Understanding the Spirit vs. the Letter of Probability

My apologies for there being so little activity on Civitas Humana for a long while now. I have been insanely busy and stressed lately (both professionally and personally), and I have only recently been able to catch up with blogging.

I’ll begin pumping some fresh blood into Civ by discussing Bayes’ theorem, the resurrection of Jesus, and why I think that, even with a non-zero prior (which is still very, very low) for the resurrection event, Paul’s letters and the Gospels are far too weak of consequent evidence to offset more probable (naturalistic or mundane) explanations for the same data.

Over a decade ago (March 2006) secular New Testament scholar Bart D. Ehrman debated Christian philosopher and theologian William Lane Craig about the evidence for the resurrection of Jesus (the transcript of the debate can be read here). Overall, the debate left me with the impression that Ehrman made a better case for naturalistic or non-paranormal explanations being more probable than a veridical resurrection event, with regards to the origin of the resurrection belief among Jesus’ disciples and the first generation of Christians. But there was one area where I think Craig scored a technical, though relatively minor point against Ehrman (as will be discussed below), and this was with regards to how Ehrman was defining a miracle event and conflating prior probability with posterior probability.

Lowder’s Summary of Craig’s First Rebuttal

Jeff Lowder on the Secular Outpost has made a useful summary of Craig’s critique of how Ehrman was defining a miracle event, and the arguments Ehrman had presented (in earlier publications) for why historians cannot argue that a miracle is the most probable explanation for a past event. This summary can be read in Lowder’s post “William Lane Craig’s Critique of Bart Ehrman on the Probability of Miracles.” Since the ensuing discussion involves Bayesian reasoning, you can read my essay “History, Probability, and Miracles” for a basic overview of how Bayesian logic works, if you are unfamiliar with the theorem.

Lowder begins by listing two published statements by Ehrman, which were quoted by Craig during the debate (bolding is my own):

(1) “Because historians can only establish what probably happened, and a miracle of this nature is highly improbable, the historian cannot say it probably occurred.”
(The Historical Jesus, part 2, page 50)
(2) “Since historians can establish only what probably happened in the past, they cannot show that miracles happened, since this would involve a contradiction — that the most improbable event is the most probable.”
(The New Testament: A Historical Introduction, page 229)
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In his response to these statements of Ehrman, Craig critiques his line of reasoning by arguing that Ehrman is conflating prior probability with posterior probability. The odds that a given individual may resurrect from the dead could, indeed, be very, very low. But if there is very, very good evidence that such a resurrection event has occurred, it may offset the low prior, and even outweigh alternative explanations, to degree such that Pr (R/B & E) > 0.5 (perhaps even by a wide margin, e.g., +0.9).
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Here is what Craig states in his own words (bolding is my own):
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“In other words, in calculating the probability of Jesus’ resurrection, the only factor he [Ehrman] considers is the intrinsic probability of the resurrection alone [Pr(R/B)]. He just ignores all of the other factors. And that’s just mathematically fallacious. The probability of the resurrection could still be very high even though the Pr(R/B) alone is terribly low.”
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Lowder likewise offers his own interpretation of Ehrman’s two quotations, and here is what he states regarding the first:
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“I am inclined to interpret (1) as the following claim: (1′) Pr(R/B) is so low that it is impossible, even in theory, for there to be sufficient evidence to confer a high final epistemic probability on R, i.e., Pr(R/B & E) > 0.5.”
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I would argue that to describe a miracle as an event that cannot be probable, even in theory, one would need to assign its prior probability a value of zero. And this is the same conclusion that Lowder reaches, when he states (bolding is my own):

The only way to reconcile (1′) with BT would be to assign Pr(R/B) a value of zero. If Pr(R/B) = 0, then it follows from BT that Pr(R/B&E;)=0. So, on the basis of (1) alone, as Craig has quoted Ehrman, I think it is premature to assume that Ehrman ‘just ignores all of the other factors.’ Maybe he does do that, but the quotation provided in (1) doesn’t show that. What I can say is that either Ehrman ignores all of the other factors or Ehrman assumes that historians must assign Pr(R/B) a value of zero. If the latter, then I think that is false.”

With regards to Ehrman’s second quotation, Lowder briefly states:

“Turning to (2), I don’t have much to say, other than I think Craig is 100% correct when he says that Ehrman ‘Confuses Pr (R/B & E) with Pr (R/B).’”

My Thoughts on Ehrman’s Quotes

At the end of this essay, I will make some suggestions for improving Ehrman’s arguments (which in spirit I think are correct, even if they may be formally invalid at parts). That said, I agree with Lowder’s conclusions on both accounts, for at least three reasons:

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Cosmology and Time in Metaphysical Naturalism

For the next part of my series about the ‘metaphysics’ in metaphysical naturalism I will be analyzing how modern scientific theories about cosmology fit in to the naturalist worldview. Since I am not a professional scientist, I will be quoting authorities for all critical information. The purpose of this article is more philosophical than scientific, in that it does not seek to advance a particular scientific theory, but rather to demonstrate how modern cosmological theories align with the definition of metaphysical naturalism discussed earlier in this series. Feedback is welcome from professionals, if any of the scientific discussion below has factual errors or is unclear. I have worked to quote scientific authorities in their own words as much as possible, in order that their theories be represented as close as possible to their own views.

The study of cosmology has a long history (see here), but since around the end of the 20th century scientists have reached a generally cohesive view of what our universe looks like. The observable universe that we live in is a sphere with a radius of about 46 billion lightyears. Beyond that the unobservable universe is much larger, and is still inflating rapidly. Within this observable part of the universe alone there are at least 100 billion galaxies (and possibly 500 billion galaxies in the whole universe), and, if modern observational estimates among astronomers are correct about there being 17 billion Earth-sized planets in our galaxy, then the rest of the universe no doubt contains many, many more.

For a musical description of the vast scale of our galaxy and universe, I recommend the Galaxy Song in Monty Python’s The Meaning of Life.

In the 1920’s American astronomer Edwin P. Hubble discovered that our universe is not static. Instead, space is expanding rapidly. Current estimates calculate the rate of expansion at 74.3 (plus or minus 2.1) kilometers per second per megaparsec (a megaparsec is roughly 3 million light-years). Since, looking towards the future, the universe is expanding out of control, looking towards the past, we would expect the universe to have emerged from a much smaller point. 

The modern theory of the Big Bang answers this question. Scientists have traced the expansion of our universe to a very small initial state about 13.82 billion years ago. Before the expansion, our universe, including its Big Bang Expansionmatter and radiation, was compressed into a very hot and very dense point of mass just a few millimeters across. This state is theorized to have existed for a fraction of the first second of time, before a massive blast caused the universe’s matter and energy, and even space and time, to expand rapidly. In the trillionth of a trillionth of a second after the Big Bang, the universe expanded at an unfathomable rate from merely the size of a pebble to being of astronomical scale.

This sequence of events has left us with a vexing question: what caused the Big Bang?

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