Lydia McGrew on Testability, Likelihoods, and Design

Here.

Doctor Logic and Lydia McGrew on Likelilhoods, Design, and Probabilities

Doctor Logic: If an all powerful being were designing life, we don't expect descent, common descent, common composition or a gradual appearance of features and species. How many ways can a God create life in a universe? The number of ways a God can do this is vastly greater than the number of ways unguided evolution can do so. For example, gods don't even need to create life consistent with physical laws because they can create ghosts. There's no need for descent (birth) because God can make animals outright or create factories (no car has ever been born to another car). Even keeping the species the same and changing their natural histories and genomics gives a God vastly more options than evolution. I think theists would be tempted to say that there are infinitely more ways God could create life than ways that evolution could create life.


This is a simple problem in Bayesian reasoning. Finding ourselves in a world that is consistent with unguided evolution implies that the probability that we're designed is extremely close to zero.

In other words, if God exists, then there are a million ways in which God could create things, including Young Earth Creationism, etc. If atheism is true, then if intelligent life is going to emerge, it's got to emerge through naturalistic evolution. So, if the evidence is compatible with naturalistic evolution, then the evidence very strong supports naturalistic evolution, since this evidence is very likely given atheism and vanishingly unlikely given theism.

Lydia McGrew's paper on design and likelihoods might serve as a way for theists to respond here. Because God could do it a certain way doesn't mean that it would be reasonable for God to do so.

McGrew on ECREE

From his essay on evidence.

Extraordinary Claims and Extraordinary Evidence


Another common slogan, also popularized by Sagan, is that Extraordinary claims require extraordinary evidence. Much depends, of course, on what counts as extraordinary, both in a claim and in evidence. It cannot be simply that a claim is unprecedented. At a certain level of detail, almost any claim is unprecedented; but this does not necessarily mean that it requires evidence out of the ordinary to establish it. Consider this claim: “Aunt Matilda won a game of Scrabble Thursday night with a score of 438 while sipping a cup of mint tea.” Each successive modifying phrase renders the claim less likely to have occurred before; yet there is nothing particularly unbelievable about the claim, and the evidence of a single credible eyewitness might well persuade us that it is true.
The case is more difficult with respect to types of events that are deemed to be improbable or rare in principle, such as miracles. It is generally agreed in such discussions that such events cannot be common and that it requires more evidence to render them credible than is required in ordinary cases. (Sherlock 1769) David Hume famously advanced the maxim that No testimony is sufficient to establish a miracle, unless the testimony be of such a kind, that its falsehood would be more miraculous, than the fact, which it endeavours to establish (Beauchamp 2000, p. 87), which may have been the original inspiration for the slogan about extraordinary evidence. The proper interpretation of Hume’s maxim has been a source of some debate among Hume scholars, but one plausible formulation in probabilistic terms is that
P(MT) > P(~MT) only if P(M) > P(T~M),
where M is the proposition that a miracle has occurred and T is the proposition describing testimonial evidence that it has occurred. This conditional statement is not a consequence of Bayes’s Theorem, but the terms of the latter inequality are good approximations for the terms of the exact inequality.
P(M) P(TM) > P(~M) P(T~M) when both P(~M) and P(TM) are close to 1. There is, then, a plausible Bayesian rationale for Hume’s maxim so long as we understand it to be an approximation.

It does not follow that the maxim will do the work that Hume (arguably) and many of his followers (unquestionably) have hoped it would. Hume appears to have thought that his maxim would place certain antecedently very improbable events beyond the reach of evidence. But as John Earman has argued (Earman 2000), an event that is antecedently extremely improbable, and in this sense extraordinary, may be rendered probable under the right evidential circumstances, since it is possible in principle that

P(TM)/P(T~M) > P(~M)/P(M),

a condition sufficient to satisfy the rigorous condition underlying Hume’s maxim and the slogan about extraordinary events. The maxim is therefore less useful as a dialectical weapon than is often supposed. It may help to focus disagreements over extraordinary events, but it cannot resolve them.

Probabilities, miracles, and design

I do believe that a case can be made for the claim that the Christian story about what happened in the life of Jesus makes more sense of the evidence than any possible naturalistic story, so long as you are willing to allow for a God who might do such a thing. 

But here Hume keeps coming back. If you base probabilities on what is most frequently found in nature, and you don't introduce the possibility of a non-human designer, then it looks as if the frequency of dead people who stay dead defeats anything but "extraordinary" (read virtually impossible) evidence for, say, a resurrection. 

But, the believer responds, causing the miracles in the life of Jesus seems like something a God might do. It makes sense from a theistic perspective, as opposed to, say, claiming that God caused a bunch of people to hallucinate, or caused a bunch of people to propagate a hoax that would ultimately result in them ending up on the kind of cross that Jesus was crucified on. 

But, the reply goes, likelihoods about what a divine agent might or might not do can't be brought in. They aren't based on experience, the way, say, the frequency of dead people who stay dead does. If you bring God in, you play a wild card. Anything goes. 

But, the theist replies, we can draw inferences about possible divine designers from analogy to human designers. 

That's why I think Lydia McGrew's paper on design and probabilities is relevant to this whole debate, which I linked to a few days ago.

Lydia McGrew on identifying intelligent agents

This looks like an intriguing paper.

Abstract: It is often assumed by friends and foes alike of intelligent design that a likelihood approach to design inferences will require evidence regarding the specific motives and abilities of any hypothetical designer. Elliott Sober, like Venn before him, indicates that this information is unavailable when the designer is not human (or at least finite) and concludes that there is no good argument for design in biology. I argue that a knowledge of motives and abilities is not always necessary for obtaining a likelihood on design. In many cases, including the case of irreducibly complex objects, frequencies from known agents can supply the likelihood. I argue against the claim that data gathered from humans is inapplicable to non-human agents. Finally, I point out that a broadly Bayesian approach to design inferences, such as that advocated by Sober, is actually advantagous to design advocates in that it frees them from the Popperian requirement that they construct an overarching science which makes high-likelihood predictions.

Straw Men Burning: Tim McGrew on Misinterpretations of the McGrews' article on the Resurrection

It's easy to dismiss and discredit an opponent when you don't make any effort to understand what that opponent has written. There is the idea about that the McGrews actually calculated the odds of the Resurrection, or that they maintain the strict and complete independence of the New Testament sources, when in fact they say no such thing. That's life in the blogosphere; in peer-reviewed journals editors and referees are there to at least try to keep this sort of things from happening. Of course, as Lewis pointed out, it is sometimes difficult to understand a position to which you are antipathetic, even if you try to understand it. Anyway, Tim responds here. 


TM: One of the hazards of writing technical philosophy is the risk that someone who lacks the appropriate expertise will attempt to critique it. In the case of the article on the resurrection that Lydia and I wrote for The Blackwell Companion to Natural Theology, this has already happened. It is hard enough to correct misimpressions of this sort on a relatively neutral topic; when the subject rouses passions of the sort that, as Hume reminds us, religious disputes are apt to generate, then the difficulties are redoubled. 

But one thing that we did not anticipate is that people who are completely clueless would undertake to explain the article to the rest of the world, in the process completely garbling the central claim and shedding absolutely no light on any of the surrounding issues. Since this particular exhibition of aggressive incompetence is now being uncritically rebroadcast by people who are unable or unwilling actually to read the article, it is worth making a few salient points: 

1. Nowhere in the article do we give, estimate, or suggest "odds on the resurrection." Near the outset we explicitly disclaim any attempt to do so, writing:

Even as we focus on the resurrection of Jesus, our aim is limited. To show that the probability of R given all evidence relevant to it is high would require us to examine other evidence bearing on the existence of God, since such other evidence – both positive and negative – is indirectly relevant to the occurrence of the resurrection. Examining every piece of data relevant to R more directly – including, for example, the many issues in textual scholarship and archeology which we shall discuss only briefly – would require many volumes. Our intent, rather, is to examine a small set of salient public facts that strongly support R. The historical facts in question are, we believe, those most pertinent to the argument. Our aim is to show that this evidence, taken cumulatively, provides a strong argument of the sort Richard Swinburne calls “C-inductive” – that is, whether or not P(R) is greater than some specified value such as .5 or .9 given allevidence, this evidence itself heavily favors R over ~R.

The ratio of 10^44 to 1 is a likelihood ratio, not odds. People who do not understand the difference between these two ratios should not attempt to discuss the mathematical parts of the article.

2. We are very explicit about our assumptions. In the online version of the article, on p. 39, we make it plain that our calculation

is predicated on the assumption that in matters other than the explicit claims of miracles, the gospels and the book of Acts are generally reliable – that they may be trusted as much as any ordinary document of secular history with respect to the secularly describable facts they affirm. And where they do recount miraculous events, such as Jesus' post-resurrection appearances, we assume that they are authentic – that is, that they tell us what the disciples claimed. This calculation tells us little about the evidence for the resurrection if those assumptions are false. We have provided reasons to accept them, but of course there is much more to be said on the issue.

3. We are quite aware that the assumption of independence is critical, and we discuss this matter extensively on pp. 40-46. It is wearying to see commentators who have not bothered actually to read the article confidently proclaiming that we have overlooked the possibility of dependence.

Readers are of course free to disagree with our actual conclusions. It would be cheering, however, if they would first take the trouble to understand what those conclusions are.

Lydia McGrew on the Naturalistic induction

Lydia formulates the "naturalistic induction" as follows. 

Most problems which were unexplained by science in purely naturalistic terms have now been explained by science in purely naturalistic terms. So, by direct induction, any alleged evidence against naturalism has a scientific explanation in purely naturalistic terms.

Science has made and continues to make such great progress throughout history, gradually whittling away at the set of things that were previously not scientifically understood, that whatever it is that you are presently bringing forth as evidence against naturalism, I am sure that science will eventually get to that in time and explain it, as well, as entirely the product of natural causes.

 And then she argues that this induction is not going to work. And this refers to the Balfour quote she references.

For further discussion of the McGrew-Babinski post

There are complaints about what Blogger does after a long thread, so I am setting it up so that the discussion can continue here.

Richard Carrier Replies on Lydia's Blog

With some concessions and apologies. The fundamental disagreements, of course, remain.

Less Wrong on the McGrews' Essay

Luke, at Common Sense Atheism, thinks that the these criticisms of the McGrews' Essay are more substantial than those put forward by Carrier.

Pride Goeth

Here's what Carrier says about his chapter of The Christian Delusion. 


Two of The Christian Delusion's fifteen chapters are mine. The first is Why the Resurrection Is Unbelievable, which is the most definitive refutation of warranted belief in the resurrection I have ever composed. It's a deliberate tour de force, such that I doubt I'll ever have to write another. It even takes down recent attempts to use Bayes' Theorem to argue for the resurrection, and it contextualizes everything so there just isn't any rational basis left for claiming the resurrection is historically proven.


In the next paragraph he refers to both of his contributions as tours de force. 


When you talk like that, you had better be able to take out the McGrews. In my brainwashed opinion, that's a chess game he has no chance of winning. 

Lydia McGrew rebuts Richard Carrier.

I understand that the current atheist meme on this, which shows a rather striking lack of understanding of probability, is to say that if one does not argue for a particular prior probability for some proposition, one literally can say nothing meaningful about the confirmation provided by evidence beyond the statement that there is some confirmation or other.


This is flatly false, as both the second of the quotations above from the paper and my rather detailed explanation to Luke M. show.

Was the McGrews' article on the Resurrection Not Even Worth Citing?

Richard Carrier thinks so, calling it "crappy." Rumor has it that Tim and Lydia disagree. I will tell you this much. If I could get Richard Carrier or anyone else to raise their probability for the resurrection from 1% to 10%, I'd consider it an enormous accomplishment.

The McGrews defend the Resurrection

A redated post.

This is a chapter in the Blackwell Companion to Natural Theology also includes

 my essay on the argument from reason. Tim is a master-strength chessplayer who had the Gambit Cartel column in Chess Cafe for between 2002 and 2005.