Saturday, December 30, 2017

Infinite monkey theorem

I was asked to comment on a post by Matthew Ferguson:

1. Ferguson says he's interested quality rather than quantity. However, we're often warranted in believing something happened or something exists due to the sheer number of independent reports. So why should we have a different standard for miracles? 

2. I generally agree with Ferguson's definition of a miracle. Among other things, he says:

Miracles involve agencies, wills, or intentions, causally working from outside of the physical order, intervening in the physical order to cause events that cannot be explained by physical causes alone...Hence why the molecules of Jesus’ corpse cannot cause him to immortally rise from death. Hence why the water molecules in a jar cannot explain sudden transformation into wine. Instead, an agency, will, or intention working from outside of the physical order is intervening to cause an occurrence that would otherwise not be possible within the physical order...Miracles are not generally understood as unconscious accidents, but happen for intentional reasons. Answers to prayers, healing bodies in very specific ways, and producing very specific effects, such as parting the Red Sea specifically in front of the Judeans, all imply intelligent design.

In other words, the same causes produce the same effects. Christians don't deny that. But this creates no presumption against a different cause producing a different effect. A miracle happens when a new cause (e.g. divine action), outside the causal continuum, produces a new effect. 

3. I agree with his definition of agency-centered teleology, although I disagree with his naturalistic definition of biological teleology. 

4. He cites two putative coincidence miracles:

Don brought up (part 2, 40:40) a girl that lost her pet parakeet, prayed for a new parakeet, and then had another parakeet fly into her yard the next day. Don also brought up a couple that had prayed for a very specific amount of money, and then received that exact sum of money. 

But dismisses them:

these events can still be plausibly explained as coincidences. We live in a world of more than 7 billion people, where extraordinarily rare events are happening everyday.

Yet there are problems with that response:

i) He fails to define a coincidence. Here's one definition:

A coincidence is a surprising concurrence of events, perceived as meaningfully related, with no apparent causal connection. D. Bartholomew, Uncertain Belief (Oxford 2000), 101. 

But in that event, can he justifiably dismiss these examples as merely coincidental unless he can establish that the relation is in fact random? How does he discharge his burden of proof in that regard? 

ii) What's his practical criterion to distinguish a coincidence from an orchestrated event? For instance, consider circumstantial evidence that implicates a suspect in a crime. But given his standard, why can't we say that in a world with more than 7 billion humans, the evidence of criminal activity can always be chalked up to coincidence? 

iii) How often must a certain kind of event occur before we recognize a pattern rather than a coincidence? What's his threshold? 

5. Apropos (4), he quotes Richard Carrier:

the Law of Large Numbers is also used to refer to what causes the Infinite Monkey Theorem to be true … The point is the same: the more occasions for a coincidence to occur, the more such coincidences will occur. And without a mathematical check, we cannot know from our isolated POV whether we are one of those coincidences or not.

Yet how is that a mathematical check in practice? According to the infinite monkey theorem, one monkey with infinite time, or infinite monkeys with finite time, typing keys at random, will eventually produce a particular finite text like Hamlet. 

i) But what's the real-world analogue? An atheist can't appeal to infinite time or infinite random factors to provide a naturalistic explanation for coincidence miracles. 

ii) In addition, consider how the gibberish texts would astronomically outnumber the intelligible texts. But is that ratio comparable to reported miracles? 

6. Two problems with his comment on the argument from prophecy:

i) A prophecy might be ambiguous in advance respecting the process by which it will be fulfilled, yet unambiguous after the fact.

ii) The argument from prophecy doesn't turn on the probability of prophetic fulfillment considered in isolation, but the combined probability of many convergent prophecies. 

7. He says:

If a miracle worker could perform miracles on demand in modern times, then he could do it when doctors and scientists are present. This would provide perhaps the strongest evidence there is of a miracle.

But that's an artificial bar because it assumes a miracle worker has the ability to perform miracles at will. While that was true of Jesus, given his divinity, that's not a given with respect to miracle workers in general.

8. He says:

Nevertheless, a genuine miracle worker, who could repeat miracles, could provide empirical evidence of miracles to scientists and doctors in a controlled setting. 

That piggybacks on the same dubious assumption noted under (7). In addition, unless there's a presumption that God wants to prove his existence to everyone, there's no reason to think miracles will routinely occur in a controlled setting. On some occasions, God's intention to heal someone in particular might take place in a controlled setting (e.g. a hospital). 

9. He says:

Miracles such as raising the dead, walking on water, or turning water into wine likewise would involve demonstrable, empirical change. If such miracles existed, science could find them.

“[W. L. Craig] Natural laws have implicit ceteris paribus conditions … In other words, natural laws assume that no other natural or supernatural factors are interfering with the operation that the law describes.”

Ceteris paribus is a Latin term meaning “all other things being equal.” Science can tell us, for example, that a human being’s weight placed on the surface of liquid water will be too great for the surface friction on top of the water to support, causing the person to sink. This pattern can be demonstrated again and again through empirical testing. We know from science, therefore, that a human being walking on water would defy ordinary physical causality. If such an action were performed, therefore, especially by someone reputed to be a miracle worker, this would provide prima facie evidence of a miraculous event.

Science can also distinguish intelligently-driven behavior from natural occurrences, due to the goal orientation, design, and intentionality reflected in intelligent behavior. Empirical science, therefore, provides us with all of the tools that we need to study the existence of miracles.

That's a useful corrective to methodological naturalism.

10. He says:

What naturalists maintain, however, is that, no miracle events will be able to be supported by verifiable empirical evidence. Only a single example of such verifiable evidence, even if no others occurred for all of history, would be enough to disprove this view.

That's very significant to the burden of proof. Naturalism is a universal negative in reference to miracles. In principle, it only takes one counterexample to falsify naturalism. 

Therefore, the Christian has a trivially low burden of proof while the atheist has an insurmountably high burden of proof. An atheist must be able to discount every reported miracle.

11. He says:

“extraordinary” does not mean that the type of evidence itself has to be remarkable. Video tapes, x-rays, medical records, and so on are all part of ordinary life experience. What is meant by “extraordinary” in this case is that the evidence in question cannot be equally explained by a wide range of causes, but is only rendered probable under a very specific hypothesis. The problem with miracle reports is that they can be explained by a wide range of non-miraculous causes–such as misinterpretations of one’s senses, misdiagnosed medical conditions, remarkable coincidences, constructed memories, hearsay, and plain old lies. 

While I appreciate the definition, his escape clauses amount to special pleading. 

12. He says:

We can assess the likelihood of such events based on empirical evidence and simple statistics. As Cavin explains, a low prior probability for miracles can be shown by a simple statistical syllogism (slide 110):

99%+ of Xs are Ys
A is an X
Therefore, A is probably a Y

In the case of a miracle such as Jesus rising from the dead, the question is not whether God wants to raise Jesus from the dead, but simply the question of how often these kinds of events empirically take place in the world. 

But that's simplistic:

i) Suppose I drive my friend to the airport. My car is just one of a thousand other cars in the parking garage. Does this mean there's only a one in a thousand chance that I will drive my own car home? 

The other 999 cars are irrelevant to the odds that I will drive my own car home, because my selection isn't random. In fact, it's not a question of mathematical odds at all. 

ii) What are the odds that I will be dealt a royal flush? Depends. Is the deck fair or stacked. If the deck is stacked, then it may be inevitable that I will be dealt a royal flush.

iii) What are the odds that the deck will be stacked? I don't think that's quantifiable. Rather, it's a question of whether the dealer and I are in cahoots. The probability that he and I conspired isn't a question of mathematical odds.

13. He says:

First, miracles are events that people look and hope for. People pray everyday for miracles to occur, and they look for their prayers to be answered. This will not only cause people to see miracles in places where they may very well have not occurred, but it will also cause people to believe in miracles when they are told about them by others.

Although that's sometimes true, it's an overgeneralization. Reported miracles also happen to people who weren't looking for them. Some Christian miracles that happen to atheists, Jews, and Muslims, despite their predisposition to reject Christian miracles due to the social cost of conversion.

14. He says:

Human psychology is likewise wired to often see agencies in places where there are none. Early humans lived on a planet teeming with life, much of which was hostile and dangerous. Accordingly, early humans had to compete with other animals (and sometimes other humans) to survive, which selected our minds to detect agency and to seek out intelligence that threatened us. An accidental side effect of this, however, was that our minds became programmed for agency over-detection.

i) That combines a tendentious Just-So story with a tendentious psychological mechanism. 

ii) Moreover, we could just as well or better say that atheists suffer from an agency under-detection strategy. 

15. He says:

Simply documenting a multitude of such reports, therefore, does not mean that one has provided a compelling case for their actual occurrence.

That fails to distinguish between a multiple derivative reports of the same event, multiple independent reports of the same event, and multiple independent reports of different events.

16. He says:

Merely documenting anecdotal evidence and miraculous reports is not enough.

Finally, any researcher who seeks to make a persuasive case for the existence of miracles will need to research miracles in every possible context that they can. This means looking for evidence of miracles occurring in a Hindu context, a Muslim context, a Catholic context, a Native American context, a Pagan context, and others, besides a solely a Protestant and Pentecostal context, for example.

i) Yet that's in tension with his prior admission that:

Only a single example of such verifiable evidence, even if no others occurred for all of history, would be enough to disprove this view.

Anecdotal evidence can be quite sufficient to overturn a universal negative. 

The weakness of anecdotal evidence is when one attempts generalize from a few examples, since that may not be a representative sample. But disproving a universal negative doesn't require extrapolation. 

ii) In addition, he seems to think the occurrence of non-Christian miracles poses a problem for Christianity, although he fails to explain why. Perhaps his unstated objection is that if the argument from miracles is used to prove Christianity, then non-Christian miracles cancel out that line of evidence. If that's what he has in mind, I'd say the following:

iii) Even if the argument from miracles is insufficient to prove Christianity, it can be sufficient to disprove naturalism. And that can figure in a cumulative case argument for Christianity, by eliminating a major contender. 

iv) Likewise, even if the argument from miracles is insufficient to single out Christianity, it can figure in a cumulative case argument for Christianity. The case for Christianity doesn't hinge on a crucial piece of evidence, but multiple lines of evidence. 

v) If miracles cluster around Christianity, then they point to Christianity.

1 comment:

  1. Regarding "empirical evidence of miracles to scientists and doctors in a controlled setting", we've had that kind of evidence for some paranormal phenomena, as critics of the paranormal have sometimes admitted. But the critic can then, and sometimes has, changed his standard. He'll ask for the experiment to be repeated. Or he'll say that even though the paranormal phenomenon in question met the standard of a controlled scientific experiment, we should hold paranormal phenomena to a higher standard, so that no number of controlled scientific experiments would be sufficient. Or he'll say that we need to suspend judgment indefinitely while we keep looking for a normal explanation of what happened. And so on. For some examples of how skeptics reject even controlled scientific experiments supporting the paranormal when provided with that sort of evidence, see here, here, and here.