 Jeffery Jay Lowder

    Hi Paul — I don't have much to say about the AS an argument against Christian theism (CT), other than what I've already written above. I think my comments about WAP address the objection that, on CT, creation "testifies" to its maker.

    In my opinion, a much more promising reply to AS is to grant its very limited evidential force and argue that some other piece of evidence (i.e., fine-tuning) completely outweighs the evidence of scale. And notice that reply is available to theists in general, not just Christian theists.

  • http://www.blogger.com/profile/15227129983621069565 Paul

    Hi Jeff, I'm not seeing how WAP addresses the idea that we should expect a large scale universe given Christian theism; or, at least that we can see how a large scale universe fits perfectly on the assumptions of a Christian doctrine of the relation between Creator and creation. How does WAP address the Christian conception that creation testifies or bears the marks of or points to to its creator? Above it seemed you applied WAP to theism, and bracketed out Christian theism. What am I missing?

  • http://www.blogger.com/profile/15227129983621069565 Paul

    Also, would you say that Everitt had Abrahamic theism in mind? If he only had generic theism in mind, where does he get the "man is the jewell of creation" premise from? That seems to me to be taken from a misunderstanding of claims made in Abrahamic theism.

  • http://www.blogger.com/profile/01786844757672182664 Some Guy

    I completely fail to see that the Argument from Scale has any merit. There is more than one way to determine the value of something based on size and age. Think about what makes diamonds so valuable. It is that they are incredibly rare amongst all the various natural resources and also because they take lots of time and special circumstances to make. Now, I found it ironic that Everit uses the phrase "jewel of creation" because 'jewels' and diamonds are so valuable because of how rare they are despite their size, and precisely because of how long it takes natural processes to make them. So, why couldn't we view human beings like diamonds that are so valuable precisely because to find them in the history of the universe is so rare, and takes so long to process them? I think this reveals how utterly subjective the argument from scale is. I means, why not think that instead of the universe's size and age revealing something about us, that it reveals the infinitude of the desinger with respect to his eternality and omnipresence.

  • http://www.blogger.com/profile/10289884295542007401 Jeffery Jay Lowder

    Hi Paul — Regarding your 6:16pm CST comment, my answer is, "I'm not sure." As I wrote in part 1 of my series on AS, I do not find Everitt's term "classical theism" to be as well-defined as I would like. My Bayesian formulation of AS appeals to the same data in E as Everitt does in his premise (2), but the background information in my B is different from the assumptions he seems (?) to make.

    Regarding your 5:59pm CST comment, if you can send me an email, I'd like to send you privately a paper which I think might address your question in a roundabout way. (I'm too lazy to try to summarize it right now. :) )

  • http://www.blogger.com/profile/10289884295542007401 Jeffery Jay Lowder

    Some Guy — I agree with you Everitt's formulation of AS, as it stands, does not have merit. I think when the AS is reformulated as a Bayesian argument, as I have done, it then becomes a sound argument, albeit one that provides extremely weak evidence against theism.

    I'm not sure if you consider your comments relevant to the Bayesian argument I provided in this post. Do you? If yes, then they would have to be an objection to:

    (2) Pr(E/N&B;) > Pr(E/T&B;).

    My defense of (2), however, does not depend upon claims about value based on size and age. In fact, I agree with your analogy about diamonds! This may be a crucial distinction between Everitt's formulation of AS and mine. (I would need to re-read Everitt's chapter to see if he constures his point as a point about value, but, regardless, my argument isn't about that.)

  • http://www.blogger.com/profile/01786844757672182664 Some Guy

    Hello Jeff,

    Thanks for your patience with me as I try to understand your argument. Now, the crucial premise as I understand it is your Bayesian (2). Are you saying that if God fine-tuned the universe for embodied moral agents that if follows that the universe would be to scale for such embodied moral agents? That seems to be the key move in your argument. If so, what is your argument for that move?

    Also, I think that if we were observers in a universe that was to human scale that that would actually support atheism and not theism. With respect to the fine-tuning, a possible naturalistic explanation for that fine-tuning is to appeal to some sort of multiverse. But as you probably, know, if we were in such a multiverse, then it is incredibly more probable that we would be Boltzman brains in a universe that was a small thermodynamic fluctuation that wouldn't be any bigger than our solar system. But then, we wouldn't be embodied moral agents, and we shouldn't believe in God because the fine-tuning would have a natural explanation. So, a universe that was to human scale isn't what a theist wants after all.

  • http://www.blogger.com/profile/10289884295542007401 Jeffery Jay Lowder

    Some Guy — No, I am not saying, "if God fine-tuned the universe for embodied moral agents that if follows that the universe would be to scale for such embodied moral agents."

    Rather, what I am saying is that FTAs and the Bayesian AS share a premise. This premise is often unstated in FTAs but I have explicitly stated it and identified it above as B3. Without B3 (or something like it), I can't see how an AS could even get off the ground. With B3, as I've argued in this post, I think it slightly raises the ratio of the probability of naturalism to the probability of theism, but only slightly.

    I do not understand why you think that a human scale of the universe would support atheism, not theism.

    (Aside: as I have written before on this blog, I am not a fan of the multiverse objection to the FTA.)

  • http://www.blogger.com/profile/16342860692268708455 Angra Mainyu

    Jeffery,

    I have a few doubts and questions:

    My first doubt is common to a number of probabilistic arguments for or against theism, in my view.

    I might be missing something, but there seems to be a difficulty in the assumption that greater scope entails strictly lower probability, in a context in which (by assumption, it seems to me) probabilities can be assigned to arbitrary metaphysical hypotheses.

    For example, let C be a set of cardinal numbers of greater cardinality than the set of real numbers, and let's define, for any x in C:


    L(x): There exists at least one being who knows whether there exist at least y minds, for any cardinal number y such that y ≤ x.

    If x(1) < x(2), then L(x(2)) entails L(x(1)), but L(x(1)) does not entail L(x(2)).

    Hence, L(x(2)) has greater scope than L(x(1)).

    Hence, by assumption, P(L(x(2)) < P(L(x(1)))

    Let's define:

    S := { P(L(x)): x is in C }

    Then, S is a subset of the interval [0,1], and the function that assigns to each element x of C the probability P(L(x)) is an injection from C into the set of real numbers, which is a contradiction given the choice of C.

    So, it seems to me that – under the assumption that we can assign probabilities in that context – there are non-contradictory hypotheses with probability zero, and hypotheses a and b such that a is strictly contained in b, but they both have the same probability.

    The second is a question about S: What do you mean by saying that the temporal and spatial scale of the universe is favorable to human beings? (i.e, in which sense of "favorable").

    The third is a question about your reasoning for the conclusion that P(S|M) > P(~S|M).

    A potential difficulty I see is as follows:

    Let B be some embodied beings such that a scale favorable to them is a scale not favorable to humans, and vice versa (i.e., any scale favorable to humans is not favorable to them), and let S' be the hypothesis that God created the universe in a B-scale.

    Unless such beings B are impossible, then someone might similarly conclude that P(S'|M) > P(~S'|M), which would create a problem.

    Also, I'd like to ask about your reasoning from "Pr(E|M) will be closer to Pr(E|M&S;) than to (Pr(E|M&~S)" to "Pr(E | N & B) > Pr(E | T & B)".

  • http://www.blogger.com/profile/01786844757672182664 Some Guy

    Ohhh, now I get your argument. However, let me try to defeat it by stating more clearly why a universe that is more to human scale supports atheism.

    If something like Vilenkin's Many Worlds Ensemble is correct, then it is overwhelmingly more probable that we should be observing a much different different universe then we in fact observe.

    Roger Penrose calculates that the odds of our universe's low entropy condition obtaining by chance alone are on the order of 1:10^10(123). If our universe were but one member of a collection of randomly ordered worlds, then it is vastly more probable that we should be observing a much much smaller universe (Penrose, Road to Reality, 762-65).

    Universes that are to human scale are much more plenteous on the ensemble of universes. Thus, if we were in such a universe, then that would constitute strong support for Vilenkin's hypothesis which would mean that chance would be the best explanation of our fine-tuning and thus, this would constitute evidence against theism.

    Thus, God wouldn't create a universe to human scale with human beings in it.

  • http://www.blogger.com/profile/10289884295542007401 Jeffery Jay Lowder

    Angra —

    Wow! Your comment wins the prize for the most challenging comment I've received in a long time.

    (Aside: I just looked at the two posts on your own blog and was very impressed. You've clearly thought long and hard about cosmological arguments for theism. If and when you are so inclined, you should consider submitting them for publication in the Secular Web's Modern Library.)

    Regarding your doubts and questions:

    (1) This is a very interesting and challenging question. One thing to keep in mind is that scope is simply one factor out of two I mentioned which help to determine the prior probability of a hypothesis; the final probability of a hypothesis is a function of both prior probability and explanatory power. So it would be a mistake to say that "greater scope entails strictly lower probability" (my italics). What I am prepared to say, I think, is that, if two hypotheses are equal in terms of simplicity but inequal in terms of scope, the hypothesis with the greater scope will have a lower prior probability than the hypothesis with the smaller scope.

    I want to think about the scope of L(1) and L(2) before commenting further about that. And notice that the prior probability for L(1) and L(2) is also a function of simplicity. I think L(2) is slightly simpler than L(1).

    (2) By "favorable" to human beings, I mean spatial or temporal features of the universe which are neither unremittingly hostile nor indifferent to human flourishing.

    (3) I will have to get back to you in a later comment; I've run out of time for now!

  • http://www.blogger.com/profile/16342860692268708455 Angra Mainyu

    Jeffery,

    Thanks; regarding scope and simplicity, you're right. I was assuming equal simplicity for the sake of the argument, since I thought that L(x(1)) and L(x(2)) would be either equally simple, or the former would be simpler.

    The reason for that conclusion was as follows:

    You explained (in the second part of the AS) that simplicity is "a measure of the degree of (objective) uniformity that the theory attributes to the world", and that N is simpler than T since the latter "includes at least one radically different kind of entity (i.e., a supernatural person) which N denies".

    I have to admit that I have some difficulty understanding the relevant concepts of simplicity or (objective) uniformity, and of the supernatural, but even so, I reasoned as follows:

    If we have two hypotheses, H(1) and H(2), and hypothesis H(2) logically entails H(1), it cannot be that H(1) includes more entities, or more kinds of entities than H(2), or that H(1) includes any entity or kind of entities that H(2) does not include.

    Hence – at least, going by what I got from your previous post as a means of ascertaining simplicity -, my conclusion was that if H(2) entails H(1), then H(2) is not simpler H(1).

    In light of the previous conclusion, I reckoned that L(x(2)) is not simpler than L(x(1)) (assuming always x(1) < x(2)), since L(x(2)) entails L(x(1)).

    So, since simplicity would not make L(x(2)) more probable than L(x(1)), then I thought I might as well assume that they're equally simple, concluding that L(x(2)) – which has greater scope than L(x(1)) – is less probable.

    One could drop the assumption of equal simplicity, but that would not change the conclusion that L(x(2)) is less probable than L(x(1)) as long as the conclusion that the simplicity of L(x(1)) is no less than that of L(x(2)) holds, since in that case, L(x(1)) has strictly less scope and no less simplicity than L(x(2)).

    That said, now that you say that you think that L(x(2)) is slightly simpler than L(x(1)), I suppose I may have missed some of the means by which you measure simplicity.

    As I admitted above, I have some difficulty understanding what the relevant terms (e.g., "objective uniformity") mean, so I was making the simplicity assessment based on the standards I was able to infer from your previous post.

    However, if there is more to the standards for measuring simplicity, that may well have caused me to make a mistaken assessment – i.e., mistakenly concluding that a hypothesis cannot be simpler than one of the hypotheses it entails.

    If that is the case, I would like to ask you if you could briefly outline what features of a hypothesis one needs to take into consideration in order to measure simplicity, or, alternatively, let me know where I could find some information on the issue of how simplicity is measured.

    That said, even if my assessment of simplicity was mistaken, it's still the case that L(x(1)) is no less probable than L(x(2)) – since L(x(2)) entails L(x(1)).

    Also, it can't be that L(x(2)) is always less probable than L(x(1)) for all such x(1) < x(2) – else, a contradiction follows, as in my earlier construction -, so there are some cardinals x,y such that x

    Hence, since L(y) entails L(x):

    P(L(x)) = P(L(x)&¬L(y)) + P(L(x)&L;(y)) = P(L(x)&¬L(y)) + P(L(y)) = P(L(x)&¬L(y)) + P(L(x))

    Hence, P(L(x)&¬L(y)) = 0.

    So, there are non-contradictory hypothesis of probability zero (in fact, there are infinitely many of them) – and thus, not logically necessary hypothesis of probability 1.

    I'll continue below due to the 4096 characters limit.

  • http://www.blogger.com/profile/16342860692268708455 Angra Mainyu

    Given the above, one could start with a hypothesis H, then add another hypothesis E with probability 1, then H&E; has the same probability as H, and has greater scope if E makes some claims that H does not make.

    Unless any such E actually increases simplicity, in some cases H&E; would have no greater simplicity than H, greater scope than H, and equal probability as H.

    I'd need more information on how to measure simplicity before I can tell whether that would be a problem, though.

    P.S: regarding my arguments, thank you; I appreciate the suggestion.
    I've actually considered submitting them for publication, but concluded that my articles do not meet the formatting or style requirements.
    However, I realized they wouldn't be accepted, since they don't meet the formatting or style requirements, and adapting them would take me a lot more time than I have these days.
    For instance, the format of my articles is "not clean" html, or .pdf., and I don't have the time at the moment to learn enough programming to re-write them.
    Also, the writing style does not meet the standards of Chicago Manual of Style, so I would need to study that manual and re-write the articles in accordance to it.
    In short, I'm afraid I won't be able to adapt my articles to the requirements for publication for the foreseeable future.
    Also, I still appreciate some degree of anonymity – yes, I know, the internet isn't really anonymous, but it's not as non-anonymous as publishing under my name, either -, though I would probably still choose to publish them if I could.
    Anyway, thank you, and I'll keep that possibility in mind.

  • http://www.blogger.com/profile/10289884295542007401 Jeffery Jay Lowder

    Angra — Your questions are outstanding. I realize I need to brush up on set theory to be able to answer them. I haven't read everything or even close to everything on confirmation theory, but I've read a decent amount. I've never run across an objection like yours to the idea of smaller scope accords greater prior probability. That leads me to wonder if I have somehow misstated the point.

    As an aside — I now think there is a stronger version of the Bayesian AS. Here it is:

    In this version, I am going to switch the focus of the argument from the scale of the universe to the fact that humans don't have a privileged position (spatially or temporally) in the universe.

    Preliminaries

    B: The Relevant Background Evidence

    1. A physical universe, which operates according to natural laws and which supports the possibility of intelligent life, exists.

    2. Human beings are a type of intelligent life and exist only on Earth.

    E: The Evidence to be Explained

    1. Non-Privileged Temporal Position: Humans did not exist right from the start of the universe.

    2. Non-Privileged Spatial Position: The earth is not the center of the universe.

    H: Rival Explanatory Hypotheses

    theism (T): the hypothesis that there exists an omnipotent, omniscient, and morally perfect person (God) who created the universe.

    metaphysical naturalism (N): the hypothesis that the universe is a closed system, which means that nothing that is not part of the natural world affects it.

    Bayesian Argument Version 3 Formulated

    (1) E is known to be true.
    (2) Pr(E/N&B;) > Pr(E/T&B;).
    (3) Pr(N/B) > Pr(T/B).
    (4) Therefore, Pr(N | E&B;) > Pr(T/E&B;). [From (2) and (3)]
    (5) N entails that T is false.
    (6) Therefore, other evidence held equal, Pr(T | E&B;) < 0.5. [From (4) and (5)]

    Defense of Premise 2

    Premise (2) is a comparative claim; it does not claim that we would expect E given T, i.e., Pr(E/T&B;) > 0.5. In fact, I think Pr(E/T&B;) < 0.5. Rather, the claim is that E is slightly more likely given T than given N. This is because it is slightly more likely on T than on N that there would be a reason why we would have a spatially or temporally privileged position (e.g., God's desire to relate to us immediately after His creation of the universe rather than waiting billions of years, God's desire to emphasize our importance to Him, etc.).[1]

    Notes

    [1] I owe this point to Paul Draper.

  • http://www.blogger.com/profile/01786844757672182664 Some Guy

    It seems like your argument assumes that we can reliably judge what different laws of nature would be like because it is obvious that on the current law of nature, there is no way we could exist right from the start unless our universe was the result of a thermodynamic fluctuation in which case we would be Blotzman brains in a universe that would confirm atheism, and disconfirm theism.

    Also, there is no such thing as the center of the universe. That is a pretty basic consequence of the topography of our universe.

    I agree with Angra that explanatory scope and power are the most important virtues an explanation can have such that if theism had greater explanatory scope and power with respect to the many aspects of the fine-tuning then it is to be preferred over another explanation that may ormay not be simpler. Moreover I have given a rebutting defeater to your premise (2).

    Let me also state that what yuor argument seems to be after is that if God created us, then he would let us know that we are intended for some purpose. I do not think that the this can be read off the fine-tuning, or if we were at the 'center' of the universe which is physically impossible anyway (the ancient Greeks saw the center of the universe as the refuse of the universe by the way), all such notions are either to vague, awaiting further revelation, or too subjective.

    However, a Christian theist can claim that God let us know that we were intended and meant for a specific purporse based on the teachings, life, death, and resurrection of Jesus who was God incarnate! (if true).

    Moreover, I would caution against doing to much armchair philosophy without checking the science. For, in addition to my other defeater, it can be added that the mass-density of our universe is such that if it were off by a grain of sand, then the expansion rate of the universe would have precluded the existence of complex life ever coming to be. This means tat our universe has to be as massive and the expansion of space has to be incredibly fine-tuned for a universe to be life-permitting as ours is.

    Also, our universe is more mathematically elegant than any bubble universe would be and that is to be expected on theism over naturalism as well. Also, recent research on super-earths has revealed that on our laws of nature, our Earth is the about as large as it can be before the density and distribution of water would prevent complex life! That may seem counterintuitive but so much for your intuitions.

    There is more, but I think you can see that if we were in a universe like the one your argument thinks we should be in, we couldn't be embodied moral agents and such observations would disconfirm theism. Moreover, theism has greater explanatory scope and power with respect to the fine-tuning compared to naturalism which trumps any imagined simplicity a human scale universe may have. But, it turns out that our Earth is as big as it can be, and it is necessary for our universe to be as we observe it accorsing to additional parameteres of fine-tuning.

    Lastly, God wouldn't play around if He wanted us to know that we were intended for some purpose, He would just tell us, as He did through the incarnation.

  • http://www.blogger.com/profile/10289884295542007401 Jeffery Jay Lowder

    Hi Paul — Out of curiosity, are you Paul Manata?

    I never got an email from you, but I do see that Paul Manata posted an article, "Theism and the Size fot he Universe", on his Analytic Theology, et cetera blog. Your comments here are very similar to Paul M's comments there.

    Online identities aside, I do agree with Paul M's comments that Everitt's formulation of the argument is not compelling. On the other hand, Paul M's comments don't address the Bayesian version of AS. On the other hand, I was disappointed to read Patrick Chan's insult against atheists: "Another thing I'd add is so many of these atheists have so little imagination." I do not find evidence for Chan's assertion: "They seem to expect if God exists then everything in creation must serve a specific, useful, and perfectly logical (to humans) purpose. Otherwise God doesn’t exist."

  • http://www.blogger.com/profile/16342860692268708455 Angra Mainyu

    Some Guy,

    I disagree with most of your claims – unsurprisingly, since I'm an atheist – but, due to limited time, I won't be able to engage in a debate – too many discussions on my plate!

    I will just point out, though, that you've misinterpreted what I said.

    I did not say that explanatory scope and power are the most important virtues of an explanation.

    In fact, a greater scope, in the sense in which we've been using the term "scope" in our discussion, does not entail greater probability of a hypothesis, all other things equal – what we've been discussing is whether it always entails lower probability, all other things equal.

  • http://www.blogger.com/profile/16342860692268708455 Angra Mainyu

    Jeffery,

    Thanks.

    I've not seen that objection before, either.

    As I see it, a potential reply would be based on the philosophy of mathematics (e.g., rejecting infinities, or rejecting the use of cardinals for some reason), but those objections have their problems too – and a burden on the claimant.

    Regarding your new argument, it's interesting; I'd have to think more about the substantive issues to make an assessment, though.

    Side note: I think there is a typo:

    You said: "Premise (2) is a comparative claim; it does not claim that we would expect E given T, i.e., Pr(E/T&B;) > 0.5. In fact, I think Pr(E/T&B;) < 0.5. Rather, the claim is that E is slightly more likely given T than given N".

    Did you mean that E is slightly more likely given N than given T?

    Also, in the first part, did you mean Pr(E/N&B;) < 0.5?

  • http://www.blogger.com/profile/11832363773872711595 Vic Stenger

    This addresses the claim made by Some Guy:

    "it can be added that the mass-density of our universe is such that if it were off by a grain of sand, then the expansion rate of the universe would have precluded the existence of complex life ever coming to be. This means that our universe has to be as massive and the expansion of space has to be incredibly fine-tuned for a universe to be life-permitting as ours is."

    The mass density is related to the expansion rate of the universe. Both are claimed to be fine-tuned to enormous precision. Neither are even parameters in the standard model of cosmology since their values are given in that model.

    Here's what I said about this in my recent book The Fallacy of Fine Tuning (Prometheus Books 2011), pp. 202-203:

    ". . .in a number of his debates William Lane Craig has said, “Stephen Hawking has estimated that if the rate of the universe's expansion one second after the Big Bang had been smaller by even one part in a hundred thousand million million, the universe would have re-collapsed into a hot fireball.” In his book Life After Death, Dinesh D’Souza used the same allusion: “If the rate of expansion one second after the Big Bang had been smaller by even one part in a hundred thousand million million, the universe would have collapsed before it ever reached its present size.” Neither Craig nor D’Souza give the reference but I have found the quotation on page 121 of Hawking’s A Brief History of Time."

    The two apologists have again* lifted the quote out of context to support their own ill-founded beliefs. A few pages later, Hawking explains how this problem is solved in inflationary cosmology. On page 128 of A Brief History of Time, Hawking talks about the inflationary model of the early universe, which was still relatively new in 1988 when his book was published. In the inflationary picture, Hawking notes:

    "The rate of expansion of the universe would automatically become very close to the critical rate determined by the energy density of the universe. This could then explain why the rate of expansion is still so close to the critical rate, without having to assume that the initial rate of expansion of the universe was very carefully chosen."

    *They also did this to Hawking on the matter of the universe beginning with a singularity.

  • http://www.blogger.com/profile/11832363773872711595 Vic Stenger

    This is response to another statement by Some Guy:

    "Also, our universe is more mathematically elegant than any bubble universe would be and that is to be expected on theism over naturalism as well. Also, recent research on super-earths has revealed that on our laws of nature, our Earth is the about as large as it can be before the density and distribution of water would prevent complex life! That may seem counterintuitive but so much for your intuitions."

    There are a hundred billion galaxies in the visible universe. Each has a hundred billion stars. Each star has ten planets. (Order of magnitude calculation here). That's 10^21 planets. Beyond our light horizon it is estimated that there are 10^100 times as many as this. Now, how unlikely do you think it is that a planet like Earth occurred somewhere?

  • http://www.blogger.com/profile/17668854596329493360 ZAROVE

    Mr. Stenger, deposit matter how likely a Planet like the Earth forms?

    The argument from Scale against God's existence remains unconvincing, as it presupposes that belief in God must rely upon the Universe being built for Humanity. But even the Christian Faith, its principal Target, doesn’t actually say this.

    I just used the Mormons as an example in another Thread. I am not a Mormon. However, using their Theology as a prominent example, Mormons teach that God created numerous habitable worlds across the Universe. Mormonism thus explicitly teaches that life exists on other planets, and that the Universe is very large. Wouldn’t the very large scale of the Universe we see thus conform to the expectations the Mormons have? While not saying this proves Mormonism True, it doesn’t really work against it in any feasible way either.

    Conversely, even the more mainstream of Christian Churches, such as Catholicism or Anglicanism, seem to view the Creation as God’s self expression, not as something created solely for Man. This sentiment is in fact found in most Churches, from the Presbyterian Church to the Methodist Church to even the Churches of Christ. While it is an opinion of some Evangelical Christians, the vast majority of Christians seem to think that the Grand Scale of the Universe is not only not a problem to their own view of God, but actually expected.

    This isn’t even new, as we can cite Churchmen in the Middle Ages postulating the possibility of a Large Universe and life on other worlds, with the reason this didn’t become prominent resting on Ptolemy and Aristotle, not the Bible.

    While, again, this doesn’t prove that God in fact does exist, it does counter the claim that the Large Scale of the Universe is an effective Argument against God’s existence. The Argument relies on assuming that not only did God create the Universe, and Man, but that he created the Universe for man. If you reject the Latter proposition, as most Christians actually do, then the argument has no impact.

    Further, even if we accept the idea that the Universe was created for man, it can equally be argued that God anticipated Human Ingenuity to take him one day to the distant worlds we see via a Telescope. Or perhaps in a world before the Fall man would have been able to Live forever and thus have his Children spread across an infinite ( Or seemingly so) Sea of Stars.

    Thus, even if we make the assumption that Man is the reason for all other things in the Universe, the Grand Scale of the Universe remains unconvincing. Even the lack of Habitability or outright hostility isn’t much of an argument if we live in a Fallen world.

    So, I am afraid the Scale argument simply fails to convince anyone. Those who do think Man is the reason for Creation will see the Grand Scale of the Universe as a part of God’s providence, whilst the Majority of Christians do not even think the Universe was made explicitly for Man.

    And that is just Christianity. What about Hinduism? Or Buddhists who believe in various gods? Or Shinto?

    I’m sorry, but the argument is meaningless. Mr. Lowder is correct in his criticism of it as an Argument for Atheism.

  • http://www.blogger.com/profile/16342860692268708455 Angra Mainyu

    Jeffery,

    I've been thinking about possible replies to the objection I mentioned; I don't know what your assessment of Richard Swinburne's account of probability is, but according to his view, while there are objective inductive probabilities, those do not have to have an actual numerical value – just relations of equality and inequality.

    I'm not sure how that could work, though: if they have such relations, why would there be no values?

    And if they have no values, how could one apply Bayes' theorem, etc.?

    So, I don't know whether that could work system – I'd have to consider it more carefully, but I won't be able to do so for the moment -, but I thought I mentioned it, since – if successful – that would block the cardinality objection to the argument.

  • http://www.blogger.com/profile/10289884295542007401 Jeffery Jay Lowder

    Angra — Thanks. Yes, I've read quite a bit by Swinburne about his views on probability, but it's been a while. I also once read something by Paul Draper which (I think) suggested a similar view, but I'm not confident about that. Regardless of who has espoused the view, I have the same questions as you do.

  • http://www.blogger.com/profile/10289884295542007401 Jeffery Jay Lowder

    Hi Paul,

    You wrote:

    Hi Jeff, I'm not seeing how WAP addresses the idea that we should expect a large scale universe given Christian theism; or, at least that we can see how a large scale universe fits perfectly on the assumptions of a Christian doctrine of the relation between Creator and creation. How does WAP address the Christian conception that creation testifies or bears the marks of or points to to its creator? Above it seemed you applied WAP to theism, and bracketed out Christian theism. What am I missing?

    Regarding the idea that creation testifies to its maker, that idea is not of obvious relevance to (2), since it is logically possible that creation testifies to its maker and (2) is true. For example, it's possible that the beginning of the universe and the life-permitting conditions of the universe provide evidence favoring theism over naturalism; the scale of the universe provides evidence favoring naturalism over theism; and the total evidence about creation overwhelmingly favors theism over naturalism in such a way that humans are "compelled to see" God. Indeed, this possibility regarding the total evidence is even logically compatible with the position, "All human beings know that [the Christian] God exists."

    Let us now suppose that there is some Christian doctrine which does give us an antecedent reason–that is, a reason independent of the evidence for E–to expect, not just that creation testifies to its maker, but also the non-human scale of the universe. Would that defeat premise (2)?

    No, for two reasons.

    First, if (2) is true, then (2) is, at least, relevant to Christian theism for the simple reason that Christian theism entails theism. If B entails A and Pr(A)=x, then Pr(B)<=x..

    Of course, it's possible that Christian doctrines (or any other religious, ethical, metaphysical, or epistemological beliefs) could raise Pr(E|T&B;) or lower Pr(E|N&B;). The Weighted Average Principle (WAP) is a mechanism for evaluating the evidential relevance of other beliefs to (2):

    Pr(E | T & B) = Pr(E | T & B & CD) x Pr(CD | T) + Pr(E | T & B & ~CD) x Pr(~CD | T)

    If CD is some Christian doctrine, then Pr(E | T & B) will be an average of Pr(E | T & B & CD) and Pr(E | T & B & ~CD). It is not necessarily a straight average, however, because Pr(CD | T) and Pr(~CD | T) may not equal 1/2. Thus, if Pr(CD/T) = 3/4 and Pr(~CD/T) =1/4, then Pr(E | T & B & CD) is given three times as much weight as Pr(E | T & B & ~CD) in calculating the average.

    The upshot is that, even if we assume that Pr(E | T & B & CD) is extremely high, we still have to address Pr(CD | T) and Pr(~CD | T) before we can conclude that CD raises Pr(E | T & B). I am unable to see how one could show that Pr(CD | T) > Pr(~CD | T), for some relevant CD, but I do not rule out the possibility that someone may discover a way to show that. The important point, however, is that it needs to be shown, not assumed.

    Second, (2) is a comparative claim: it claims that Pr(E/T&B;) is slightly more likely than Pr(E/N&B;). Thus, arguments about the non-comparative value of Pr(E/T&B;) are, by themselves, not relevant. Note that such arguments are irrelevant even if they establish that Pr(E/T&B;) is high. Again, the whole point of the argument is to compare the ratio of Pr(E/N&B;) to Pr(E/T&B;). For example, hypothetically speaking, if your response to (2) were to consist solely in the claim that Pr(E/T&B;)= .99, it could still be the case that Pr(E/N&B;)=.999, in which case (2) would still be true.

  • http://www.blogger.com/profile/10289884295542007401 Jeffery Jay Lowder

    Hi Angra — I don't have a reply to your objection regarding my claim that greater scope always entails lower probability, all other things held equal. But it did occur to me that I could easily modify my argument in a way which, I think, would make this a moot issue.

    I could modify (3) as follows:

    (3') Pr(N/B) >= Pr(T/B).

    Even if the prior probabilities of N and T are equal, the argument still works. And I am very confident that the prior probability of N is at least as high as that of T.

    FYI: I took version 3 of the AS posted in an earlier comment on this post, and devoted an entire post to it. See here.

  • http://www.blogger.com/profile/16342860692268708455 Angra Mainyu

    Hi, Jeffery

    I agree, that makes that issue moot.

    I have to go now, but I will take a look at the new version of your argument tomorrow (though I'm working on a full reply to Swinburne's "The Existence of God", which is taking most of my time for philosophical discussions at the moment, so I'm afraid I can't post often).

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