The Purposes of God

Whether a theist says “God created all living things” or “God created the universe” or “God raised Jesus from the dead” the point is to give a personal explanation for some facts (or alleged facts) as opposed to a physical or scientific explanation. When giving a personal explanation for some fact, information about motivations or purposes is obviously relevant evidence.

If we know that just one person committed the murder of a rich man, and if we know that it was either the butler or the maid who killed him, a good question to investigate would be, “Who had a strong motive for killing the rich man?” If the butler had a strong motive but the maid did not, that would make the butler the primary suspect. That would make it more probable that the butler committed the murder than that the maid did, other things being equal.

In addition to motive, there are also considerations of means and opportunity. If the rich man was shot to death, we could ask some other relevant questions: “Did the gun used in the killing belong to the butler or to the maid or to someone else? Did the butler have access to that gun? Did the maid have access to the gun? Are there fingerprints on the gun? If so, do those fingerprints match the fingerprints of the butler or the maid?”

Such evidence, however, is not relevant in the case of God. If God were to kill someone, God would not need a gun, even to kill someone by “shooting them to death”. God can create speeding bullets out of thin air by simply willing them into existence. If God did choose to use a gun to kill someone, God would not leave her fingerprints.

If God did leave fingerprints, it would not be prints from her own fingers, since God is a bodiless spirit who has no hands and no fingers. God has access to all guns and can create a gun of any kind instantaneously, fire the gun, and then instantly make the gun cease to exist. So, when it comes to God, means are irrelevant. God needs no means or tools to do something, and if God chooses to use some means or tools to achieve some end, God can instantly create and instantly destroy any means or tools she wishes to use.

In the case of the butler and the maid, we should ask, “Was he/she in the vicinity of the victim about the time that the murder was committed?” If the butler was ten miles away picking up dry cleaned clothes at the time of the murder, then the butler is off the hook. Such questions of opportunity don’t apply to God. God is, by definition, all-knowing and all-powerful, so God is, in effect, present at all places and all events. God, unlike finite human beings, always has opportunity in all times and at all places. God can bring about any logically possible event at any time or place God chooses.

Therefore, since means and opportunity are irrelevant in determining whether or not God performed some action, motive is of great significance in questions about what God did or did not do.

Did God raise Jesus from the dead? There appears to be a big hurdle to jump before this question can be answered: Did Jesus rise from the dead? As Dianelos points out, there are good reasons to doubt claims about events that involve violation of the laws of nature. If Jesus did rise from the dead, that would rule out naturalism, or would at least be a good reason for doubting naturalism. One could reasonably claim that the probability of Jesus rising from the dead given naturalism is a fairly low probability.

But as my refinement of Dianelos’ formulation of the logic of theistic arguments shows, there is a comparison being made between the relative merits of theism and naturalism:

r: Jesus rose from the dead.
t: Theism is true.
n: Naturalism is true.

1. P(r//t) = x
2. P(r//n) = y
3. x > y
4. r is true.
Therefore:
5. P(t) > P(n) …other things being equal.

Premise (2) means: The probability that Jesus rose from the dead given that naturalism is true is equal to y.

It seems reasonable to believe that y is going to be a fairly low probability. Naturalism is not very compatible with resurrections.

But in order for this argument to work, we need to show that the probability of this event is greater on the assumption that theism is true. Premise (1) means: The probability that Jesus rose from the dead given that theism is true is equal to x. The theist needs to establish that x is significantly larger than y for this argument to carry some weight.

I don’t see how one could establish this apart from establishing some theory about the likely motivations and purposes of God. If we don’t know what God’s motivations and purposes are (or what they would be if there were a God), how can we have any confidence that raising Jesus from the dead is the sort of thing that God might do? The mere fact that God (if she exists) had the power to raise Jesus from the dead does not show it to be at all likely that God would do so. I have the power to burn my own feet off with a blow torch, but it is very unlikely that I will chose to do so.

If my thinking about the logic of resurrection is correct, then the next question to consider is whether the alleged motivations and purposes of God are similarly critical to design arguments that infer the activity of God based on the existence and nature of the universe.

About Bradley Bowen
  • http://www.blogger.com/profile/05693985638589020492 Mark

    I don't think this is the apologist's argument. They'll say that the best explanation of Jesus' resurrection is that he had some supernatural connection; and given this, the best explanation of Jesus' claim to be God is that Jesus was correct.

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

    Mark said: "I don't think this is the apologist's argument."

    There are lots of apologists with different and various arguments about the resurrection of Jesus. Did you have any particular apologist(s) in mind?

    The general pattern of apologetic arguments, initiated by the thinking of Aquinas, is to first establish the existence of God, and then appeal to miracles as a way of establishing the true religion.

    So, the argument from resurrection to the existence of God (i.e. theism) presented in my post does not fit with the general pattern of apologetics. However, at least one prominent apologist, Gary Habermas, uses the resurrection as evidence for the existence of God.

    In his argument for the resurrection, Swinburne assumes that there is a 50/50 chance that God exists. But his conclusion is that it is highly probable (aprox. .97) that "God became incarnate in Jesus Christ who rose from the dead." (The Resurrection of God Incarnate, p.214). So, Swinburne uses the resurrection to bump up the probability of theism from .5 to more than .97.

    The argument I presented does not represent Swinburne's argument, but neither does your brief characterization of how apologists argue about the resurrection.

    McDowell tries to eliminate various naturalistic explanations for the facts about Jesus' alleged resurrection, and then concludes that we must accept a supernatural explanation. But he immediately infers God as the cause: "Only one conclusion takes into account all the facts and does not adjust them to preconceived notions. It is the conclusion that Christ is in fact risen – a supernatural act of God in history." (The Resurrection Factor, p.102).

  • http://www.blogger.com/profile/05693985638589020492 Mark

    I'm not saying the resurrection isn't (supposed to be) evidence for God. I'm saying that I don't think the resurrection merely in itself is supposed to confirm theism over naturalism (though it may confirm supernaturalism over naturalism), at least for most apologists I've encountered (who are always at pains to stress Jesus' self-identification as God along with the resurrection). Also note the hypothesis that apologists would be wanting to look at is Christian theism, not theism simpliciter. According to Christian theism, Jesus was the son of God and had to vicariously atone for mankind's sins by a fatal sacrifice from which he would emerge victorious, yada yada.

  • http://www.blogger.com/profile/13116034158087704885 March Hare

    Assumptions galore…

    "God is, by definition, all-knowing and all-powerful"

    Only because you use a capital G. By using the God version you make god monotheistic, almost definitely Abrahimic and all the omni- things that go along with that.

    god is not necessarily alone, not necessarily all-powerful or all knowing. (In fact, any reading of the Old Testament shows that God to be clearly not omniscient.)

    Jesus (supposedly) raised Lazarus from the dead. The same theistic argument can be framed around Lazarus with no reference to Jesus which would render this argument moot with regards to Christianity over any other religion.

    The argument also assumes Jesus existed and that he died in roughly the way described. Neither of which are mentioned yet both need to be true or the rest is pointless. We must attach a probability onto Jesus' existence and then onto his 'death' on the cross.

    This may not shift the probabilities enough to change anything, but it might get people thinking about what assumptions they are making prior to attaching a probability to a statement.

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

    Mark said:
    "I don't think the resurrection merely in itself is supposed to confirm theism over naturalism (though it may confirm supernaturalism over naturalism), at least for most apologists I've encountered (who are always at pains to stress Jesus' self-identification as God along with the resurrection)."

    Gary Habermas is one apologist who uses the resurrection of Jesus as an argument for God's existence. What you are saying applies to Habermas. Here is a quote from his book The Resurrection of Jesus:

    "…combining the historical event of the resurrection with the message of Jesus does make Jesus' theistic world view probable. Jesus claimed to be Deity and he also claimed to be fulfilling His Father's will in a very special sense by proclaiming a unique message. Are these claims valid? To verify them Jesus performed miracles as a sign of His credibility. His resurrection from the dead, in particular, was singled out and predicted in advance to be the sign to vindicate His message and His own claim to Deity." (ROJ, p.58)

    Since Habermas is a leading Christian apologist on the issue of the resurrection of Jesus, I take it your point is confirmed.

    So, does this mean that my refined version of Dianelos' formulation of the general logic of arguments for God fails to capture how apologists use the resurrection of Jesus as an argument for God?

    It certainly casts doubt on the specific instance that I gave, where the key factual premise states just one fact:

    4. r is true.

    r: Jesus rose from the dead.

    But we could repair this defect by adding more factual/historical claims to r:

    4a. (r & m & d & p) is true.

    m: Jesus preached messages that he claimed were from God.

    d: Jesus claimed to be the divine Son of God.

    p: Jesus predicted that he would be killed and that God would bring him back to life to show that Jesus' teachings and claims were true.

    So, if we enrich premise (4) with additional historical claims, and make parellel ammendments to the premises (1) and (2), then I think the form of the argument will work to capture how Habermas and other apologists argue from the resurrection to the existence of God.

    This actually reinforces my central point, which is that the purposes of God are critical in this argument, and possibly in other arguments for God.

    The other historical points are there to provide a background upon which the resurrection can be seen as a significant or meaningful event as opposed to simply a wierd fluke. The meaningfulness of the event is fundamentally to be seen in the motivations and purposes of God. God has a message to communicate to humans, and God is using an intermediary to do this, and God wants to give his messenger credibility so that people will be able to recognize that the messenger is truly and accurately speaking a message from God, etc.

    The additional historical facts help to tell a story about God's activity and God's motivations. A miracle is not simply an odd or inexplicable event, it is a revelatory event, a meaningful event, and the meaning has to do with showing something about God's nature and purposes.

    It is not a necessary condition that an event reveal something about God in order for it to be a miracle, but in order for humans to be able to recognize an event as being a miracle, it does seem necessary that the miracle in question have some fairly obvious significance in relation to our thinking about God.

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

    March Hare said:

    Assumptions galore…

    "God is, by definition, all-knowing and all-powerful"

    Only because you use a capital G.
    =========
    No. I'm using the word "God" here in the context of arguments between skeptics and theistic philosophers from Western religious traditions. That God is all-powerful and all-knowing (omnipotent and omniscient) is a standard part of how "God" is defined or understood by most theistic philosophers from Western religious traditions (i.e. Judaism, Christianity, Islam).

    In the context of arguments with polytheists, New Agers, or people from Eastern religious traditions, the word "God" might well be given a different definition or meaning. But that is a different context than what I'm concened with here.

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

    March Hare said:

    "The argument also assumes Jesus existed and that he died in roughly the way described. Neither of which are mentioned yet both need to be true or the rest is pointless. We must attach a probability onto Jesus' existence and then onto his 'death' on the cross."

    Yes. That is all assumed in making the claim that Jesus rose from the dead. You are pointing out legitimate historical problems with premise (4).

    I'm not claiming that the argument is a good or strong argument; I'm just trying to understand and clarify the logic of the argument, and especially the role that is played here by the alleged purposes or motivations of God.

    If it is essential to establish certain purposes or motivations of God (or to show that if God were to exist, then God would probably have such-and-such a motivation) in order to make this argument(and other apologetic arguments) work, then that would be another area of objections, in addition to the usual historical objections.

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

    It is not as easy as I had thought to modify premises (1) and (2) to correspond with my suggested modification of premise (4).

    My first thought was to simply replace r with the conjunction of historical claims (r and m and d and p):

    1a. P(r&m;&d;&p;//t) = x
    2a. P(r&m;&d;&p;//n) = y
    3. x > y
    4a. (r&m;&d;&p;) is true
    Therefore,
    5. P(t) > P(n) …other things being equal

    But (1a) doesn't seem to make the intended point. Theism by itself does not have anything to say about the particular "facts" that Jesus claimed to be divine, claimed to preach a message from God, etc. And naturalism also does not have anything to say one way or the other about such claims being made by Jesus.

    So, I think that these additional historical claims belong in the assumption or given part of the probability equation:

    1b. P(r//t&m;&d;&p;)= x
    2b. P(r//n&m;&d;&p;)= y
    3. x > y
    4a. (r&m;&d;&p;)is true
    Therefore,
    5. P(t) > P(n) …other things being equal.

    I'm not sure if I have captured all the assumptions required to make the inference here logical, but I think the first two premises make more sense on this second formulation of the reasoning.

  • http://www.blogger.com/profile/05693985638589020492 Mark

    This comment has been removed by the author.

  • http://www.blogger.com/profile/05693985638589020492 Mark

    That does seem like a better representation of the argument, since it's specifically Christian doctrines about God that the resurrection is supposed to ultimately be supporting. However, I don't think this form of argument is the one being employed by apologists (e.g., it employs a very crude form of the prosecutor's fallacy). They're using abductive inference, which can't be neatly summarized by comparing likelihoods of hypotheses. First, they attempt to establish the resurrection is a historical probability. Then they say that the simplest, most powerful explanation of Jesus' resurrection that comports well with other known facts about Jesus and his ministry is that God raised Jesus from the dead. This differs from merely arguing the probability of the resurrection is higher on God's activity than it is on naturalistic hypotheses.

  • http://www.blogger.com/profile/05693985638589020492 Mark

    For comparison, suppose you hear a rumbling sound coming from your attic. Then P(rumbling|gremlins in attic) may be higher than P(rumbling|mice in attic), but this doesn't mean gremlins are a better explanation of the rumbling than mice.

  • http://www.blogger.com/profile/13116034158087704885 March Hare

    Mark, that is precisely what having a higher probability means – it is a better (more likely) explanation for something.

    The problem I am having with this (and failing to adequately express previously) is that if we are assigning probabilities to various events to try to work out which is most likely, in the minds of apologists at least, then why do we have any assumptions?

    We are taking the resurrection of Jesus as read but surely we can assign probabilities to this as other explanations are possible e.g. there are drugs that can slow heart rate and respiration to make someone appear dead; the guardians of the tomb may have fallen asleep and someone moved the rock and stole the body (alive or dead); the tale may be an exaggeration; the tomb may have had another, hidden, entrance; etc. etc.

    I think my problem is that we take an unlikely assumption and then try to build probabilities around that when my brain refuses to get over the suspension of disbelief required when someone says not only did Jesus rise from the dead but that he escaped from a tomb and some people that later saw him didn't recognise him at first. These are all possible, but highly improbable.

  • http://www.blogger.com/profile/05693985638589020492 Mark

    Mark, that is precisely what having a higher probability means – it is a better (more likely) explanation for something.

    I'm not quite sure what you're referring to, but "X is more probable than Y" is clearly not synonymous with "X is a better explanation than Y," although sometimes we can infer the former from the latter. Anyway, the point was that abductive inference doesn't involve inferring anything about hypotheses' posterior probabilities from facts about their likelihoods.

  • http://www.blogger.com/profile/13116034158087704885 March Hare

    I don't know if I'm being obtuse here, but I thought that X being more probable than Y was synonymous with X being a better explanation than Y, given only the information used to generate the probabilities.

    For example, a person hearing a roaring lion, with no other information would say that it was probable the roar came from a lion. Given more information that may change (they live in San Diego, or they live near a zoo, or their neighbours play films very loudly etc. etc.

    I would appreciate an example where something being the more probable is NOT the best explanation for something.

  • http://www.blogger.com/profile/05693985638589020492 Mark

    I don't know if I'm being obtuse here, but I thought that X being more probable than Y was synonymous with X being a better explanation than Y, given only the information used to generate the probabilities.

    If you're a Bayesian, the probability of something is roughly synonymous with your private degree of belief in it. An example would be the probability (for you) that all apples in the world are red. Otherwise, the probability of an event is some physical property of a system that plays a certain role in our scientific theories. An example would be the probability of a coin landing heads when flipped.

    Even when one hypothesis better explains some fact than another, that needn't translate to anything about probabilities. Some non-Bayesians wouldn't even talk about probabilities of hypotheses outside of tightly constrained scenarios. Even for Bayesians this will sometimes be true. E.g., that Smith was drunk last night might explain his lewdness better than that he was sober, but he might be more probably sober for other reasons.

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

    Mark said:

    "For comparison, suppose you hear a rumbling sound coming from your attic. Then P(rumbling|gremlins in attic) may be higher than P(rumbling|mice in attic), but this doesn't mean gremlins are a better explanation of the rumbling than mice."

    Sorry to take so long to respond, Work has been demanding this week.

    Thank you for this nice example. I'm no expert on probability, but I would like to better understand at least some basic uses of it in arguments for God and miracles.

    In the case of gremlins vs. mice in the attic it seems to me that there is important background information that impacts our evaluation of these alternative hypotheses. We know that mice live in many attics, probably in most attics. Let's say that mice live in 75% of attics in the U.S. What about gremlins? Probably there are zero attics in the US that have gremlins.

    But presumably someone who believes in gremlins would offer an argument like you have suggested as evidence for the existence of gremlins. So, to be generous and to avoid begging the question, we might grant, for the sake of argument, that there could be a small number of attics in the US that have gremlins.

    Given that there is no solid evidence for the existence of gremlins, if there are any gremlins, the percent of attics with gremlins must be very small, probably less than .01%.

    Isn't it this background information that casts doubt on the gremlin hypothesis? If so, then this information needs to be accounted for in how we represent the situation in terms of the probability of the alternative hypotheses. If we account for this added information, won't probability indicate that the mice hypothesis is better than the gremlin hypothesis?

  • http://www.blogger.com/profile/13116034158087704885 March Hare

    That's kind of the point I was getting at: if something is more probable it is a better explanation.

    This is by de3finition as far as I can tell.

    With regards to religion I think the gremlin example is perfect. While I see many explanations for unlikely events (e.g. remission of cancer) that are more likely than miracles (because I assign an extremely low probability to miracles) a religious person would see the miracle as a better and more likely explanation.

    The one thing that is on my side would be that I can scientifically test many claims and assign a more accurate probability of a miracle occurring than a religious person.

    When you invoke science you remove the personal (in)credulity when assigning the probabilities and you get a much more accurate sense of what is likely to be the best explanation because it's the most probable, and it isn't gremlins.

  • http://www.blogger.com/profile/05693985638589020492 Mark

    The background information casts great doubt on the gremlin hypothesis. And while our background information regarding biology also casts doubt on the Jesus resurrection hypothesis, apologists will say the specific facts of the case nevertheless boost back the resurrection hypothesis above naturalistic hypotheses.

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

    I'm going to try to work out a probability analysis of the gremlins hypothesis vs. mice hypothesis. I have no idea whether I will be successful, but it seems worth a try. (If I fail, perhaps someone else can jump in and do the job right for me.)

    Thinking about my own attic, there are four logical possibilities:

    1. M & G
    2. M & ~G
    3. ~M & G
    4. ~M & ~G

    G= There are gremlins in my attic
    M = There are mice in my attic.

    I think these four logical possibilities could be the foundation for a probability tree, in which one could assign subjective probabilities for each of these conditions leading to a rumbling sound coming from my attic (on some particular day).

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

    Here is a possible probability tree to use in thinking about the two alternative hypotheses:

    The first branching could be for the possibilities of M or ~M:

    Either there are mice in my attic or it is not the case that there are mice in my attic.

    The next branching could be for the possibilities of G or ~G:

    Either there are gremlins in my attic or it is not the case that there are gremlins in my attic.

    After the two branchings we get four possible intermediary outcomes:

    1. M & G
    2. M & ~G

    3. ~M & G
    4. ~M & ~G

    Since it is conceivable that a single mouse or a single gremlin could cause rumbling in my attic, we should understand "mice" to mean "at least one mouse", and "gremlins" to mean "at least one gremlin".

    Each of the four above possibilities could be evaluated in terms of the probability of rumbling occuring in my attic today (i.e. on any given day).

    R= Rumbling will come from my attic today.

    The third branching of the probability tree would be between R and ~R:

    Either rumbling will come from my attic today or it is not the case that rumbling will come from my attic today.

    The goal (or intermediate goal) is to figure out probabilities for the outcomes after the third branching.

    For example, one of the possibilities after the second branching is (M & ~G). What is the probability of rumbling in my attic today, given that there are mice in my attic but no gremlins in my attic?

    P(R|M&~G)= ?

    Actually, I think the place to start would be with the miscelaneous or catch-all possibility: ~M & ~G.

    There are many other possible explanations of rumbling in my attic other than mice and gremlins: rats, cats, bats, owls, dogs, people, wind, fire, thunder, lightning, hail, firecrackers, earthquakes, sonic booms, bullets, bombs, meteors,ghosts, demons, gods, angels, fairies, witches, wizards, etc.

    So, what we need here is a general background probability of rumbling in the attic, without the presence of mice or gremlins. How frequently is there rumbling in an attic, that is caused by something other than mice or gremlins? Let's not specify a number just yet. Instead, we can assign a variable:

    P(R|~M&~G)= x

    If we add mice into the picture, then the probability will increase, at least slightly:

    P(R|M&~G) = x+y

    Similarly if we add Gremlins (instead of mice) into the picture:

    P(R|~M&G;) = x+z

    If we make a simplifying assumption that gremlins don't interfere with the activity of mice and that mice don't interfere with the activity of gremlins (since we have no empirical studies of gremlin behavior or interactions with mice I cannot base this assumption on solid facts), then we can determine another probability formula:

    P(R|M&G;) = x+y+z

    To be continued…

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

    Qualification:

    Adding mice into the picture does not necessarily increase the probability of rumbling, because the presence of mice could impact some other source of rumbling.

    For example, if mice were present, and there was a cat in my attic, the cat might become stealthy, more quiet and still, in an effort to sneak up on a mouse, thus reducing the chance of rumbling due to a cat in the attic. Or the presence of mice could impact the presence or behavior of rats in my attic. Perhaps rats prefer to avoid mice (?) and would thus be less likely to remain in the attic. Perhaps rats become quiter or less active in the presence of mice.

    So, it is not a matter of logic that adding mice into the picture increases the probability of rumbling in the attic. I would have to assume that the impact of mice on other likely causes of rumbling is too small to make a significant difference.

  • http://www.blogger.com/profile/13116034158087704885 March Hare

    Without going too deep into the rest of the problem I think we have already hit the real issue (with apologists) using just mice and gremlins…

    The probability of mice causing rumbling is low, but the probability of mice being in my attic is high.
    Overall probability of this naturalistic explanation is low but possible.

    The probability of a gremlin being in my attic is very low – even a gremlin apologist would concede that. However the probability of a gremlin causing rumbling is unknown.

    There are two probabilities that cause concern: P(gremlin in the attic) – take this as a miracle – I would say was vanishingly small. Using every scientific method would show that to be the case. However a gremlin apologist would say that by their nature gremlins are improbable, e.g. only happening once every hundred years, so it isn't fair to use that probability;
    Then there is the probability that a gremlin would cause a rumbling. I have no evidence they do, never having seen one, but the apologist knows that this is what they do so that probability is very high – something I may even concede to the Gremlinologist.

    So it appears that the issue is that Gremlinologists want to avoid using the scarcity of gremlins or evidence of their existence when working out the probability of a gremlin causing rumbling.

    I'm not sure if you can apply this directly to the religious apologist but it looks like a good fit for some of what they claim.

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

    March Hare said:

    "The probability of a gremlin being in my attic is very low – even a gremlin apologist would concede that. However the probability of a gremlin causing rumbling is unknown."

    The tendency of gremlins to cause rumbling in an attic that they inhabit does seem analogous to my concern about God's tendency to intervene in the world in a particular way on a particular occasion.

    Even if we grant, for the sake of argument, that there is a God and that God on rare occasions intervenes in the world, we have no solid data indicating God's tendencies to act. In short, we don't know about God's purposes, motivations, plans, or policies.

    This seems analogous to granting, for the sake of argument, that there
    are a few houses in the US with gremlines in the attic. Since we have no solid data on gremlin activity and behavior, it is hard to determine how likely it is for a gremlin (or group of gremlins) to cause rumbling in an attic that they occupy.

    However, in the case of gremlins, we probably have a bit more of an empirical basis for an educated guess than we do in the case of God. Gremlins are presumably similar to medium-sized animals (cats, dogs, rabbits); they are a bit like children or small adults.

    God too can be said to be like an adult person ("God, our Father"), but God is also supposed to be radically different than animals and people. God is infinite spirit, the transcendent source of all being, who exists outside of time, and who needs no body or tools or devices or time to accomplish any task he wishes, etc.

    Thus, although we might be able to do some reasoning by analogy about the activities and tendencies of gremlins, it is not clear that we can be as successful or confident in reasoning by analogy about God's activity and purposes.

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

    I have worked out a probability tree for mice vs gremlins causing a rumbling in the attic of a particular house on a given day. The probability tree is, however, partially incomplete because I have used some variables in place of some to-be-determined values.

    There are about 125 million households in the USA. But some households are in apartments, some are in condos, some are in mobile homes, dormitory rooms, etc. Many households are not in houses. I don't have a figure on how many houses there are in the USA, so I'm going to guess that a little less than half of households are in houses (we only need a ballpark number for purposes of this exercise): there are about 60 million houses in the USA. Not every house has an attic. Again, I will just estimate that one-third of houses have an attic: there are about 20 million houses that have attics in USA.

    One important constraint on the maximum percentage of houses with attics that have gremlins in the attic is the fact that this must be a fairly rare occurance since there is no solid evidence for the existence of gremlins, and perhaps none at all for the occupation of attics by gremlins.

    If just 10% of 20 million houses with attics have gremlins in the attic, that would mean that there were 2 million houses in the USA with gremlins in the attic. Clearly if this were the case there would be hourly contacts between humans and gremlins and there would be no need for any arguments about the existence of gremlins.

    Similarly, if only 1% of houses with attics had gremlins in the attic, then that would mean that 200 thousand houses in the USA have gremlins in the attic. Again, if this were the case, then contacts between humans and gremlins would be very frequent (daily?), and we would have many photos, videos, and sound recordings of gremlins, gremlin droppings, and even live caged gremlins.

    Clearly, the % of houses with attics that have gremlins in the attic must be less than 1%. Exactly how much less is, no doubt, not an objective fact, but a subjective judgment.

    If there were only 200 houses (in the USA) with attics that had gremlins in the attic, it seems somewhat plausible (to me) that this situation might exist for a number of years without there being a significant number of contacts between humans and gremlins.

    So, I would be willing to grant, for the sake of argument, that one in one hundred thousand houses with attics has gremlins in the attic. I might even be willing to grant that five in one hundred thousand houses with attics has gremlins in the attic (that would mean that about 1,000 houses with attics in the USA have gremlins in the attic).

    The second more generous estimate would mean that the probability that a house randomly selected from the pool of houses with attics in the USA would have gremlins in the attic is: .00005

    Now for mice. I'm going to make a guess here and say that most houses with attics have mice in the attic, say 60%. So, the probability that a house randomly selected from the pool of houses in the USA that have attics will have (on any particular day) mice in the attic is .6 , and the probability that it won't have mice in the attic is .4 .

    To be continued…

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

    Based on the previous estimated probability for the presence of mice in an attic and the estimated (maximum possible) probability for the presence of gremlins in an attic, the probabilities of the four logically possible circumstances are as follows:

    P(M and G) = .6 x .00005 = .00003
    P(M and ~G) = .6 x .99995 = .59997
    P(~M and G) = .4 x .00005 = .00002
    P(~M and ~G) = .4 x .99995 = .39998

    As previously mentioned, this assumes that the presence of mice and the presence of gremlins are independent events. If mice were a primary source of food for gremlins, then gremlins might have a tendency to reside in attics that had mice. Or if gremlins were afraid of mice, there might be the opposite tendency. Since I don't have any data on gremlin behavior and diet, I have no basis for concluding that the presence of mice in an attic would impact the likelihoood of the presence of gremlins. So, I am making a simplifying assumption that any such affect is insignificant.

    Another qualification: since my estimated probabilities have only one significant figure, the above calculated probabilities have pseudo precision. If they were my final conclusion, the results should be rounded to a single significant figure. Since this is not my final conclusion, I believe it is acceptable to maintain the overly precise figures, and do the rounding in the final calculation step (when determining the probability of rumbling noise coming from the attic of a house).

    The next step is to determine the probability that there will be a rumbling sound from the attic on a given day, for each of the four logically possible circumstances.

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

    I previously noted a way of using variables in probability statements to represent the probabilities of the four possible situations under consideration:

    P(R|~M and ~G)= x

    P(R|M and ~G) = x+y

    P(R|~M and G) = x+z

    P(R|M and G) = x+y+z

    We can reduce the number of variables to two, by making the probability of gremlins causing rumbling in the attic a multiple of the probability of mice causing rumbling in the attic.

    I realize that we have no data on gremlin behavior to base this on, but the point of this exercise is to try to grant as much as possible to the gremlin believer, while insisting that gremlin-occupied attics are very rare at best (analogous to miracles being rare events), and to see whether the probability calculation comes out in line with skeptical intuitions or not.

    So, in the spirit of conceding as much as possible to the gremlin believer, I would try the assumption that gremlins are ten times more likely than mice to cause rumbling in an attic.

    For example, if mice cause rumbling in an attic in one out of a thousand days (on average) in attics that are occupied by mice, then gremlins would be assumed to cause rumbling in the attic in one out of a hundred days (on average) in attics that are occupied by gremlins.

    This allows us to replace the variable "z" with "10y":

    P(R|~M and G) = x+10y

    P(R|M and G) = x+y+10y = x+11y

    I'm tempted to make a similar move and to use some factor of "x" as the additional probability of rumbling that results from mice being present in an attic.

    If the background frequency of rumbling occuring in an attic that has no mice and no gremlins is one day in a thousand, we could make the addition of mice double that probability: two days in a thousand, on average.

    Here is one way to reduce the probabilities to a single variable:

    P(R|~M and ~G)= x

    P(R|M and ~G) = x+x = 2x

    P(R|~M and G) = x+10x = 11x

    P(R|M and G) = x+x+10x = 12x

    If I can assign a value to x, then the probabilities for each of the four possible cases can be calculated. Then we can think about prior probabilities (working backward from the outcome to the probabilities of prior events).

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

    P(R|~M and ~G)= x

    This means "The probability that it will rumble in my attic today (or on any particular day) given that there are no mice and no gremlins in my attic is equal to: x".

    This is a "background" probability of rumbling in an attic, apart from mice or gremlins causing rumbling in the attic.

    I have lived in a number of different houses for a number of years in each house, and I cannot recall any mysterious rumbling from an attic (or crawlspace). There may have been rumbling that had an obvious cause (e.g. somebody was walking around or working on the roof or in the attic or crawlspace).

    My inference, based on personal experience is that rumbling from an attic is fairly infrequent. One day per year on average, seems too high of a frequency. One day per decade on average seems a bit too low. So, I'm going to assume a background frequency of rumbling in an attic (from causes other than mice and gremlins) as being about one day in a thousand days, on average. This would mean that
    x = .001

    Now we can calculate probabilities of the four possible cases, based on the assumptions that I have made so far:

    P(R|~M and ~G)= x = .001

    P(R|M and ~G) = x+x = 2x = .002

    P(R|~M and G) = x+10x = 11x = .011

    P(R|M and G) = x+x+10x = 12x = .012

    I was thinking that the probabilities of these four cases should add up to 1.0, which they don't. However, these are just the probabilities related to rumbling in the attic, and that leaves out the probabilities of it not rumbling in my attic today.

    Given that rumbling in the attic is rare, the probabilities for it not rumbling in the attic will be fairly high, for each of the four possible cases. It is the combination of all four probabilities for it rumbling in the attic today with four probabilities for it not rumbling in the attic today that should add up to 1.0

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

    Based on previously mentioned frequency or probability estimates, I have constructed a probability tree. The probabilities of some of the outcomes (in cases where gremlins are involved) are quite small. So, it is easier to grasp the ratios and numbers if we look at a large number of houses with attics and break that number down into the number of houses in subcategories and outcomes.

    Let's start with 10 million houses with attics in the US (about half of the total number that I estimated exist in the US) and break that number down into the sub-categories. If 60% of 10 million houses had mice in the attic,this would be 6 million houses with mice in the attic and 4 million without mice in the attic.

    Of the 6 million houses with mice in the attic only 300 houses would also have gremlins in the attic (M and G), and the remaining 5,999,700 would not have gremlins in the attic (M and ~G).

    Of the 4 million houses without mice in the attic, only 200 would have gremlins in the attic (~M and G), and the remaining 3,999,800 would not have gremlins in the attic (~M and ~G).

    Out of the 300 houses with both mice and gremlins (M and G), only 3.6 would have rumbling from the attic on a given day (and 3.0 of those cases of rumbling would have been caused by gremlins, on average).

    Out of the 5,999,700 houses with mice but no gremlins (M and ~G), there would be 11,999.4 houses with rumbling from the attic on a given day (and half of those cases of rumbling would have been caused by mice, on average: 5,999.7)

    Out of the 200 houses without mice but with gremlins (~M and G), there would be 2.2 houses with rumbling in the attic on a given day (and 2.0 of those cases of rumbling would have been caused by gremlins, on average).

    Out of the 3,999,800 houses without mice and without gremlins (~M and ~G), there would be 3,999.8 houses with rumbling in the attic (all caused by something other than mice or gremlins in the attic).

    So, out of the 10 million houses with attics (a large sample constituting about half of such houses in the US), there would be 16,005 houses with rumbling from the attic on a given day, on average. 5 of those cases of rumbling would have been caused by gremlins. So the probability of gremlins being the cause of rumbling in the attic would be:

    5/16,005 = .000312402

    or aprox. .0003

    Out of the 16,005 cases of rumbling from the attic on a given day, about 6,000 of those cases would have been caused by mice. So the probability of mice being the cause of rumbling in the attic would be:

    6,000/16,005 = .374882849

    or aprox. .37

    The chance that mice are the cause is more than one in three, while the chance that gremlins are the cause is less than one in a thousand. Clearly, the rarity of gremlins in the attic compared with the prevalence of mice in the attic has overwhelmed the assumed greater tendency of gremlins to cause rumbling in the attic (ten times as frequent as with mice).

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

    Even if I make significant revisions to my frequency estimates in favor the gremlin hypothesis, the mouse explanation still comes out more likely, so I don't think that I have stacked the deck against the gremlin hypothesis.

    Let's start again with a randomly selected population of 10 million houses with attics in the US.

    Instead of assuming that most houses with attics have mice in the attic, I will assume that most do not (40% have mice in the attic, and 60% don't have mice in the attic). That means we have 4 million houses with mice in the attic and 6 million houses without mice in the attic.

    Instead of assuming that only 5 out of 100,000 houses with attics have gremlins in the attic, we will make the much more generous assumption that 5 out of 10,000 houses with attics have gremlins in the attic. This means that we are granting the absurdly generous assumption that 5,000 houses out of the 10 million houses with attics have gremlins in the attic.

    The breakdown of the four logical possibilities would be as follows:

    (M and G) 2,000 houses
    (M and ~G) 3,998,000 houses

    (~M and G) 3,000 houses
    (~M and ~G) 5,997,000 houses

    Furthermore, instead of assuming that gremlins were 10 times more likely to cause rumbling in the attic than mice (i.e. houses with only gremlins in the attic will have rumbling in the attic 10 times as many days as houses with only mice in the attic, on average over a period of months or years), we will assume that gremlins are 100 times more likely to cause rumbling in the attic than mice.

    I previously estimated that mice in the attic cause rumbling in the attic about 1 day out of 1,000 days on average; this means that we are now assuming that gremlins in the attic will cause rumbling in the attic about 1 day out of 10 days on average.

    Therefore on a given day rumbling in the attic will occur with the following frequencies, on average:

    (M and G) 204 houses (200 caused by gremlins, 2 caused by mice)
    (M and ~G) 7,996 houses (3,998 caused by mice, 0 caused by gremlins)

    (~M and G) 303 houses (300 caused by gremlins, 0 caused by mice)
    (~M and ~G) 5,997 houses (0 caused by mice, 0 caused by gremlins)

    The total number of houses with rumbling in the attic on a given day will be 14,500 on average.

    The probability that rumbling was caused by a mouse:

    4,000/14,500 = .275862069
    or aprox. .3

    The probability that rumbling was caused by a gremlin:

    500/14,500 = .034482759
    or aprox. .03

    So, even on these extremely generous assumptions, the mice hypothesis has three chances in ten of being correct, while the gremlin hypothesis has only 3 chances in a hundred of being correct.


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