Thursday, March 30, 2006

Wait, Er, Check Please?

This post is part of an ongoing dialog between my friend Ernie and me about the validity of Christian belief.

In my last post, Claim Check: Introduction, I listed a number of assertions about Christianity that I believe I can support and I promised to expand on those. However, in a comment there and also in A Theory, Not a Law, Ernie requested that rather than simply present arguments against Christianity that I also present an alternative, a null hypothesis against which these claims can be compared, so I will try to spell that out a little first. I also have a question for Ernie that comes up when I compare A Theory, Not a Law with his prior post Reality Check.

In response to my introductory list of claims, Ernie brings up a valid question. When I make various claims against Christianity, what do I mean be Christianity? This question has come up before, in Ernie's It Takes Tao to Tango and I responded in The (No So) Terrible Tao's with:

  1. Monotheistic, but...
  2. Jesus is/was God
  3. Jesus' death and resurrection enable our salvation
  4. Bible is revealed or inspired scripture

This question about what Christianity is is a bit difficult, because it does mean so many things to different people. Sometimes it seems that any assertion you make about Christianity will be contradicted by someone who claims to be a Christian. I am not disputing those claims, nor claiming that this problem is unique to Christianity, but just saying that it makes things more difficult. Despite my list above, for instance, I know personally a devout Christian who denies that Jesus is co-equal or identical with God, a position he reached after much struggle and research into the beliefs of the early church.

Early on in A Theory, Not a Law, Ernie proposes categorizing Christianity as "a theory about divinity", where divinity is "that which is ultimately, non-contingently real". Earlier, in Altimeters for Divinity, when Ernie first introduced this definition of divinity, he said

Christian theism asserts that divinity is

  1. singular
  2. transcendent, and
  3. self-giving

Based on these two lists, and I think unsurprisingly, we agree that Christianity is a monotheistic belief system. That sets up a contrast with atheism, but Ernie sees a difficulty there:

Given that Christianity is a theory, then what is it a theory about? Well, Christianity has always primarily presented itself in terms of beliefs about God, so hopefully that aspect is non-controrversial. However, defining Christianity as "a theory about God's existence" would make atheism "a theory about God's non-existence", which are difficult items to compare; zeroes and infinities are always problematic in formal systems, as anyone who's used FORTRAN knows. :-)

That is why I propose we instead view this as a contest between different theories about the nature of ultimate reality...

If I were to propose alternative belief system to contrast with theism, it would be naturalism, but not because I think naturalism necessarily reflects ultimate reality, but only that there is insufficient evidence (or reason) to go further. I do not recall if I have mentioned this before, but part of my "deconversion" was an explicit decision to believe "less", to remain undecided about matters that are uncertain. I am more certain that Christian theism is "false" than I am certain that naturalism is "true".

Given that asymmetry, I am a bit uncomfortable with "view[ing] this as a contest between different theories about the nature of ultimate reality". Would it be assuming too much to say "observable reality" instead? Also, I expect that Ernie, physics Ph.D. that he is, would grant that there are natural explanations for some things, so that rather than comparing N (naturalistic theories) to T (theistic theories), we would be comparing N to N + T. But this reduces to arguing about whether T is "zero" or "non-zero"; in other words we are back to N being the null hypothesis and arguing for and against T.

I can appreciate Ernie's preference for two competing theories, but I am not sure if N vs. N+T qualifies in Ernie's view, nor do I have anything beyond N to offer. What do you think, Ernie?

Before I wrap up, I wanted to raise one other question related to Ernie's complex vector belief field. In Reality CheckErnie defined "imaginary beliefs" as

Belief A is imaginary if A is true if and only if someone believes A is true

As an example of an imaginary belief, Ernie offered "Money is valuable." Later, he said,

So, in these terms, I fully concede that belief in God is partly imaginary.The question is, can Alan offer compelling evidence that it isn't really complex?

It seems to me that given this definition of imaginary beliefs, the truth of imaginary beliefs is just about as contingent as is possible. But as we saw earlier, Ernie suggested the definition of divinity to be "that which is ultimately, non-contingently real". Ernie, can you clarify?

Tuesday, March 28, 2006

Claim Check: Introduction

This post is part of an ongoing dialog between my friend Ernie and me about the validity of Christian belief.

In Reality Check, Ernie suggests that

... Alan's critique of Christianity appears (key word: appears) to be largely orthogonal to my defense of Christianity. That is, it seems almost (key word: almost) as if we could each grant each other's basic arguments -- and facts -- yet still not resolve the underlying question.

In particular, Alan's two favorite arguments against Christianity appear to be:

  1. The Bible we use today is an imperfect document created by fallible human beings
  2. The Biblical description of Hell is incompatible a rational understanding of Justice


On my side, my basic claim is that Christianity -- as a theory -- provides better explanation of observed phenomena (which I trust Alan will allow to include retrodiction as well as prediction) than atheism. However Alan -- again, as far as I can tell -- appears willing to concede that the "idea of God" may well provide all the salutary effects I claim for it, but still argues that this does not constitute empirical support for Christianity.

That strikes me as a fairly reasonable summary of where we are. (My statement about the Bible would be a bit stronger, but I will return to that in a moment.) Ernie suggests that we each take some time to "spell out our core rationales for why we each prefer our belief system to the other's." I am agreeable to that.

I will start with a list of arguments, without elaboration. In later posts, I will elaborate as it seems helpful.

I assert:

  1. That (some) Biblical authors, beyond being imperfect and fallible, were actively dishonest
  2. That the historical record contained in the Bible is insufficient to warrant belief in the critical events on which Christianity rests
  3. That eternal damnation is unjust and contrary to the supposed character of God; further, that alternate conceptions of hell are ad hoc rationalizations.
  4. That the history of Christianity and of Judaism before it is best explained as a purely human development, evolving primarily due to cultural and political influences.
  5. That Christianity does not offer a reliable method for separating truth from error
  6. That subjective experiences offered as evidence of God's intervention in our lives are common to otherwise contradictory belief systems, and so are not evidence of the truth of any of them.
  7. That Christians have throughout history engaged in evil due to their flawed understanding of reality, and especially because of the supposed ultimate authority of their God. This continues today.
  8. That Christianity promotes submission to authority at the expense of personal responsibility and critical thinking.

I may think of something else tomorrow, but that is at least a good starting point. Please keep in mind that these are only brief statements. I can anticipate some objections, and perhaps if I were sufficiently skilled, I could avoid them here. Instead, I will try to respond to them as I flesh these out.

Now, I can imagine a belief system that is (in my opinion) vaguely Christian but which sidesteps these objections. This system would accept these flaws as being part of humanity's slow and often confused process of discovering God. Even so, I think there is insufficient positive evidence for such a position, and that agnosticism is the more appropriate response.

If both Ernie and I are simply going to take a few posts to elaborate on our core rationales for our preferred belief systems, I am not sure that strict alternation of posts is really necessary. I may just charge ahead as time permits, unless Ernie prefers otherwise.

Saturday, March 25, 2006

On History, Experience and Sundry Modelling Details

This post is part of an ongoing dialog between my friend Ernie and me about the validity of Christian belief.

After a bit of a hiatus, Ernie is back with Altimeters for Divinity. The "altimeter" idea comes from my earlier post Belief Optimization, in which I described a sort of quasi-mathematical model for describing systems of beliefs, where our goal is to find the global minimum of contradiction in our beliefs.

Ernie had previously alluded to a possibly similar concept, and he has now highlighted a difference between our models, as I have described a multidimensional vector field of real (in the mathematical sense) values, where Ernie would use complex (in the mathematical sense) values. I had previously understood him to be using complex only in the sense of non-scalar, not specifically in the sense of complex numbers. While Ernie has not explained just what each such value means in his model, I will note that such numbers are composed of both real and imaginary parts. I will refrain from commenting about Ernie's imaginary beliefs at this time. ;-)

Ernie listed four of my previous posts that he had to "chew on", and I just want to clarify that, for whatever it is worth, I had not considered The Ugaritic Pantheon to be part of this dialog. That may or may not have contributed to Ernie saying

However, the larger issue is that Alan appears to evaluate Christianity in historical terms, whereas I judge it on empirical grounds.

I am not quite sure why he says that I appear to evaluate Christianity on (solely) historical terms when we have spent so much time talking about the problem of hell, for instance. I do think that it is important to understand the historical development of Christianity, but that is not my sole basis of evaluation. Similarly, whether or not historical considerations contribute to Ernie's personal evaluation of Christianity, he has made various claims about its history that I have taken to indicate that he attaches some importance to it. For instance, in A Post-Modern Faith in Jesus, Ernie wrote:

I believe (and am willing to defend) the following to be true and knowable according to traditional scientific standards of evidence:


f. That *someone* and *something* -very unusual- happened in the first century AD that gave birth to the Christian movement, in a way that allows enormous diversity yet amazing continuity across both space and time.

Later, in The Tao of Hell (or perhaps vice versa), he wrote

Further, I believe I can justify -- and would willingly attempt to defend -- this position [the consequences of ignoring the Tao]:

  • scripturally
  • historically
  • anthropologically
  • psychologically
  • philosophically

Still later in Truth or Cons[ist]equences?, Ernie wrote

Thus, all I can really say a priori is that "I believe" certain things are true: ... I believe in transcendent virtues such as justice, humility, and love, and that historical Christianity demonstrates both a deep understanding of those virtues and a remarkable power to nurture them.

My stress of some of these historical considerations was partly due to statements such as these, so I think that Ernie's contrast between my "historical terms" and his "empirical" grounds is a bit unfair.

For that matter, some of what Ernie goes on to say also touches on historical considerations. For instance,

Further, it [Christian theism] claims that we can and do know this because of the testimony and person of Jesus Christ, as reflected in both those who knew him while he lived on earth and those (including myself) who have had spiritual encounters with him afterwards.


In particular, I believe that I can demonstrate -- both historically and theoretically -- that the resulting claims have far greater explanatory power than those built on alternative assumptions, especially atheism.

I am, no doubt, blowing this out of proportion, and perhaps I misunderstand what Ernie is trying to say, but it bothers me that Ernie has provided a contrast that appears inaccurate to me.

Now that we have that out of the way, let's look at the meat of Ernie's post.

Because of this, I believe Christianity (my "theory of Christ") makes a range of specific, testable predictions that apply to the modern world (i.e., "acts of faith" are essentially experiments, providing noisy, but still valid data). In particular, I believe that I can demonstrate -- both historically and theoretically -- that the resulting claims have far greater explanatory power than those built on alternative assumptions, especially atheism. For example, I predict that individuals and communities at every point in the continuum would be improved by more accurately understanding and experiencing the divinity represented by Jesus Christ.

This isn't to deny that all other systems may have *some* explanatory power (to Alan's point about non-Christian conversion stories). However, I assert that their (lesser) power can be plausibly explained by demonstrating their implicit or explicit adoption of a subset of Christian theism (thus my allusion to presuppositionalism earlier, even if I'm still not sure what that means :-). Conversely, if Christianity is just a crude approximation of reality -- as Alan seems to assert -- then the onus would be on him to show that his "divinity" (mind, matter, reason, whatever) provides greater predictive power than mine. That is, he would need to explain not just why "belief in God" works well in certain regions (as he admits), but also where and why it fall short of his superior naturalistic explanation.

Regarding the prediction about individuals and communities improving based on more accurate understanding and experience of Jesus Christ, the inclusion of "improvement" here would require us to agree on what constitutes improvement. Does that require ethical judgement? We have not agreed on an ethical framework, but we have agreed that epistemology precedes ethics (other than epistemic virtue), so I wonder how we could proceed on this point. If the notion of improvement does not imply ethical consideration, what kind of improvement are we looking for?

For that matter, how will we know what understanding and experience of Jesus Christ is more accurate? Is that not part of the question we are seeking to answer?

Regarding the explanatory power of other religious systems, Ernie suggests that this is due to their adoption of some subset of Christian theism. He specifically mentions my "point about non-Christian conversion stories" (see Making Change), but I want to emphasize that point again here. The specific question was, do changed lives provide evidence for the truth of what one believes? Ernie may claim that Mormons' lives are changed because Mormon beliefs overlap with Christian truth, but the Mormons could likewise claim that Christian' lives are changed because Christian beliefs overlap with Mormon truth. Unless the changes are materially different between Mormon and Christian believers, it remains hard to see how changed lives could be evidence for one and not the other. (Mormons might not agree with my distinction between Mormonism and Christianity, but it is merely that some difference in beliefs exists that matters. We could contrast Catholicism and Protestantism, for that matter.) What little research I have done into non-Christian conversion stories leads me to believe that changes reported by Christians are not sufficiently different to warrant any particular evidentiary weight.

As for explaining why belief in God "works well in certain regions" under naturalistic explanations, I will try to develop that more fully in another post, but let me make a distinction between "works well" and "causes change". I assert that beliefs do cause change, and I agree that those who describe the changes are likely to describe them as good changes. My stress in discussing this subject is not on whether I consider those changes good, but that reports of changed lives speak more about the relationship between belief and behavior than about the truth of the beliefs.

Finally, Ernie finished with

We've already agreed that "more accurate knowledge enables more accurate predictions", so this seems a suitably neutral altimeter.

Fair enough, Alan?

In the context of my quasi-mathematical model of beliefs, predictions are belief statements concerning the results of future observations, like "I believe the voltmeter will read 1.5 +/- 0.2V when connected to a fresh AA battery, with confidence 95%." The actual observations become further belief statements, possibly very concrete beliefs, like "I believe the voltmeter read 1.47V when I connected its probes to the battery, with confidence 99.9%." As long as I keep making the same prediction, each confirming measurement lowers my measured belief altitude and each disconfirming measurement raises my measured belief altitude. If I modify my predictive beliefs, the altitude measurement begins anew with further tests.

In other words, I agree that predictions are one means for measuring belief altitude. Since belief altitude as I have described it is a measurement of total contradiction, predictions create opportunities for contradiction to occur. However, a static analysis of currently-held beliefs can also reveal contradiction. I have not thought much about how to tie that together with claims of understanding, of preference for simpler explanations (Ockham's Razor), and so on. Whether this distinction between the roles of prediction and contradiction in the model really matters to our discussion, I believe it does, but only with a confidence value of 55% (that is, +0.1 on the -1 to 1 scale).

Wednesday, March 22, 2006

Coral Clocks

Creationism, in its guises of Intelligent Design and "teach the controversy", has been popping up all over, often in school boards and state legislatures. The ignorance displayed by the the proponents of the various laws, policies and curricula is staggering, and this is most true for the literalist Young Earth Creationists (YEC's) that believe in a six-day creation six thousand or so years ago.

There are numerous lines of evidence pointing to a much older earth and still older universe. Various radiometric dating methods (oft-maligned by YEC's) all give general agreement that the age of the earth is roughly 4.5 billion years old. In the last ten or fifteen years, observations first by the COBE satellite and more recently by the WMAP satellite have pinned the age of the universe to roughly 13.7 billion years.

My favorite line of evidence for an old earth does not actually give a precise age, other than establishing a minimum age of about 500 million years. The reason I like it, I think, is that it brings together two seemingly unrelated things: the moon and coral. What could they possibly have to do with each other? I am glad you asked.

The current consensus is that the moon was formed when an impactor roughly the size of Mars struck a glancing blow on the early Earth. Much of that mass was incorporated into the Earth itself, but a sizeable amount of mass, especially lighter elements (like iron, as compared to nickel) was flung into low earth orbit where much of it eventually coalesced into the moon. While the moon is currently about 250,000 miles from Earth, it would have formed much closer.

If it formed closer to the Earth, why is it farther away now? The answer to that question lies in the ocean. (But no, we are not to the coral yet.) The gravitational interaction between the Earth and the moon produces tides, and the tides slow down the Earth's rotation. But if the Earth's rotation is slowing down, it is losing energy, and energy must be conserved, so where is the energy going? The energy is being transferred to the moon, which slowly moves farther away. This slow retreat has been measured to be (currently) about 3.8 cm per year with a corresponding decrease in the rotational period of the Earth.

Now if the rotation of the Earth is slowing down, and has been for billions of years, then it must have been rotating faster before. On the other hand, the time required for the Earth to revolve around the sun is expected to be essentially constant. That means that the number of rotations (days) per revolution (year) has been going down and was higher in the past. And that is where the corals come in.

Corals grow layer by very thin layer, with identifiable layers produced each day. Monthly and yearly variations are also detectible, and in modern corals (as you would expect) you find 365 daily layers per yearly cycle. But these layers can also be examined in fossilized corals from various time periods. By this point, you should not be surprised to learn that coral fossils (dated using geologic and radiometric techniques) have more daily layers per yearly cycle, and the ratio increases with the age of the fossil. Fossils from the Pennsylvanian period (325 to 280 million years ago) have about 387 daily layers per year. Fossils from the Devonian (408 to 360 million years ago) have about 400 layers. Fossils from the Cambrian (540 to 500 million years ago) have about 412 layers per year. These values are in rough agreement with those calculated based on Earth/moon tidal dynamics, which is more complicated than you might think because the continents get in the way, and worse, the continents move over these timescales.

Cool, huh?

Monday, March 20, 2006

Better Than Fine Gold

My ongoing discussion with Ernie has been on hold for awhile since Ernie has been busy with other concerns, just minor stuff like his job. I have a few ideas for things to write about, including the results of what searching I did for conversion stories for other religions, but obviously I have not actually written any of those things. And in fact, I am not writing any of those things tonight either.

Instead, I want to touch on something related to recent events in the political arena, specifically the resolution introduced by Senator Feingold to censure President Bush. There has been some debate over whether this was a good move, politically, and I am not going to address any of that, though I have my opinion. What I would like to do instead is address the idea that Feingold was motivated to do this primarily by considerations related to a possible presidential run in 2008.

Naturally I do not have special insight into Senator Feingold's motivation, but what I can describe is what I have observed about Feingold in the years he has been a senator, I think since 1992. (He is one of my senators, living in Wisconsin as I do.) I have not always agreed with Feingold, though my own views have changed since then. But he has earned my respect. Feingold was the only Democratic senator who voted in favor of impeachment hearings for Clinton because he thought it important to actually hear the evidence presented. He was the only senator to vote against the Patriot Act, despite a political climate in which such a vote might have been viewed as, well, unpatriotic. Yet I think we have seen substantial evidence that he was right to be very concerned about some of its provisions.

Beyond those sorts of things, one of the things that I most appreciate about Feingold is how he campaigns. His ads talk about what he has done and what he wants to do. I cannot recall him even mentioning his opponent, and I appreciate that immensely. As far as I can tell, he acts with integrity and he takes his job as a public servant seriously.

That's my plug for Feingold.

Wednesday, March 15, 2006

The Ugaritic Pantheon

Growing up in the church, you hear Bible stories about, for instance, Elijah and the prophets of Baal, and perhaps also the goddess Asherah. The Israelites are often rebuked for their worship of the Canaanite gods, gods worshipped by those that lived in and around the Promised Land when it was given to the Israelites by God. The Israelites had their one God, Yahweh, making them a relatively unique monotheistic religion in a world full of divine pantheons. Right?

Maybe. Maybe not. I earlier described the Documentary Hypothesis, which (among other things) dates significant portions of the first books of the Bible to the late seventh century BCE, and it is especially these portions that decry the worship of these other gods. Is it possible that monotheism in Israel was actually a rather late development? Let's look at some of the reasons that may be true.

In 1928, the ancient city of Ugarit was discovered, and with it a number of tablets that describe the Canaanite gods. With the limited reading I have done, I am not sure how much of what follows comes from those tablets specifically, and how much has been attested elsewhere, but I gather that this archeological discovery was relatively important in expanding our knowledge of the beliefs of this region in the second millenium BCE, roughly the time where the Israelites (supposedly) returned from Egypt. In any case, the Canaanite pantheon had as its chief god El with Asherah being his consort or wife. They had seventy divine children (all sons?), including Baal and possibly Yahweh.

I say "possibly" because some accounts I have read say yes and some don't say. For instance, in The Origins of Biblical Monotheism: Israel's Polytheistic Background and the Ugaritic Texts, Mark Smith says "In the earliest stage, it would appear that Yahweh was one of these seventy children". Ugarit and the Bible also places Yahweh in this group of seventy. Other sources (that I have read) that describe the Ugaritic texts tend not to mention Yahweh, but neither do they list all of the seventy divine children, so this is a bit of an open question for me. However, we will encounter some other reasons to suspect that Yahweh was a member of this pantheon in a moment.

Before we get to that, though, there is one more word that requires some elaboration: "elohim". The elohim are the sons of El; it is plural. Some of you will recognize this word as being used in the Bible to describe God. Why plural then? Naturally there have been a variety of suggested explanations for this. But as we continue, consider how much sense that "sons of El" makes where "elohim" is used.

Let us consider then the hypothesis that the Israelites were polythestic until relatively late in their history, perhaps until approximately the time that the Deuteronomist did his work. We would expect, then, that earlier writing would retain references to this polytheism, even in the Bible. Are there such references? Here are some examples.

First, Deuteronomy 32:8-9./p>

When the Most High [El] gave the nations their inheritance, when he divided all mankind, he set up boundaries for the peoples according to the number of the sons of Israel [sons of El]. For the LORD's [Yahweh's] portion is his people, Jacob his allotted inheritance.

Here would we have El dividing up the nations among his sons, with Yahweh receiving Jacob's people. An interesting note is that the phrase "sons of Israel" is found in the Masoretic Text, but the Dead Sea Scrolls and Septuagint say "sons of God". So Yahweh would be the national deity for Israel, and other nations would have others. (This is an important point in Mark Smith's proposed explanation for the development of monotheism.)

One difficulty with some of these passages is that modern translations may be colored by modern expectations about what was meant. Not being able to read Hebrew myself, I cannot vouch for some of the translations below. I will compare them with a couple of common translations. Checking against some kind of Hebrew interlinear translation would be helpful, but I have not done that.

Consider these translations from Canaanite Gods Mentioned in the Bible:

  • Psalm 82:1: Elohim has taken his place in the assembly of EL, in the midst of the elohim He holds judgment.
  • Psalm 29:1: Ascribe to Yahweh, O sons of EL, ascribe to Yahweh glory and strength.
  • Psalm 89:6: For who in the skies can be compared to Yahweh, who among the sons of EL is like Yahweh,

In the NIV, these are translated:

  • Psalm 82:1: God presides in the great assembly; he gives judgment among the "gods"
  • Psalm 29:1: Ascribe to the LORD, O mighty ones, ascribe to the LORD glory and strength.
  • Psalm 89:6: For who in the skies above can compare with the LORD? Who is like the LORD among the heavenly beings?

And in NASB:

  • Psalm 82:1: God takes His stand in His own congregation; He judges in the midst of the rulers.
  • Psalm 29:1: Ascribe to the LORD, O sons of the mighty, Ascribe to the LORD glory and strength.
  • Psalm 89:6: For who in the skies is comparable to the LORD? Who among the sons of the mighty is like the LORD,

Over time, the roles of the various players seem to have changed. Eventually, Yahweh became (to the Israelites at least) interchangeable with El. Asherah (previously El's consort or wife) becomes associated with Yahweh, as two inscriptions from around 850 to 750 BCE relate:

I bless you through Yahweh of Samaria, and through his Asherah!


Uriyahu, the king, has written this. Blessed be Uriyahu through Yahweh, and his enemies have been conquered through Yahweh’s Asherah.

(From Ugarit and the Bible)

As I said, this is not anything that I have studied extensively, and certainly I have not even included here everything that I have read. I do find it a very interesting hypothesis (that Israelite polytheism was normal and prevalent until rather late). Will continued research support this hypothesis? What would it mean for you if it could be proven?

Saturday, March 11, 2006

Belief Optimization

This post is part of an ongoing dialog between my friend Ernie and me about the validity of Christian belief (roughly speaking).

Ernie had asked me to respond to his description of beliefs as a complex vector field. If you have math anxiety, you might want to stop reading now.

Ernie wrote:

Perhaps even more importantly, I interpret this as more like a complex vector field than a series of Booleans. That is, each Belief is not a simple, independent True/False decision, but a complex system with varying degrees of precision, confidence, applicability, and inter-relatedness. The value of logic is that it uses analytic propositions to link two synthetic Beliefs in a discrete chain, so that one testable or accepted Belief can be used to validate another, thus untangling the web into a series of more-or-less distinct strands.

My own view, or mental model really, is similar, but not quite the same. The way I think about this (when I think about it in this way at all) is more like a series of belief values, where each value ranges from from 0 to 1, expressing the strength of my belief about (or confidence in) an individual statement. (Or, perhaps from -1 to 1, with -1 being certainty that it is false, to 1 being certainty that it is true.) The varying degrees of precision and applicability would be reflected in the individual statements themselves, not in the values associated with those statements. Likewise, the interrelatedness of beliefs would be reflected in relations external to the belief values themselves.

Some statements may contradict other statements. If so, I cannot assign them both high belief values. If I do have high belief values in contradictory statements, I have to lower some or all of them. Of course, each belief statement is related to many others, so I cannot just lower one or two in isolation. If I lower my confidence Bi in statement Si but Si is strongly implied by Sj and my corresponding Bj is high, then I have a new kind of contradiction. Conceptually, I can calculate the total contradiction score C(B1, ..., BN) that exists among my beliefs. So my goal is to find the set of values B1, ..., BN that minimizes C.1

Now, there are necessarily a very large number of related statements. That is, N is large. So I am searching an N-dimensional space for that point with the absolute minimum value of C(B1, ..., BN). This is conceptually just like many other searching problems that are encountered in various applications.

For instance, the software that I work on for my job does automated employee scheduling. For each employee there are a number of rules that constrain what they can do and when, and there also varying staffing needs. This can be viewed as a discrete searching problem, where each possible assignment to each possible staff person is a different variable that can be assigned either 0 or 1, corresponding to that assignment being made or not. The goal is to meet all the staffing needs without breaking any of the rules. Each rule broken is assigned a penalty, so we are trying to minimize the penalty. For a typical schedule, the search space can easily have 10,000 binary variables, so that there are 210,000 or about 103,500 possible solutions. This is a vast number. There are less than 10100 particles in the visible universe. As it happens, though, this search space can be "pruned" extensively, and reasonable (though not necessarily optimal) solutions can be found in as little as a couple of minutes, depending on the number of rules. (And, in actuality, I do not actually model the problem as a set of binary variables, but that is not important here.)

Anyway, I bring that up because for me, thinking about beliefs as an optimization problem allows me to apply what I know about optimization to beliefs. For instance, a simple approach to solving a maximization problem is called hill-climbing. (For a minimization problem, you just invert everything.) In hill-climbing, you pick a point at random from the entire search space and evaluate your objective function (the function that you are trying to maximize). Then you pick one dimension and move along that dimension as long as the value of the objective function increases. (If the objective function is differentiable, this is an exercise in calculus; otherwise, you have to sample various points and hope that the objective function is not too "wild".) Once you find the maximum along one dimension, you switch dimensions and do it again. You keep cycling through all the dimensions until you can no longer find an improvement along any dimension. In two dimensions, you can think about a landscape. First you walk north or south until you are as high as you can get. Then you walk east or west, until you as high as you can get, then north or south, etc. Eventually, you will not be able to go any higher in either direction.

Hill-climbing is very simple, and for certain kinds of objective functions it works splendidly. If there is a single big hill on your landscape, then hill-climbing will find the top. But if there are bumps, mounds and small hills in addition to the largest hill, hill-climbing can get stuck on one of these "local maxima". That's bad. Other searching techniques use a variety of mechanisms to avoid getting stuck. For instance, you might take steps of a fixed size in each direction. If the step takes you higher, you always take it. If it takes you lower, you accept it only with probability P. As time goes on, you lower P. Early on, you avoid getting stuck on local maxima because the higher initial value for P allows you "escape". Later, as P gets lower, escaping becomes less likely and the search (hopefully) converges on a better solution. This kind of approach is called simulated annealing. There are many others as well.

Bringing this back to the whole vector-of-beliefs idea, where we are trying to minimize C(B1, ..., BN), a local minimum is a place where any small adjustments to each Bi cause C to increase (meaning that my beliefs become increasingly contradictory). But that does not mean that I am at the global minimum. A sufficiently large adjustment to my belief vector may allow me to escape a local minimum and reach another one that is lower. Probably nobody is actually at even a local minimum, since even evaluating the objective function is beyond us. But we are not all in even the same valley. Loosely speaking, Christianity might be one valley, Islam another, atheism another and so on. Each valley has smaller gullies and various Christian denominations might be found at the bottom of different gully within the larger Christian valley. Some people may be far away from even local minima, perhaps even living near the peaks. We might call such people crazy, or at least irrational, since this means that their own beliefs are highly contradictory.

Ernie thinks his valley is lower than mine. I think mine is lower than his. We are trying to agree on something we can use an altimeter. But I think the geek-meter just went off the chart.

1 Actually, the objective function would probably have some terms related to the total amount of certainty. If I use values from -1 to 1, then my objective function would include, for all i, Bi2.

Thursday, March 09, 2006

Naturalism Vs. Theism, Chapter 3

Just a quick note: second rebuttals are now available in the Carrier-Wanchick Naturalism vs Theism debate.

Wednesday, March 08, 2006

Making Change

This post is part of an ongoing dialog between my friend Ernie and me about the validity of Christian belief (roughly speaking).

Ernie invited me to critique the arguments for belief that he included in his testimony, recently posted but originally written years ago. If he had not invited me to comment, I would have left it alone, just as I have avoided commenting on his recent string of posts drawn from A Purpose-Filled Life by Rick Warren. But since he asked...

In the past year and a half, I have talked to a number of people, both friends and family, about my leaving Christianity. Most of those people are still Christians; one never was, and one (who was very influential in my development as a Christian) has also left Christianity behind. With those who are Christians, when I explain my reasons for disbelief, a common response is something like "But I know it's true, because my life changed when I believed" or other similar experiential reasoning. And at the core, that is what I see in Ernie's testimony as well.

Ernie describes an experience that is relatively common, at least generally speaking. He was a teen-ager, accomplished, comfortable, loved by family but lonely. He was unhappy, and felt that his life would always be that way, a life that would not then be worth living. But perhaps the answer to his troubles lay with God. Perhaps by devoting his life to God, his life would be worth living. So he made his decision. And his life changed. (This is, of course, my short summary of what Ernie wrote. I hope that I am being fair in this characterization, knowing that the Ernie's "authoritative" version is only a click away for you.)

What was this change like? The two sentences that best captures that change, in my opinion, are these:

The one thing that did happen immediately was that I had hope. I knew that there was someone there who would share in my struggles, and more importantly would help me overcome them.

I do not doubt that Ernie's life changed. But what I hear him describing is a situation in which he was desperate for a change. His decision to trust God gave him hope. He no longer felt alone. Those were powerful incentives to believe and powerful causes for change once he did believe, so long as he did believe. Belief in God, I submit, was enough to explain the change, regardless of the actual existence of God. And as we have been discussing recently, our beliefs tend to frame how we interpret future experience, so that we have a strong tendency to reinforce those core beliefs.

But this kind of experience is not unique to Christianity. Members of most (all?) religions could relate similar stories. Christians of all flavors, Muslims, Jews, Mormons, Scientologists, Zen Buddhists, New Agers, on and on. Many will tell you their lives were changed, and generally they will be right. Many will be certain about what they believe because of this change. But unless we are prepared to accept that all of those beliefs are true, how can we trust this kind of evidence at all? Is not the more reasonable conclusion that there are common, purely natural reasons that underly these common experiences?

(Some might suggest that the experiences of those others are counterfeit, maybe even produced by demons. But this helps not at all. How would I know that I was not the one being deceived? Either way, we must look for other kinds of evidence.)

I have a homework assignment for anybody who cares to try. Collect testimonies from people of as many different religions as you can find and compare them. If you like, send them to me at "alan DOT lund AT gmail DOT com" or leave a comment here. I will post everything I receive or find myself.

Programming Note

As far as my ongoing conversation with Ernie, I think the ball is my court, either to respond to his characterization of belief as a "complex vector function" of trust, experience and reason, and/or to critique the arguments he recently posted in his testimony. I do hope to get to both of those things, but I picked up a small but urgent contract programming job late last week that has been consuming my extra hours. Barring unforeseen difficulties, I should be done with that tomorrow night, and will try to get back to blogging after that.

Monday, March 06, 2006

And Then There Were Three

This post is part of an ongoing dialog between my friend Ernie and me about the validity of Christian belief (roughly speaking).

This will be a brief response to Beneath Belief, the third of three posts by Ernie.

Ernie had asked for suggestions of "specific assertions, ontologies, and/or ethics" that we could examine. I proposed these four:

  • The Bible is (is not) an honest and reliable document.
  • Eternal damnation can (cannot) be justified (if the Porsche is not already red)
  • Social good is (is not) evidence for the truth of Christianity.
  • Christianity is (is not) best explained as a solely human construction.f

These were too absolute, not contextual enough for Ernie, who rewrote them this way:

  1. The Bible is sufficiently reliable to enable me to grasp truth that I could not grasp without it
  2. If there are transcendent values, then there exist systems of justice which justify eternal damnation under certain plausible circumstances
  3. Christianity has created more social good than any other belief system
  4. The success of Christianity is not adequately explained by scenarios that discount all supernatural intervention and/or inspiration

Ernie dings me for making binary statements, but with the possible exception of (1), I would consider his to be binary as well, just slightly more elaborated. And I expect that we would elaborate as necessary before and after choosing a topic. My intention was to offer short statements that captured the essence of the issues; of course, I may not have succeeded.

The rewritten (1) has completely dropped the notion of honesty, and (in my mind) lowers the bar by only requiring reliability for a non-zero amount of truth, without saying what that truth is, and without acknowledging that the Bible could, on the whole, be more unreliable than not.

(2) is fine.

With (3) I think Ernie has changed the sense of the statement in a significant way. My version stresses (more than Ernie's) the questionable utility of "social good" as an indicator of truth. Several statements that Ernie has made, as well as his recently posted testimony, lead me to believe that this is an area where we disagree, and which can be addressed as a matter of epistemology.

With (4), I do not see a tremendous difference between our two versions, other than my use of "best explained" versus his contrary "not adequately explained." Nor do I see where (4) depends so heavily on (2) or (3), or why it might require an ethical framework before it can be tackled.

I need to wrap up for the night. I am happy to discard (2) for now, but think that (1), (3) and (4) are all viable options, if suitably elaborated. Ernie, do you still think (3) and (4) are still out of reach?

Friday, March 03, 2006

Contextual Royalty

This post is part of an ongoing dialog between my friend Ernie and me about the validity of Christian belief (roughly speaking).

The second part of Ernie's response is Context is King. I had stated that

The "context" part is a bit murky here. Ernie introduced this in "Brothers, Can Youse Paradigm", but without a clear (to me) description of what is included or excluded by the context. ...

Ernie's response provides some clarification. He equates "context" with "what you're trying to do". Context is also related to an "(implicit or explicit) level of precision" within an "(implicit or explicit) domain".

For purposes of our ongoing discussion, do we need to elaborate a purpose, a required level of precision or the domain? If I am now understanding Ernie's use of "context" (which is perhaps doubtful), I think those will be reasonably clear. If there is something more that should be said now about our (shared?) context, perhaps Ernie can fill me in.

As far as this being "an apparently ad hoc approach to knowledge", that is more or less why I described the situation as "bothersome", but I did not mean to imply by that that we can do better. That has become increasingly clear to me these past few years.

Not that this necessarily fits exactly with what we are discussing, I was reminded recently of this quote from Stephen J. Gould:

In science, 'fact' can only mean confirmed to such a degree that it would be perverse to withhold provisional assent.

Since I could not remember the exact wording, I searched for it just now. One of the hits came from Darwin on Trial, a review by Raymond Bohlin of a book by the same name by Phillip Johnson. Bohlin includes the above quote, and follows it immediately by this gem:

In other words, evolution is a fact because a majority of scientists say so, and you are "perverse" if you do not agree. We quickly begin to see that evolution holds a privileged place in the scientific community, which will go to extraordinary lengths to preserve that status.

What? Is "confirmation" just "because a majority of scientists say so"? Scientists would disagree. I think Bohlin might need a new paradigm.

Thursday, March 02, 2006

The Truth, the Whole Truth, and Nothing but the Truth?

This post is part of an ongoing dialog between my friend Ernie and me about the validity of Christian belief (roughly speaking).

After my last contribution to our conversation, Ernie has responded in three parts. I will respond to just the first part tonight.

In Absolutely - Not? Ernie agreed to change the first of our four epsistemological statements to "Belief in truth is inherently good", instead of "absolutely good". But he continues:

However, I just want to make sure we're clear about what we're giving up in so doing. In particular, I don't think this statement fully supports my original definition of Hard Truths:

In short, I am asserting that it is virtuous to pursue truth (no matter the cost), and vicious to suppress truth (no matter how convenient). That may not mean we should always tell the truth to others (there's often wiggle-room for self-preservation :-), but that we should at least be honest with ourselves.

The result is what I might instead call Solid Truth. By downgrading truth from 'absolute' to 'inherent', we leave open at least the theoretical possibility that there may be other 'inherent' goods which could on occasion supersede, or at least conflict with, Truth. For example, I might say that "Health" is "inherently good", but that doesn't necessarily justify any and all measures to promote health.

Put another way, we can no longer use "Belief in Truth" as an inviolate 'greatest good', i.e., the basis of a full-blown normative ethics. We can certainly come up with "corollary goods" that are supportive of Truth's "inherent good", but we must (for now, at least) remain agnostic about whether they are "always" good. That doesn't mean they are not, or can not be, completely good -- we just don't know they are, so we can't rely on that.

All that said, I actually think this is a good change to make to ensure that this epistemology truly reflects our shared beliefs. However, I just want to make sure my understanding of the significance of the change is consistent with his.

As I think about this, the distinction I would try to make is that while it is always better to believe truth than falsehood, it is not always better to pursue truth than to do anything else. First, our choice to pursue knowledge could lead us to neglect other important ethical duties. "Sir, I see that you are drowning, and I do have a life preserver right here, but I am quite busy studying the behavior of this fly crawling along it, and as I am sure you agree, gaining knowledge is always good." That is a ridiculous example, of course, but I hope it makes the point clear. Other "goods" do sometimes supersede the activities of correcting belief. This does not mean that believing falsehood is itself ever better than believing truth; rather, the marginal utility of some improvements to belief are lower than the marginal utility of some other courses of action.

Second, the means of gaining certain kinds of knowledge may violate other ethical principles. The pursuit of truth does not justify torture, for instance. The knowledge that results is not inherently bad, but the actions we undertake to gain the knowledge may be, depending on your ethics.

These are the kinds of considerations I had in mind when I suggested replacing "absolute" with "inherent" or "non-contingent". And these are just the kind of things that Ernie suggests would be a consequence of changing the statement. My justification for these changes does involve ethical principles that we have not yet discussed, but I would not expect the details to be important in making this distinction now.