Via Jerry Coyne, I came across this exchange between Sam Harris and David Eagleman. Boring, standardized inaccuracies about the relationship between atheism, New Atheism, and certainty aside, I think that the problems with Eagleman's `Possibilianism' are deeper than Harris recognizes, insofar as such a thing is possible to say after flat-out inconsistency has been established.
The error which pervades his website and his talk is a simple one: a black/white split between commitment and non-commitment. He appears to be irretrievably mired in the old "believe X/believe not X/suspend judgment" trichotomy. Like many other three-horned creatures, this sort of thinking feels awfully... extinct. On first and other inspections, Possibilianism appears to be Bayesianism without the rigor. One simply enumerates possibilities - apparently as only emphasized for theism, though I do not see why other propositions should not be similarly attended to - and does not worry about things like analytical usefulness or Dutch-books or probabilistic consistency or positing any principled means of updating commitments. It looks like dodging and attention-getting; it smells like dodging and attention-getting; and yet here I am, about to give it a taste-test as well. I suspect this is about to get deeply unhealthy.
Perhaps Eagleman is wholly unfamiliar with analytic philosophy or the philosophy of science, despite his heavy allusions to the same. In Bayesianism, one holds `multiple ideas' in ones head, but not simply as possibilities but as articles with differing probabilities. As one of the simplest theories in probability runs, prob(X)+prob(~X)=1, a statement that generalizes to any finite partitioning of possibilities on the assumption of finite additivity, which is itself an implication of the stronger assumption of countable additivity, which itself yields an analogous result. Another popular standard, widely-assumed, is regularity, which states that all possible propositions have probability greater than 0.
So a Bayesian who accepts regularity as regards coherently formulated definitions of God is already holding the possibilities in mind. Further, the confidences allotted to the differing possibilities are reflected in one's prior whenever updating on new discoveries. One may even update on uncertain propositions using Jeffrey Conditioning. All around the world today, Bayesians are wagering on uncertainty and on propositions for which no decisive evidence exists. For all of these methods, there are various arguments, and the limits and applications of these methods are items of active research and discussion. In the absence of any evidence, equivocation is the most popular method. So, what exactly does David Eagleman have to offer?
T-shirts and confusion and "boy is this Universe is a counter-intuitive and amazing place!"
He uses terms like `likelihood' and other probabilistic language, but does not seem to understand probabilism. In this matter, he appears to be similar to (most of) the New Atheists, minus his uncomprehending overview. The New Atheists are if anything more consistent with probabilism in their language than is Eagleman.
It really is that bad. This sort of `oh look at my radical new way of thinking about knowledge (especially theistic belief)' annoys me to no end, especially when it comes in the form of a condescending lecture to us over-certain militant atheists/theists. If only we opened our minds to uncertainty and possibility! Then we'd all get along.
Whether it's the `God transcends existence' crowd or the `we need a new agnosticism crowd', the boring, ignorant element remains. Because these are all useless, they are all doomed to be fads, the passing symptoms of those who are uncomfortable with using accurate words for self-description, these being loathed due to exposure to various sorts of reaction and cheap sloganeering. "Oh I don't want to be dogmatic like those atheists," or "oh I don't want to be a fundamentalist like those theists." Those. Those. Not me. No way. They lazily search for Third Ways that already exist and in a form superior to their imaginations, or they simply wax incoherent; they pay little attention to existing criticisms, which they cannot know to be relevant because they are ignorant.
Gimme my TED talk, please! I'd love to profit from an exciting, revolutionary proposal of stuff that's been around for centuries. Hell, I'll make up my own new word for probabilism and decision theory and have my own movement. I'll call it `nicepersonopenmindednessism' or `uncertaintyisgoodpolicyism'. Goodness, I could write a book! To ensure originality, I'll fudge a few details. I'd hate to be thought a plagiarist. `Mysterianism' is already taken, alas. (I note that Mysterianism is actually worth looking at.)
Edit (9/5/2011): I would recommend reading this before watching the TED talk.
Showing posts with label Bayesianism. Show all posts
Showing posts with label Bayesianism. Show all posts
Saturday, September 3, 2011
Wednesday, August 24, 2011
The power of moral non-realist subjectivism
Over on Facebook, Massimo Pigliucci links an NYT article describing a conversion to non-realism. As I usually recommend Dr. Pigliucci as an expert on ethics, I was perturbed to find that he did not understand how moral non-realists could conduct "moral argument." Because after all, he argues, ethical statements are akin to trivial preferences like "milk chocolate versus dark chocolate" in a non-realist account.
This is profoundly misguided, and I was surprised to hear it from Dr. Pigliucci. There is a trivial sense in which it is correct, but there is a very non-trivial sense in which it is deeply confused, a confusion which often leads people to say things like, "but non-realists cannot conduct sensible moral argument."
To shoulder the responsibilities which come with idiosyncrasy, I will give a formal account of how moral argumentation `works' in a non-realist conception. I am convinced that moral non-realism can do almost everything that realists want their metaethics to do, barring the over-confident usage of a few unimportant phrases. I think that, properly understood, moral realism is paltry in light of a developed non-realism. Further, I want to show that moral realisms are in practice a special case of ethical subjectivism.
So how can one capture non-realism in an analytically useful way? For this, we turn to Bayesianism. Recalling that Bayesians assign subjective probabilities to subsets of a sample space, we simply omit `ethical propositions' from the sample space.
Cool. We can still ascribe probabilities to things like `x causes suffering', `I want to do x', and `doing x would conform to principles protecting free expression', but unless statements like `I ought to do x' wholly reduce to `factual' statements, they are not ascribed probabilities. Many `realists' attempt to claim truth-values for ethical propositions by claiming that what we really `mean' by `I ought to do x' reduces to such statements. In this case, they accomplish nothing but a loss of generality. As we will see later, their position can be described using subjective utilities.
So let's say that you are a coherent, well-calibrated Bayesian with probability distribution p who wants to make a choice between two actions, X and ~X. Better yet, let's say you act and let's find out what that means. To capture it, we can say that you prefer X to not ~X by choosing X. We can capture this simple preference with a subjective utility function u{p,C}, where p is your distribution and C is the choice `X or ~X'. Such binary actions will allow for a trivial ordering relation u(X)>=u(~X) wherever you do X. One can easily see that for a finite set of mutually exclusive choices, a similar ordering can capture the selection of one of the options. So we can assume that this function maps actions into some one-dimensional set of numbers, say the reals. So subjective utilities are functions from actions into the real numbers. If you like, you could let utilities map into the extended reals (i.e. take infinite values), but such functions risk collapsing into triviality unless you are careful to avoid the paradoxes that result
We notice immediately that we are now firmly in the domain of Bayesian decision theory. This is good news; we have a lot of accepted formal tools to use for our moral thinking. Better yet, we have kept things general enough to account for actions as demanded by any other moral system. To see how, let Up be the set of all possible utility functions uC=(u(X),u(~X)) where (u(X),u(~X)) is a pair of real numbers. This allows for any preference to any degree. (If moral absolutism-by-degree (say a Kantian imperative) is in play, reintroduce the extended reals.) So the demands of any moral system as applied to a rational agent faced with a choice can be captured. If we have a very clearly defined system S that says something like "X is permissible iff ...", then utility functions can be sorted into a blocks: the u's consistent with S in one, and the u's inconsistent with S in another. More generally, one can define subsets of utility functions consistent with a moral theory. Better yet, we may introduce fuzziness by probabilizing relationships like "u conforms to the principles of free expression", though as far as I can tell uncertainty with regards to conformity with principle may be subsumed in one's utility function. (One may still want to do this for judging other utility functions.)
Cool. So non-realists can even talk about conformity to abstract principles in a principled way without making charges of irrationality concerning preferences. So how does moral argument look? As factual information is introduced, the restrictions on utility functions which do not commit `horrendous' decisions are increased. So a Bayesian who wants to murder for fun could not ascribe a high value to life, or to non-violence, or to the autonomy of humans, or to the prevention of suffering, or...
He may remain perfectly consistent in adopting such a function. But such functions are very rare. Moral argument works so long as we expect humans to have common concerns and interests. There are limits, but it can be done. Further, I think we can expect a non-realist approach to be just as convincing to those who actually do want to murder for fun as a realist approach.
Which is not very. All the realist gains is the satisfaction of calling such a person irrational, instead of a monster or thug or authoritarian.
Chomsky often invokes `elementary principles', like avoidance of hypocrisy, when beginning a speech. He invokes international law and other `moral truisms'. And yet he doesn't strike me as a realist, and if he were to simply demonstrate that US foreign policy and its media defense is hypocritical, I do not think it would be necessary for him to say "and hypocrisy is something we should be avoid." Do we need to insist on truth-values for statements like "we should not tolerate a racist, censorious, unrepresentative, and violent state"?
Our preferences are not drawn out of a hat. Normal people can ascribe meaning to principles and commit to them. That's why moral argument works, even if irreducible `should' statements are not truth-valued.
Now for the inevitable objections. As I put it on Facebook:
So, let's talk about what subjective utility functions we would like people to have, which have nice properties, and other swell things. Or not. But don't tell me I cannot have that conversation.
What I have not been saying: I have not insisted that all reasonable people be moral non-realists. I'm just pointing out that you can do a lot with a non-realist account. I of course have problems with realist accounts, but that's a different discussion.
This is profoundly misguided, and I was surprised to hear it from Dr. Pigliucci. There is a trivial sense in which it is correct, but there is a very non-trivial sense in which it is deeply confused, a confusion which often leads people to say things like, "but non-realists cannot conduct sensible moral argument."
To shoulder the responsibilities which come with idiosyncrasy, I will give a formal account of how moral argumentation `works' in a non-realist conception. I am convinced that moral non-realism can do almost everything that realists want their metaethics to do, barring the over-confident usage of a few unimportant phrases. I think that, properly understood, moral realism is paltry in light of a developed non-realism. Further, I want to show that moral realisms are in practice a special case of ethical subjectivism.
So how can one capture non-realism in an analytically useful way? For this, we turn to Bayesianism. Recalling that Bayesians assign subjective probabilities to subsets of a sample space, we simply omit `ethical propositions' from the sample space.
Cool. We can still ascribe probabilities to things like `x causes suffering', `I want to do x', and `doing x would conform to principles protecting free expression', but unless statements like `I ought to do x' wholly reduce to `factual' statements, they are not ascribed probabilities. Many `realists' attempt to claim truth-values for ethical propositions by claiming that what we really `mean' by `I ought to do x' reduces to such statements. In this case, they accomplish nothing but a loss of generality. As we will see later, their position can be described using subjective utilities.
So let's say that you are a coherent, well-calibrated Bayesian with probability distribution p who wants to make a choice between two actions, X and ~X. Better yet, let's say you act and let's find out what that means. To capture it, we can say that you prefer X to not ~X by choosing X. We can capture this simple preference with a subjective utility function u{p,C}, where p is your distribution and C is the choice `X or ~X'. Such binary actions will allow for a trivial ordering relation u(X)>=u(~X) wherever you do X. One can easily see that for a finite set of mutually exclusive choices, a similar ordering can capture the selection of one of the options. So we can assume that this function maps actions into some one-dimensional set of numbers, say the reals. So subjective utilities are functions from actions into the real numbers. If you like, you could let utilities map into the extended reals (i.e. take infinite values), but such functions risk collapsing into triviality unless you are careful to avoid the paradoxes that result
We notice immediately that we are now firmly in the domain of Bayesian decision theory. This is good news; we have a lot of accepted formal tools to use for our moral thinking. Better yet, we have kept things general enough to account for actions as demanded by any other moral system. To see how, let Up be the set of all possible utility functions uC=(u(X),u(~X)) where (u(X),u(~X)) is a pair of real numbers. This allows for any preference to any degree. (If moral absolutism-by-degree (say a Kantian imperative) is in play, reintroduce the extended reals.) So the demands of any moral system as applied to a rational agent faced with a choice can be captured. If we have a very clearly defined system S that says something like "X is permissible iff ...", then utility functions can be sorted into a blocks: the u's consistent with S in one, and the u's inconsistent with S in another. More generally, one can define subsets of utility functions consistent with a moral theory. Better yet, we may introduce fuzziness by probabilizing relationships like "u conforms to the principles of free expression", though as far as I can tell uncertainty with regards to conformity with principle may be subsumed in one's utility function. (One may still want to do this for judging other utility functions.)
Cool. So non-realists can even talk about conformity to abstract principles in a principled way without making charges of irrationality concerning preferences. So how does moral argument look? As factual information is introduced, the restrictions on utility functions which do not commit `horrendous' decisions are increased. So a Bayesian who wants to murder for fun could not ascribe a high value to life, or to non-violence, or to the autonomy of humans, or to the prevention of suffering, or...
He may remain perfectly consistent in adopting such a function. But such functions are very rare. Moral argument works so long as we expect humans to have common concerns and interests. There are limits, but it can be done. Further, I think we can expect a non-realist approach to be just as convincing to those who actually do want to murder for fun as a realist approach.
Which is not very. All the realist gains is the satisfaction of calling such a person irrational, instead of a monster or thug or authoritarian.
Chomsky often invokes `elementary principles', like avoidance of hypocrisy, when beginning a speech. He invokes international law and other `moral truisms'. And yet he doesn't strike me as a realist, and if he were to simply demonstrate that US foreign policy and its media defense is hypocritical, I do not think it would be necessary for him to say "and hypocrisy is something we should be avoid." Do we need to insist on truth-values for statements like "we should not tolerate a racist, censorious, unrepresentative, and violent state"?
Our preferences are not drawn out of a hat. Normal people can ascribe meaning to principles and commit to them. That's why moral argument works, even if irreducible `should' statements are not truth-valued.
Now for the inevitable objections. As I put it on Facebook:
People license themselves to every imaginable silliness whenever terms like `moral non-realist' or `ethical subjectivist' show up; and so I, vainly fending off frustration and fury, must patiently answer such profound arguments as "but moral non-realism means morals aren't truth-valued", "but subjective utilities are subjective", and "but people who want to murder for fun might not care about the consequences", all while having to defend newly controversial propositions like, "peoples' preferences do not tend to be randomized".Objections to non-realism, or moral skepticism (see esp. error theory), are almost always confusions. I am not a nihilist; I think we can and do make meaningful preferences. Or, as seen in the SEP article, there are noises about `presumptions against moral skepticism'. I think that my account, since it can generalize other systems, should not be victim of some prior prejudice. (And in general, I don't like noise about burdens of proof.)
So, let's talk about what subjective utility functions we would like people to have, which have nice properties, and other swell things. Or not. But don't tell me I cannot have that conversation.
What I have not been saying: I have not insisted that all reasonable people be moral non-realists. I'm just pointing out that you can do a lot with a non-realist account. I of course have problems with realist accounts, but that's a different discussion.
Saturday, August 20, 2011
Commonplaces and Comments 5
I'm working on a very long post on a topic that's sure to be of local interest. In the meantime, I've found a copy of Richard Jeffrey's Logic of Decision1, in which his generalization of Bayesian conditioning, probability kinematics, was first published. Decision theory is one of the greatest applications of Bayesian instruments, so I surprise myself in not having discussed it earlier. To motivate interest, I'll discuss what is probably the most famous decision-theoretic argument of all time, Pascal's wager.
As those familiar with the argument know, Pascal's wager is an argument for the strategy of belief in Christian theology, not an argument for its truth. Hitchens dismisses this approach as mere hucksterism, but it need not be so crude. Pascal did not require that we flick on the `believe in God' switch in our heads, nor that we attempt to fool God through insincere belief. Rather, the intended conclusion of the argument is this: that one should by the best strategy available attempt to arrive at sincere Christian belief.
Pascal's argument is often presented using a decision-matrix (see the previous link). If we accept his options - Christianity or atheism - as being exhaustive, the payoff of correctly wagering on Christianity (infinite) is greater than the payoff of correctly wagering against it (finite), just as it is greater than the payoff of incorrect wagers with respect to Christianity (finite). If we denote the payoff of wagering correctly on atheism by x and wagering correctly on Christianity by y, the expected utility of wagering on Christianity is
prob(Christianity)*y+prob(Atheism)*x. So as long as the probability of Christianity is greater than zero, the payoff is infinite. Similarly, wagering against Christianity has `infinitely negative' expected utility. So even if one ascribes prob(Atheism)=1-1/[Graham's number], the infinite payoffs of correct Christian belief swamp the expected utilities.
The most common objection to Pascal's wager - which I think sound - is that the payoff matrix is not comprehensive, i.e. the argument is unsound. So long as we can imagine differing possible `infinite' payoffs against Christian belief, no best strategy follows. But there is another, more interesting objection - which I discovered via Alan Hájek - which disputes the validity of the argument, not the soundness.
To see why, recall that the intended conclusion of the argument is to convince skeptics that a strategy maximizing the likelihood of their arrival at sincere belief is the wisest strategy. Call such a strategy S, say living amongst worshippers and partaking in Christian missionary activities. Let's say the probability that adopting S results in Christian belief is 0.99. Now let's take another strategy, T, which does not likely result in Christian belief, say having a beer, where the probability of `success' is 0.0001. Check the following to your own satisfaction: the utilities of these strategies are the same. In fact, any `mixed strategy' is equally good, so long as there is a non-zero probability that Christian belief will result.
Cool. That's what happens when we play around with infinite utilities, and not just for Christian belief. This is a much more interesting and illuminating objection to Pascal's wager than dry statements about the decision-matrix. See why I think that philosophy of religion is a great `gateway drug' for the rest of philosophy? Whenever I see the Wager being discussed in the future, I'll try boring people with decision theory.
Onto The Logic of Decision, then.
Dominance is an introductory topic in The Logic of Decision, like that which appears in Pascal's wager. His more secular example is that of nuclear disarmament (p8). Consider the general 2x2 decision array:
Let the first column correspond to an outbreak of war, and the second to the maintenance of peace. Similarly, let the first row correspond to the outcome of nuclear armament in the first column and disarmament in the second. Then d1 is the utility of nuclear weapons in the event of war, d2 is the utility of nuclear weapons in times of peace, e1 is the utility of disarmament in times of war, and e2 is the utility of disarmament in times of peace.
To illustrate, let's suppose that these utilities correspond to a naively pacifistic outlook (p2):
.
As Jeffrey notes, disarmament is a very complicated example, but proponents may argue that the values of the utilities are unimportant, so long as e1>d1 and e2>d2. Given the matrix, this condition does not appear to be overly controversial.2
Yet the argument is fallacious, and not because any utility in question purports to be infinite.
Where the `superdominance' of Pascal's decision-matrix allowed for virtually any strategy to be of equal merit, the `dominance' of this decision matrix excludes certain strategies but not all mixed strategies. As Jeffrey elaborates, deterrence is a sound counter-example to the argument:
And for that, dear reader, you'll have to wait. There are too many goodies in this book to cram into a single blog post. :D
1. Richard C. Jeffrey. The Logic of Decision (2nd Edition). UC Press: Chicago, 1983.
2. This is how I have often argued in the past, inspired by such beautiful entreaties as the Russell-Einstein Manifesto. Of course, the REM is not simply an argument for nuclear disarmament, but for the abolition of war. As the decision matrix does not account for, the likely event that disarmed countries will manufacture weapons means that in all probability, disarmament is only useful for the temporary reduction of tensions and the avoidance of horrible accidents. So though I nevertheless support it, it is not with a `golden age' in view.
As those familiar with the argument know, Pascal's wager is an argument for the strategy of belief in Christian theology, not an argument for its truth. Hitchens dismisses this approach as mere hucksterism, but it need not be so crude. Pascal did not require that we flick on the `believe in God' switch in our heads, nor that we attempt to fool God through insincere belief. Rather, the intended conclusion of the argument is this: that one should by the best strategy available attempt to arrive at sincere Christian belief.
Pascal's argument is often presented using a decision-matrix (see the previous link). If we accept his options - Christianity or atheism - as being exhaustive, the payoff of correctly wagering on Christianity (infinite) is greater than the payoff of correctly wagering against it (finite), just as it is greater than the payoff of incorrect wagers with respect to Christianity (finite). If we denote the payoff of wagering correctly on atheism by x and wagering correctly on Christianity by y, the expected utility of wagering on Christianity is
prob(Christianity)*y+prob(Atheism)*x. So as long as the probability of Christianity is greater than zero, the payoff is infinite. Similarly, wagering against Christianity has `infinitely negative' expected utility. So even if one ascribes prob(Atheism)=1-1/[Graham's number], the infinite payoffs of correct Christian belief swamp the expected utilities.
The most common objection to Pascal's wager - which I think sound - is that the payoff matrix is not comprehensive, i.e. the argument is unsound. So long as we can imagine differing possible `infinite' payoffs against Christian belief, no best strategy follows. But there is another, more interesting objection - which I discovered via Alan Hájek - which disputes the validity of the argument, not the soundness.
To see why, recall that the intended conclusion of the argument is to convince skeptics that a strategy maximizing the likelihood of their arrival at sincere belief is the wisest strategy. Call such a strategy S, say living amongst worshippers and partaking in Christian missionary activities. Let's say the probability that adopting S results in Christian belief is 0.99. Now let's take another strategy, T, which does not likely result in Christian belief, say having a beer, where the probability of `success' is 0.0001. Check the following to your own satisfaction: the utilities of these strategies are the same. In fact, any `mixed strategy' is equally good, so long as there is a non-zero probability that Christian belief will result.
Cool. That's what happens when we play around with infinite utilities, and not just for Christian belief. This is a much more interesting and illuminating objection to Pascal's wager than dry statements about the decision-matrix. See why I think that philosophy of religion is a great `gateway drug' for the rest of philosophy? Whenever I see the Wager being discussed in the future, I'll try boring people with decision theory.
Onto The Logic of Decision, then.
Dominance and Disarmament
Dominance is an introductory topic in The Logic of Decision, like that which appears in Pascal's wager. His more secular example is that of nuclear disarmament (p8). Consider the general 2x2 decision array:
Let the first column correspond to an outbreak of war, and the second to the maintenance of peace. Similarly, let the first row correspond to the outcome of nuclear armament in the first column and disarmament in the second. Then d1 is the utility of nuclear weapons in the event of war, d2 is the utility of nuclear weapons in times of peace, e1 is the utility of disarmament in times of war, and e2 is the utility of disarmament in times of peace.
To illustrate, let's suppose that these utilities correspond to a naively pacifistic outlook (p2):
.As Jeffrey notes, disarmament is a very complicated example, but proponents may argue that the values of the utilities are unimportant, so long as e1>d1 and e2>d2. Given the matrix, this condition does not appear to be overly controversial.2
Yet the argument is fallacious, and not because any utility in question purports to be infinite.
Where the `superdominance' of Pascal's decision-matrix allowed for virtually any strategy to be of equal merit, the `dominance' of this decision matrix excludes certain strategies but not all mixed strategies. As Jeffrey elaborates, deterrence is a sound counter-example to the argument:
The assumption that the dominant act is the better is correct if an extra premise is introduced, i.e., that the probabilities of the conditions are the same, no matter which act is performed. [Emphasis in original] (p9)A disarmament advocate could preserve the validity of the argument by conceding that the deterrence strategy reduces the probability of war, but that this benefit is countered by the increased probability of accidental war (p10). But the need for that additional premise remains. In general, what is needed for the argument for disarmament and other arguments is a decision-theoretic framework which allows for the effects of the strategies themselves on the probabilities of the outcomes.
And for that, dear reader, you'll have to wait. There are too many goodies in this book to cram into a single blog post. :D
1. Richard C. Jeffrey. The Logic of Decision (2nd Edition). UC Press: Chicago, 1983.
2. This is how I have often argued in the past, inspired by such beautiful entreaties as the Russell-Einstein Manifesto. Of course, the REM is not simply an argument for nuclear disarmament, but for the abolition of war. As the decision matrix does not account for, the likely event that disarmed countries will manufacture weapons means that in all probability, disarmament is only useful for the temporary reduction of tensions and the avoidance of horrible accidents. So though I nevertheless support it, it is not with a `golden age' in view.
Sunday, August 7, 2011
Trying to formalize the OTF
Via Victor Reppert, I came across another atheistic critique of the OTF by Thrasymachus. Inspired by its superior clarity, I have decided to further clarify my previous objections. Thrasymachus is also replying to a previous reply by Loftus which is better suited to my purposes than his other writings.
Thrasymachus focuses on the OTF as premised by Loftus in this post:
1. Rational people in distinct geographical locations around the globe overwhelmingly adopt and defend a wide diversity of religious faiths due to their upbringing and cultural heritage. This is the religious diversity thesis.
2. Consequently, it seems very likely that adopting one’s religious faith is not merely a matter of independent rational judgment but is causally dependent on cultural conditions to an overwhelming degree. This is the religious dependency thesis.
3. Hence the odds are highly likely that any given adopted religious faith is false.
4. So the best way to test one’s adopted religious faith is from the perspective of an outsider with the same level of skepticism used to evaluate other religious faiths. This ex-presses the OTF.
Loftus uses the phrase "the odds are highly likely" in response to the observation that a deductive equivalent of the above is invalid. But as Thrasymachus points out, it still is not clear that (3) follows from (1)/(2).
First, let me clear some fumes: I am assuming that everyone involved agrees that certainty in religious beliefs is unwarranted. I am also assuming that after this is recognized, the religious beliefs in question can be probabilized. This is not always obvious: some claims are not obviously susceptible to forceful probabilities. The doctrine of the Trinity, for example, has other conceptual issues to clear up before this may be done. Instead of throwing up our hands, we can focus on the subset of putative truths essential to Christianity (C) which can be probabilized, e.g. the Resurrection. It is the probability of these claims in conjunction that is represented by prob(C).
Second, (1) assumes that differing religious people are or can be rational, at least in the sense that their beliefs are internally consistent. Else, we have no need of the OTF, as incoherency arguments would more than suffice.
Now we can see what would be required for (3) to follow from (1) and (2). I will set as a threshold that (3)/(4) translate as requiring, at a minimum, that Christianity is not more likely to be true than not, i.e. 0.5>p(C). Denote the religious diversity thesis by Div, the religious dependency thesis by Dep, and p the prior probability of some unspecified Christian.1 The odds form of Bayes' Theorem is as follows:
.
To get (3)/(4) as I interpret them, we need
.
In order for this to be the case, we need to know three different quantities. p(C)=1-p(~C), p(Div & Dep|C), and p(Div & Dep|~C). All we can say about p(C) is that it is greater than 1/2, as we are talking about a believer's prior. So we need something at least as strong as p(Div & Dep|~C)>p(Div & Dep|C). But as I pointed out in a previous post, not even this inequality must hold.
And so we come to the reason why I did not attempt to formalize the OTF much earlier: it simply isn't a probabilistic inference; it is a demand about priors. I think this is why Loftus has yet to put an argument about probabilities in terms of formal probabilities, as far as I can find. This is not a case of updating a prior set of rational beliefs to a new probability by reasoned argument. Instead, it is an attempt to force a reworking of priors based on evidence.2 Again, I do not see why Christians need to accept this; intellectual consistency only requires that they account for Div and Dep by calculating their effects on their beliefs through conditioning.
Here we depart from the most accepted form of Bayesianism, i.e. subjective Bayesianism, entirely. We are encountering a curious version of objective Bayesianism. `Normal' objective Bayesians calculate `informationless' priors by equivocating across possibilities. What Loftus appears to want, as I noted in my previous posts, is that we gauge p(C) in something like the following way:
a. p(C)=1/N where N is the number of possible, mutually contradictory religions.
b. p(C)=1/N where N is the number of mutually contradictory religions in human history.
c. p(C)=1/N where N is the number of existing, mutually contradictory religions.
[Each of the above has an analogue where `religions' is replaced by `Christian sects'.]
d. p(C)=x where x is the frequency of the occurrence of Christians with respect to the general population. (Of the country, or world, or something.)
e. p(C)=A/B where B is the number of rational people and A is the number of rational people who are Christians.
And so on. Before moving on, the first response our Christian might deploy to any combination of the above is a simple one: No.
He is presumed to be rational and he can account for (1)/(2) in the usual way. Sorry to wax tautological, but he simply cannot be convicted of irrationality or unreasonableness whenever he is being both rational and reasonable, as judged by standard philosophical criteria. To go further with this, Loftus will have to mount a convincing attack on Bayesianism itself.
And of course we run into the earlier problem yet again; the argument Loftus presents cannot be probabilized. None of the above statements follows, or can follow, deductively or probabilistically, from (1)/(2).
I could continue on about the other problems, especially as they pertain to Loftus' desire to demand priors about religion but not about secular claims, or that this approach would most likely result in a weaker case against Christianity than the traditional arguments, but I've said this already, and Thrasymachus has done a better job explicating it. I could repeat why `skepticism' is not a sort of default, and that positive claims will be necessary to argue against Christianity. (Otherwise, it's the fallacy of probabilistic Modus Tollens all the way down.) Or, I could reiterate some of Reppert's objections; for example, (1) and (2) are not so undeniably true as Loftus suggests, and Christians may account for differing religions using faith-based claims. The Pharaoh's magicians did not perform wonders so great as Aaron's, but they still made a snake out of a staff. Also, demons and sinful nature.
I pause. Is the argument really this straightforwardly awful? How does Loftus defend it?
What else can I say? Nothing about this argument works, nor could it conceivably be reworked to capture what Loftus wants. There's a reason for this: it isn't actually an argument. It is a symptom of Loftus' assumption that he objectively and most accurately views the world in a culture-transcendent way.
I might have spoken too soon: if a Christian happens to trust Loftus more than God, there may be an opening for the OTF.
One last quibble to anticipate an objection: Loftus may claim that he is not addressing Calvinists, only evangelical Christians. That doesn't change the fact that his argument is not even an argument of that form. For this discrepancy to matter, he must restate his argument so as to account for variations in prior probability and variations in the Bayes factor specific to the religion in which he is interested. That is, he must pursue normal argumentation.
If he does so, I'll be more than happy.
1. It has to be this way, as we are interested in whether or not warrant for religion can be retained, not just how a skeptic feels about religion.
2. This is much weirder than anything attempted by normal objective Bayesians. I do not know of any accepted precedent for an approach like this.
Edit 8/8/11: I've been having a blast with acronyms lately. Please plagiarize the hell out of this excerpt from a comment at Reppert's place:
Thrasymachus focuses on the OTF as premised by Loftus in this post:
1. Rational people in distinct geographical locations around the globe overwhelmingly adopt and defend a wide diversity of religious faiths due to their upbringing and cultural heritage. This is the religious diversity thesis.
2. Consequently, it seems very likely that adopting one’s religious faith is not merely a matter of independent rational judgment but is causally dependent on cultural conditions to an overwhelming degree. This is the religious dependency thesis.
3. Hence the odds are highly likely that any given adopted religious faith is false.
4. So the best way to test one’s adopted religious faith is from the perspective of an outsider with the same level of skepticism used to evaluate other religious faiths. This ex-presses the OTF.
Loftus uses the phrase "the odds are highly likely" in response to the observation that a deductive equivalent of the above is invalid. But as Thrasymachus points out, it still is not clear that (3) follows from (1)/(2).
First, let me clear some fumes: I am assuming that everyone involved agrees that certainty in religious beliefs is unwarranted. I am also assuming that after this is recognized, the religious beliefs in question can be probabilized. This is not always obvious: some claims are not obviously susceptible to forceful probabilities. The doctrine of the Trinity, for example, has other conceptual issues to clear up before this may be done. Instead of throwing up our hands, we can focus on the subset of putative truths essential to Christianity (C) which can be probabilized, e.g. the Resurrection. It is the probability of these claims in conjunction that is represented by prob(C).
Second, (1) assumes that differing religious people are or can be rational, at least in the sense that their beliefs are internally consistent. Else, we have no need of the OTF, as incoherency arguments would more than suffice.
Now we can see what would be required for (3) to follow from (1) and (2). I will set as a threshold that (3)/(4) translate as requiring, at a minimum, that Christianity is not more likely to be true than not, i.e. 0.5>p(C). Denote the religious diversity thesis by Div, the religious dependency thesis by Dep, and p the prior probability of some unspecified Christian.1 The odds form of Bayes' Theorem is as follows:
.To get (3)/(4) as I interpret them, we need
.In order for this to be the case, we need to know three different quantities. p(C)=1-p(~C), p(Div & Dep|C), and p(Div & Dep|~C). All we can say about p(C) is that it is greater than 1/2, as we are talking about a believer's prior. So we need something at least as strong as p(Div & Dep|~C)>p(Div & Dep|C). But as I pointed out in a previous post, not even this inequality must hold.
At the end of my last post, I asked a question: what would Calvin think of the OTF? It wasn't an idle question. If you are a Christian who believes in the predestination of the Elect and the Fallen world, the fact that your religion is one amongst many is not a surprise. That few have the right faith may not bother you at all. As far as I am aware, nothing about your religion says that it should not appear to an outsider as one among many. Strange then that advocates of the OTF tell you that the existence of other religions discredits your religion. You can reasonably say, "my religion looks like one of many to you? Swell, your point being? We agree about this, and it bothers me not. For chances are that you are not one of the Elect and are not destined for Salvation and understanding. That you and others do not believe as I do does not surprise me in the least; if anything, I would be surprised if outsiders readily understood the Truth and could easily aspire to it, as I understand otherwise."But it gets worse: even in the cases where the requisite inequality does hold, it may not be large enough to require our believer to make further arguments so as to defend his faith. This is because we still need to know what values of p(C) are warranted. Sure, it's less than 1, but is it less than 0.999 or 0.8?
One can argue against such a person, but the appearance of his beliefs to a skeptic should not itself constitute an argument.
The case is different whenever we look at more common evangelical versions of Christianity, in which it is asserted that God intervenes or has intervened to aid Christianity and that the Holy Spirit works on the consciences of most or all to guide them to Truth. Free will. All that jazz. If a supernatural agency is at work in the Christian sociology of Christianity, then it is surprisingly hidden in the actual sociological details concerning Christianity. Here, the fact that Christian belief is largely a function of geography and parenting is very surprising. To a person who thinks that Christianity is a natural phenomenon, it should not be. I think that this is a very powerful argument against evangelical Christianity.
Notice then that there are at least two possible outcomes of "Christianity is like other religions to an outsider": it is irrelevant to some Christians, and it constitutes a challenging argument to others. So what we can not do is treat the motivations for the OTF as legitimizing it against religions generally, since the observations motivating the OTF are in no way an argument against certain religions. To pretend otherwise is to do nothing more than pomo an important, but narrow, point.
And so we come to the reason why I did not attempt to formalize the OTF much earlier: it simply isn't a probabilistic inference; it is a demand about priors. I think this is why Loftus has yet to put an argument about probabilities in terms of formal probabilities, as far as I can find. This is not a case of updating a prior set of rational beliefs to a new probability by reasoned argument. Instead, it is an attempt to force a reworking of priors based on evidence.2 Again, I do not see why Christians need to accept this; intellectual consistency only requires that they account for Div and Dep by calculating their effects on their beliefs through conditioning.
Here we depart from the most accepted form of Bayesianism, i.e. subjective Bayesianism, entirely. We are encountering a curious version of objective Bayesianism. `Normal' objective Bayesians calculate `informationless' priors by equivocating across possibilities. What Loftus appears to want, as I noted in my previous posts, is that we gauge p(C) in something like the following way:
a. p(C)=1/N where N is the number of possible, mutually contradictory religions.
b. p(C)=1/N where N is the number of mutually contradictory religions in human history.
c. p(C)=1/N where N is the number of existing, mutually contradictory religions.
[Each of the above has an analogue where `religions' is replaced by `Christian sects'.]
d. p(C)=x where x is the frequency of the occurrence of Christians with respect to the general population. (Of the country, or world, or something.)
e. p(C)=A/B where B is the number of rational people and A is the number of rational people who are Christians.
And so on. Before moving on, the first response our Christian might deploy to any combination of the above is a simple one: No.
He is presumed to be rational and he can account for (1)/(2) in the usual way. Sorry to wax tautological, but he simply cannot be convicted of irrationality or unreasonableness whenever he is being both rational and reasonable, as judged by standard philosophical criteria. To go further with this, Loftus will have to mount a convincing attack on Bayesianism itself.
And of course we run into the earlier problem yet again; the argument Loftus presents cannot be probabilized. None of the above statements follows, or can follow, deductively or probabilistically, from (1)/(2).
I could continue on about the other problems, especially as they pertain to Loftus' desire to demand priors about religion but not about secular claims, or that this approach would most likely result in a weaker case against Christianity than the traditional arguments, but I've said this already, and Thrasymachus has done a better job explicating it. I could repeat why `skepticism' is not a sort of default, and that positive claims will be necessary to argue against Christianity. (Otherwise, it's the fallacy of probabilistic Modus Tollens all the way down.) Or, I could reiterate some of Reppert's objections; for example, (1) and (2) are not so undeniably true as Loftus suggests, and Christians may account for differing religions using faith-based claims. The Pharaoh's magicians did not perform wonders so great as Aaron's, but they still made a snake out of a staff. Also, demons and sinful nature.
I pause. Is the argument really this straightforwardly awful? How does Loftus defend it?
One...option for the Christian might be to argue that I have not shown there is a direct causal relationship between RDPT (i.e. the Religious Dependency Thesis) (or 1) and the RDVT (i.e., the Religious Diversity Thesis) (or 2). Just because there is religious diversity doesn’t mean that religious views are overwhelmingly dependent on social and geographical factors, they might argue. Reminiscent of David Hume, who argued that we do not see cause and effect, they might try to argue I have not shown it exists between the RDPT and the RDVT. After all, if Hume can say he never sees one billiard ball “causing” another one to move just because they do so after making contact, then maybe there is no direct causal relationship between the RDPT and the RDVT. Is it possible, they might ask, that just because people have different religious faiths which are separated into distinct geographical locations on our planet, that “when and where” people are born has little to do with what they believe? My answer is that if this is possible, it is an exceedingly small possibility. Do Christians really want to hang their faith on such a slender reed as this? I’ve shown from sociological, geographical and psychological studies that what we believe is strongly influenced by “the accidents of history.” That’s all anyone can ask me to show.Actually, we can ask for a valid argument. This is simply a genetic fallacy. The deductive genetic fallacy remains a fallacy, even if you argue for odds instead of certainties.
What else can I say? Nothing about this argument works, nor could it conceivably be reworked to capture what Loftus wants. There's a reason for this: it isn't actually an argument. It is a symptom of Loftus' assumption that he objectively and most accurately views the world in a culture-transcendent way.
I might have spoken too soon: if a Christian happens to trust Loftus more than God, there may be an opening for the OTF.
One last quibble to anticipate an objection: Loftus may claim that he is not addressing Calvinists, only evangelical Christians. That doesn't change the fact that his argument is not even an argument of that form. For this discrepancy to matter, he must restate his argument so as to account for variations in prior probability and variations in the Bayes factor specific to the religion in which he is interested. That is, he must pursue normal argumentation.
If he does so, I'll be more than happy.
1. It has to be this way, as we are interested in whether or not warrant for religion can be retained, not just how a skeptic feels about religion.
2. This is much weirder than anything attempted by normal objective Bayesians. I do not know of any accepted precedent for an approach like this.
Edit 8/8/11: I've been having a blast with acronyms lately. Please plagiarize the hell out of this excerpt from a comment at Reppert's place:
I should mention that I've seen John's post that he's on a blogging break, so I do not expect any response soon.
To be honest, I don't expect a serious response. Here's what he said to Thrasymachus' post back in January:
"I see nothing here I need to respond to."
Oh, my argument is invalid, cannot be reworked to convincingly get what I want out of it, and my approach in general is a failure. Where's the problem?
Staggering. And this is followed by another unhesitant shift:
"You can insert the word “skeptical” for “outsider” if you wish. And being skeptical means doubting or rejecting anything that the sciences say otherwise."
And we return to the uniqueness problems and question-begging again...
So I'll have fun at his expense until he or others get back to me with a real argument. A satisfactory response will do the following things:
1. Restatement: the precise structure and intended conclusion(s) of the OTF must be clearly stated, along with any contested background assumptions.
2. Support: The structure and conclusions of the argument must be corroborated. Is it deductive? If so, state exactly where and why. Is it a probabilistic argument? Then capture the argument using the formal tools of probabilism and defend it. Is it an argument about prior distributions? Then state clearly why it is that a coherent agent must adopt, prior to evidence, a specific distribution based on an observation which can already accounted for by a religious person or may be calibrated in a traditional, probabilistic manner (conditionalization).
3. Comprehensiveness: Clearly state outstanding objections and why they fail or are otherwise innocuous.
I call it the Simple Test For Understanding, or STFU, because proponents of the OTF should STFU already or move on.
Friday, August 5, 2011
Hume and the confirmability of miracles
While discussing the McGrews' Bayesian analysis of the Resurrection (CCRJ), I frequently mentioned that the McGrews and myself were not attempting to derive odds on the Resurrection. Rather, we were focusing on the Bayes factor - aka the likelihood ratio - which if you recall, is the number by which the prior odds ratio p(`thing')/p(`other thing') is multiplied to yield the posterior odds ratio q(`thing')/q(`other thing'). So at the very minimum, one needs to estimate what the prior odds should be in order to derive the final odds. Since neither of our approaches were sufficiently general to capture a truly cumulative Bayes factor, even this may be inadequate, but since the factor I derived - 106 - was calibrated given generous textual assumptions in favor of the Resurrection, we may be able to tentatively estimate an upper bound on reasonable posterior odds using that factor if we have an upper bound on reasonable priors. If that upper bound is less than 10-6, we may conclude that the Resurrection probably did not occur, i.e. 0.5>q(R).
I opine that barring other arguments in the context of a natural theology, such an upper bound exists. That is, the Resurrection can not reasonably be confirmed from the textual record alone with respect to convincing background knowledge which is shared by skeptics and Christians alike. But I am interested in Hume's more general thesis, which is that miracles by their nature can not reasonably be confirmed. The details of an analysis of the Resurrection are merely an instance of a more general unconfirmability argument.
I pause to obviate a potential objection: I am fully aware that the proper interpretation of Hume's Enquiry concerning Human Understanding, especially Of Miracles, is a hotly disputed topic. I am attributing an unconfirmability argument to Hume; I doubt he can be convincingly interpreted as not making such an argument. But I am not here interested in any historical exoneration or conviction of Hume of philosophical crimes. Rather, I want to work with his apparent argument by recasting it in formal terms, propose that it is inadequate, and attempt to shape a more satisfactory unconfirmability argument.
I am neither discussing nor proposing a definition-dependent impossibility argument, e.g., "A miracle is the violation of mathematical, divine, immutable, eternal laws. By the very exposition itself, a miracle is a contradiction in terms: a law cannot at the same time be immutable and violated." Rather, I am interested in miracles loosely defined as particular exceptions to otherwise exceptionless laws or regularities of nature. In this context, the regularities of importance are putative laws, and their importance is epistemic, not ontological. Whether or not a putative law is true is largely irrelevant: what matters is how well-supported it is.
The proper definition of a miracle is also in dispute. As regards this item, I follow Tim and Lydia McGrew in treating the Resurrection as a paradigm (CCRJ, p.4). As I will explain in the course of this discussion, working with paradigm cases like the Resurrection is all that should be required. Failures of consensus on miracles are relevant to Hume's argument, but they will not prove necessary to reject his conclusion. Which is roughly as follows:
Hume's Argument: There cannot exist evidence E for a miracle M such that
.
With conditionalization, this is equivalent to stating that the posterior odds on a miracle can never be greater than 1/2.1
The initial prospects of this statement are rather dim. As is commonly pointed out, there are no a priori boundaries on the size of Bayes factors: no matter how small the prior odds on a miracle, there exist finite Bayes factors which can overcome them. Similarly, disputes concerning the definition of a miracle make it impossible to have confidence in such a general statement.
I would also add that we should not be overly interested in such an argument as employed to justify ignoring any potential evidence for miracles. The debate is worthwhile. As I have noted in a slightly different context:
I will not second another common objection: I do not think that Hume's argument, interpreted as I have interpreted it, would destroy the possibility of overturning laws in science. His "straight rule of induction" is problematic in this context (Earman, pp.31-2), but laws are not to my knowledge overturned in the way that a putative miracle claim would overturn them.
Take the Conservation of Mass. Did measurements of nuclear reactions overturn a uniform experience? No, because what changed was not the article where uniform experience applied, but where a novelty was being analyzed. If for example I react 50 grams of sodium with 70 grams of chlorine gas to form salt (NaCl) at approximately standard temperature and pressure and measure a net change in mass of 20 grams, I or my instruments screwed up. Mass is still conserved within significant margins of instrumental error for `ordinary' chemical reactions. The implications of such experience have not been contradicted, but superseded. With miracles, where the putative law needs to otherwise be intact for theological reasons, no such consideration applies. We are not talking supercessions or the overturning of laws as done in the sciences; we are talking about flat-out, singular violations of an otherwise sound natural order. We are talking about an experiment incapable of replication. Were mass conservation to always hold, and the only exception were to occur in one apparently sound experiment, we should have discounted the experiment as flawed if replication failed.
I judge Hume's argument to be a failure and its conclusion to be unsound. But this need not be the end of the story. We may yet build a better monument by clearing away the noisy rubble of Hume's rhetoric and picking out the useful pieces. That will be the subject of my next post.
1. This interpretation, though disputed, has a lot of support, perhaps apart from the target threshold 0.5>q(M). Were Hume making an impossibility argument, it is odd that he should emphasize the relative strength of evidences (p.169) and the uncertainty of the relevant propositions (pp.169-70); that he discusses evidence at all would also be strange. In addition to his use of probabilistic terminology, he also casts his argument in terms of degrees-of-confidence: "Some events are found, in all countries and all ages, to have been constantly conjoined together: Others are found to have been more variable, and sometimes to disappoint our expectations; so that, in our reasonings concerning matter of fact, there are all imaginable degrees of assurance, from the highest certainty to the lowest species of moral evidence." And he continues famously: "A wise man, therefore, proportions his belief to the evidence. In such conclusions as are founded on an infallible experience, he expects the event with the last degree of assurance, and regards his past experience as a full proof of the future existence of that event" (p.170).
With terms like `infallible' and `proof' in play, I think that Hume may be interpreted as arguing for a prior probability of zero for miracles, or perhaps an infinitesimal probability (p.171). But I do not think that such a prior is convincing to all - or many - concerned, and it is therefore useless. Many Bayesians accept - here the terminology is unfortunate - the principle of regularity, which states that all possibilities have probability greater than 0, assuming that those possibilities are uncertain and assigned any probability whatever. In any case, we are presumably inviting Christians to the discussion, so we must at least assume that non-zero priors are in play.
There are other ambiguities, and I am lead to second Earman's hostile conclusion (p.20):
I opine that barring other arguments in the context of a natural theology, such an upper bound exists. That is, the Resurrection can not reasonably be confirmed from the textual record alone with respect to convincing background knowledge which is shared by skeptics and Christians alike. But I am interested in Hume's more general thesis, which is that miracles by their nature can not reasonably be confirmed. The details of an analysis of the Resurrection are merely an instance of a more general unconfirmability argument.
I pause to obviate a potential objection: I am fully aware that the proper interpretation of Hume's Enquiry concerning Human Understanding, especially Of Miracles, is a hotly disputed topic. I am attributing an unconfirmability argument to Hume; I doubt he can be convincingly interpreted as not making such an argument. But I am not here interested in any historical exoneration or conviction of Hume of philosophical crimes. Rather, I want to work with his apparent argument by recasting it in formal terms, propose that it is inadequate, and attempt to shape a more satisfactory unconfirmability argument.
I am neither discussing nor proposing a definition-dependent impossibility argument, e.g., "A miracle is the violation of mathematical, divine, immutable, eternal laws. By the very exposition itself, a miracle is a contradiction in terms: a law cannot at the same time be immutable and violated." Rather, I am interested in miracles loosely defined as particular exceptions to otherwise exceptionless laws or regularities of nature. In this context, the regularities of importance are putative laws, and their importance is epistemic, not ontological. Whether or not a putative law is true is largely irrelevant: what matters is how well-supported it is.
The proper definition of a miracle is also in dispute. As regards this item, I follow Tim and Lydia McGrew in treating the Resurrection as a paradigm (CCRJ, p.4). As I will explain in the course of this discussion, working with paradigm cases like the Resurrection is all that should be required. Failures of consensus on miracles are relevant to Hume's argument, but they will not prove necessary to reject his conclusion. Which is roughly as follows:
Hume's Argument: There cannot exist evidence E for a miracle M such that
.With conditionalization, this is equivalent to stating that the posterior odds on a miracle can never be greater than 1/2.1
The initial prospects of this statement are rather dim. As is commonly pointed out, there are no a priori boundaries on the size of Bayes factors: no matter how small the prior odds on a miracle, there exist finite Bayes factors which can overcome them. Similarly, disputes concerning the definition of a miracle make it impossible to have confidence in such a general statement.
I would also add that we should not be overly interested in such an argument as employed to justify ignoring any potential evidence for miracles. The debate is worthwhile. As I have noted in a slightly different context:
It is very often said, by e.g. PZ Myers and Massimo Pigliucci, that one cannot evidence Christianity or gods because they are not coherent hypotheses. More needs to be said about this, but I would at least suggest the following: if the evidence for the Resurrection really is extremely convincing to reasonable people on the assumption of coherency, we should take an attitude similar to that which I think we take to science: some conceptual fuzziness is to be tolerated, barring flat contradiction, where overwhelming evidence for an aspect of a theory is available. Were I to find the evidence for the Resurrection convincing, I know I would be working very diligently to craft a coherent Christian philosophy to accommodate it. So to me, the coherency difficulty is in many ways secondary, unless that difficulty is so severe that one cannot even begin to discuss relevant evidence. I think we usually manage to do so. Wouldn't you agree?The argument also conflicts with the empirical, tentative nature of skeptical inquiry. I think we should wish to avoid such categorical statements.
The temptation to fashion such an argument is understandable. But it should be resisted. Any epistemology that does not allow for the possibility that evidence, whether from eyewitness testimony or from some other source, can establish the credibility of a UFO landing, a walking on water, or a resurrection is inadequate. (Earman, p.4)As Earman also notes, there are events which, were they to occur, surely amount to convincing evidence for a miracle claim:
Suppose, for the sake of illustration, that there is a well developed theology based on the existence of a god called Emuh. who promises an afterlife in return for certain religious observances in this life. Suppose that this theology predicts that on such-and-such a day Emuh will send a sign in the sky. And suppose that on the appointed day, the clouds over America clearly spell out in English the words “Believe in Emuh and you will have everlasting life,” while the same message is spelled out in French over France, in Deutsch over Germany, etc. Then even though these cloud formations may not contravene any of the general principles taken at the time in question to be laws of nature and, indeed, may be explicable in terms of those principles, it would not be untoward to take these extraordinary occurrences to be support for Emuh theology. (p.11)So Hume's argument, were it valid and coherent, would prove too much. It also ignores the effect of evidence for a theology and its implications for the proposed miracle claim. Were the gloating fiction of LaHaye's Left Behind series to be actualized, it would confirm the Resurrection. I am unsure as to how or why someone would seriously argue otherwise, even if the various details of Christian theology are unclear.
I will not second another common objection: I do not think that Hume's argument, interpreted as I have interpreted it, would destroy the possibility of overturning laws in science. His "straight rule of induction" is problematic in this context (Earman, pp.31-2), but laws are not to my knowledge overturned in the way that a putative miracle claim would overturn them.
Take the Conservation of Mass. Did measurements of nuclear reactions overturn a uniform experience? No, because what changed was not the article where uniform experience applied, but where a novelty was being analyzed. If for example I react 50 grams of sodium with 70 grams of chlorine gas to form salt (NaCl) at approximately standard temperature and pressure and measure a net change in mass of 20 grams, I or my instruments screwed up. Mass is still conserved within significant margins of instrumental error for `ordinary' chemical reactions. The implications of such experience have not been contradicted, but superseded. With miracles, where the putative law needs to otherwise be intact for theological reasons, no such consideration applies. We are not talking supercessions or the overturning of laws as done in the sciences; we are talking about flat-out, singular violations of an otherwise sound natural order. We are talking about an experiment incapable of replication. Were mass conservation to always hold, and the only exception were to occur in one apparently sound experiment, we should have discounted the experiment as flawed if replication failed.
I judge Hume's argument to be a failure and its conclusion to be unsound. But this need not be the end of the story. We may yet build a better monument by clearing away the noisy rubble of Hume's rhetoric and picking out the useful pieces. That will be the subject of my next post.
1. This interpretation, though disputed, has a lot of support, perhaps apart from the target threshold 0.5>q(M). Were Hume making an impossibility argument, it is odd that he should emphasize the relative strength of evidences (p.169) and the uncertainty of the relevant propositions (pp.169-70); that he discusses evidence at all would also be strange. In addition to his use of probabilistic terminology, he also casts his argument in terms of degrees-of-confidence: "Some events are found, in all countries and all ages, to have been constantly conjoined together: Others are found to have been more variable, and sometimes to disappoint our expectations; so that, in our reasonings concerning matter of fact, there are all imaginable degrees of assurance, from the highest certainty to the lowest species of moral evidence." And he continues famously: "A wise man, therefore, proportions his belief to the evidence. In such conclusions as are founded on an infallible experience, he expects the event with the last degree of assurance, and regards his past experience as a full proof of the future existence of that event" (p.170).
With terms like `infallible' and `proof' in play, I think that Hume may be interpreted as arguing for a prior probability of zero for miracles, or perhaps an infinitesimal probability (p.171). But I do not think that such a prior is convincing to all - or many - concerned, and it is therefore useless. Many Bayesians accept - here the terminology is unfortunate - the principle of regularity, which states that all possibilities have probability greater than 0, assuming that those possibilities are uncertain and assigned any probability whatever. In any case, we are presumably inviting Christians to the discussion, so we must at least assume that non-zero priors are in play.
There are other ambiguities, and I am lead to second Earman's hostile conclusion (p.20):
I defy the reader to give a short, simple, and accurate summary of the argumentation in "Of Miracles." What on first reading appears to be a seamless argument is actually a collection of considerations that sometimes mesh and sometimes don't. It will take much work to tease out the components of Hume's argument and to evaluate the soundness of individual components and the effectiveness of the entire package.Immediately after bringing up `proofs' of experience, Hume dives right back into emphasizing the fallibility of evidence, particularly witness testimony (EPHU, p.171). There are other deficiencies in his presentation. After defining miracles as putative exceptions to uniformly evidenced laws, he states the following:
There must, therefore, be a uniform experience against every miraculous event, otherwise the event would not merit that appelation. And as a uniform experience amounts to a proof, there is here a direct and full proof, from the nature of the fact, against the existence of any miracle; nor can such a proof be destroyed, or the miracle rendered credible, but by an opposite proof, which is superior. (p.173)With this stringency, the mere proposal of evidence for an event disqualifies that event's being a miracle, as experience is no longer uniformly against it. And then, the presentation of additional evidence should leave an opening. I'll stick with the Bayesian interpretation because it is the only plausible interpretation to be found.
Thursday, July 28, 2011
Resurrection round-up
Alright, I've finished my discussion of the McGrews' paper! Eight posts should be a good enough start, I hope. Anyways, start here.
As I say throughout, I think that their paper is an excellent starting point for further discussion. So I will use this post to collect future arguments about the Resurrection which fit into the discussed frameworks. I'll keep this in the sidebar. Anyways, these posts constitute 11,500 words of writing, done over the course of only a few hours (I had been sitting on these thoughts for a while). Doubtless there are errors, typographical and otherwise. If you find any, let me know.
Update (8/6/2011): Here are two posts on Hume's argument and a revision of the same.
Update (9/3/2011): I'll be regularly listing related links here.
1. Reppert on estimating priors.
As I say throughout, I think that their paper is an excellent starting point for further discussion. So I will use this post to collect future arguments about the Resurrection which fit into the discussed frameworks. I'll keep this in the sidebar. Anyways, these posts constitute 11,500 words of writing, done over the course of only a few hours (I had been sitting on these thoughts for a while). Doubtless there are errors, typographical and otherwise. If you find any, let me know.
Update (8/6/2011): Here are two posts on Hume's argument and a revision of the same.
Update (9/3/2011): I'll be regularly listing related links here.
1. Reppert on estimating priors.
Tim and Lydia McGrew on the Resurrection, part 8 (conclusion/outline)
[Continued from Part 7.]
I have tentatively argued for a Bayes factor of 106 given the textual assumptions of the McGrews. I have further proposed a way to expand the discussion to include skeptics of these assumptions. In these conclusions, I have agreed with the McGrews that their assumptions are plausible, and that on these assumptions the Resurrection is the best explanation. However, I think that they overreach when they claim, or seem to claim, that their methodology - which they agree is very partial - approximates a more general Bayes factor (p.39).
The rest of their paper (pp.46-68) discusses Hume and the objections of other apologists. As I have said, I am leaving that topic for later. Just as they have not claimed to have derived odds on the Resurrection, I do not claim to have done so either.
As I stated at the beginning, the McGrews have started an excellent conversation. I would recommend anyone who wishes to pursue a rigorous analysis of the evidence for the Resurrection to read their paper. And just as they have qualified, I must qualify that my approach has not been complete.
In particular, I have not gathered all of the relevant evidence in deriving this likelihood ratio. Many apologists insist on Paul's claim that there are 500 witnesses. Skeptics focus on potential `gaps' in the text, which become quite plausible on the (quite plausible) assumption that the relevant texts are polemical and designed to serve the Christian community. In this sense, my Bayes factor is not cumulative. My Bayes factor is also not cumulative with respect to textual criticisms. Again, I've outlined how that may be pursued. A fully rigorous analysis of all of the details will probably lead to a figure quite different from the one which I have suggested. But I think, quite plausibly, that the figure I have suggested is not a gross underestimate. And I think it quite low enough to leave anyone with a reasonable prior ratio unconvinced. If Christians think that the prior odds on the Resurrection are above something like 10-6, I hope they will tell me why this is. If they have such a value, I assume it will be within the context of a well-formed natural theology. Contrary to the McGrews (p.49), I think this will prove necessary.
So there are my efforts. I hope you will read them all before making critical comments, just as I hope you will read the McGrews' paper. If you spot a technical error or misspelling, I would of course appreciate immediate correction. Otherwise, I ask that you take time to absorb the details, and inquire for yourself how knowledge you have may further inform the discussion.
I also hope that readers can at least retrospectively appreciate the utility of Bayesian techniques in analyzing such arguments. The importance of this or that number is minimal: what is important is that they can be used to capture the arguments, show how they relate to each other, and help us to focus on the important details. They also help to understand how I, a skeptic of the Resurrection, can be quite satisfied with a statement like "the Resurrection is the best explanation of the salient facts" - a statement which is very difficult to refute, I think. Bayesian insights allow me to maintain my skepticism without undertaking hopeless endeavors, for example defending or asserting statements like "the Bible does not constitute any evidence for the Resurrection." In arguments over the Resurrection, we cannot eliminate entirely our differing private intuitions. But we can at least see what is required of those intuitions and reduce their impact when possible.
And I love this stuff for its own sake. I'm soggy like that.
Suggestions for the future: separate the witness of James the Just from that of the other apostles, subsume the testimony of the women within that of the disciples generally, and largely omit any discussion of Paul's conversion as itself evidential in favor of other details. Paul is doubtlessly important, but his importance is in his teaching and his early date. And keep it general, yo.
I have tentatively argued for a Bayes factor of 106 given the textual assumptions of the McGrews. I have further proposed a way to expand the discussion to include skeptics of these assumptions. In these conclusions, I have agreed with the McGrews that their assumptions are plausible, and that on these assumptions the Resurrection is the best explanation. However, I think that they overreach when they claim, or seem to claim, that their methodology - which they agree is very partial - approximates a more general Bayes factor (p.39).
The rest of their paper (pp.46-68) discusses Hume and the objections of other apologists. As I have said, I am leaving that topic for later. Just as they have not claimed to have derived odds on the Resurrection, I do not claim to have done so either.
As I stated at the beginning, the McGrews have started an excellent conversation. I would recommend anyone who wishes to pursue a rigorous analysis of the evidence for the Resurrection to read their paper. And just as they have qualified, I must qualify that my approach has not been complete.
In particular, I have not gathered all of the relevant evidence in deriving this likelihood ratio. Many apologists insist on Paul's claim that there are 500 witnesses. Skeptics focus on potential `gaps' in the text, which become quite plausible on the (quite plausible) assumption that the relevant texts are polemical and designed to serve the Christian community. In this sense, my Bayes factor is not cumulative. My Bayes factor is also not cumulative with respect to textual criticisms. Again, I've outlined how that may be pursued. A fully rigorous analysis of all of the details will probably lead to a figure quite different from the one which I have suggested. But I think, quite plausibly, that the figure I have suggested is not a gross underestimate. And I think it quite low enough to leave anyone with a reasonable prior ratio unconvinced. If Christians think that the prior odds on the Resurrection are above something like 10-6, I hope they will tell me why this is. If they have such a value, I assume it will be within the context of a well-formed natural theology. Contrary to the McGrews (p.49), I think this will prove necessary.
So there are my efforts. I hope you will read them all before making critical comments, just as I hope you will read the McGrews' paper. If you spot a technical error or misspelling, I would of course appreciate immediate correction. Otherwise, I ask that you take time to absorb the details, and inquire for yourself how knowledge you have may further inform the discussion.
I also hope that readers can at least retrospectively appreciate the utility of Bayesian techniques in analyzing such arguments. The importance of this or that number is minimal: what is important is that they can be used to capture the arguments, show how they relate to each other, and help us to focus on the important details. They also help to understand how I, a skeptic of the Resurrection, can be quite satisfied with a statement like "the Resurrection is the best explanation of the salient facts" - a statement which is very difficult to refute, I think. Bayesian insights allow me to maintain my skepticism without undertaking hopeless endeavors, for example defending or asserting statements like "the Bible does not constitute any evidence for the Resurrection." In arguments over the Resurrection, we cannot eliminate entirely our differing private intuitions. But we can at least see what is required of those intuitions and reduce their impact when possible.
And I love this stuff for its own sake. I'm soggy like that.
Suggestions for the future: separate the witness of James the Just from that of the other apostles, subsume the testimony of the women within that of the disciples generally, and largely omit any discussion of Paul's conversion as itself evidential in favor of other details. Paul is doubtlessly important, but his importance is in his teaching and his early date. And keep it general, yo.
Tim and Lydia McGrew on the Resurrection, part 7
[Continued from Part 6.]
Hallo and good day, weary traveler! We may now discuss in passing one final detail, i.e. the impact of the testimony of the women (W) on our final Bayes factor, which has currently been reduced from the McGrews' estimate of 1044 to 107. If I can convince you that the womens' testimony is not significant, we will arrive at a final replacement Bayes factor of 105. Then, I may finally lay my weary head to rest and fly elsewhere. Especially, I hope to soon discuss Hume's argument and attempt to estimate prior odds on the Resurrection.
I think this may be done as follows: take the alternative hypotheses to the Resurrection which I have proposed to explain the disciples' witness and subsume the womens' testimony within them. This may be done without loss of prior plausibility, especially since initial rumors already play a role. This undermines the `essential independence' of the women from the other disciples proposed by the McGrews (p.41), which I do not think defends probabilistic independence in any case. As I have discussed, the emergence of rumors would very likely have affected the reaction of the disciples. Indeed, since the witness of women would have been regarded as less credible (p.28), we may plausibly expect the disciples to have corroborated their belief - which perhaps began with the women's testimony - with witness of their own. This, I think, tentatively answers the McGrews' challenge: "why [should we not] judge p(W|R) to be at least several orders of magnitude greater than p(W|~R)?" (p.30)
To argue directly that W should have less effect than 102 on the final Bayes factor requires, I think, a questioning of the McGrews' salient facts. If we separate it out from the other details, I think that the McGrews were sufficiently generous in leaving it at 102. In assenting to this, all I am saying is the following: that the women would report an empty tomb, or seeing Jesus, had he not Resurrected has probability 0.01, assuming that they would report it had they really seen it and that the facts are as described by the McGrews. I do not think that this is too challenging an admission for a skeptic. Instead, we need not recognize this contribution as multiplicative, and regard it as diminished by other considerations.
I think this, along with any potential minor significance of Paul in light of the other reductions, can be fairly accounted for by leaving a final estimate of the Bayes factor at 106, and plausibly lower.
Now, we may finally arrive at our destination.
Hallo and good day, weary traveler! We may now discuss in passing one final detail, i.e. the impact of the testimony of the women (W) on our final Bayes factor, which has currently been reduced from the McGrews' estimate of 1044 to 107. If I can convince you that the womens' testimony is not significant, we will arrive at a final replacement Bayes factor of 105. Then, I may finally lay my weary head to rest and fly elsewhere. Especially, I hope to soon discuss Hume's argument and attempt to estimate prior odds on the Resurrection.
I think this may be done as follows: take the alternative hypotheses to the Resurrection which I have proposed to explain the disciples' witness and subsume the womens' testimony within them. This may be done without loss of prior plausibility, especially since initial rumors already play a role. This undermines the `essential independence' of the women from the other disciples proposed by the McGrews (p.41), which I do not think defends probabilistic independence in any case. As I have discussed, the emergence of rumors would very likely have affected the reaction of the disciples. Indeed, since the witness of women would have been regarded as less credible (p.28), we may plausibly expect the disciples to have corroborated their belief - which perhaps began with the women's testimony - with witness of their own. This, I think, tentatively answers the McGrews' challenge: "why [should we not] judge p(W|R) to be at least several orders of magnitude greater than p(W|~R)?" (p.30)
To argue directly that W should have less effect than 102 on the final Bayes factor requires, I think, a questioning of the McGrews' salient facts. If we separate it out from the other details, I think that the McGrews were sufficiently generous in leaving it at 102. In assenting to this, all I am saying is the following: that the women would report an empty tomb, or seeing Jesus, had he not Resurrected has probability 0.01, assuming that they would report it had they really seen it and that the facts are as described by the McGrews. I do not think that this is too challenging an admission for a skeptic. Instead, we need not recognize this contribution as multiplicative, and regard it as diminished by other considerations.
I think this, along with any potential minor significance of Paul in light of the other reductions, can be fairly accounted for by leaving a final estimate of the Bayes factor at 106, and plausibly lower.
Now, we may finally arrive at our destination.
Tim and Lydia McGrew on the Resurrection, part 6
[Continued from Part 5.]
We are now ready to focus on D, the facts about the witness of the disciples, and the independence assumptions which the McGrews make in arguing that this multiplicatively contributes 1039 to a final Bayes factor. We have already reduced the cumulative Bayes factor from 1044 to 1041 by arguing that Paul's conversion does not significantly contribute to the likelihood of the Resurrection. As noted in the last past, we are also accepting the characterization of the factual record which the McGrews make, leaving dispute of that question to a more general analysis, the outlines of which are to be found in part 2. The relevant facts, and some of the argument, which I assume in this post are to be found in part 5. You will not understand this post if you have not closely followed the previous discussion.
For simplification, we may assume - and safely - that p(D|R)=1. If you think that this compromises accuracy or is unfair, try ascribing to it a value of 1/2 or 1/10 or even 1/100, and see how much it affects my conclusions. It won't prove to be crucial. There may be room to dispute it, but that discussion falls outside of the matter at hand, which is to question the conclusions of the McGrews while sharing their premises. This done, we may focus entirely on p(D|~R). This single value is the most important that occurs in their analysis, so it merits the closest focus.
Recall that there are 13 disciples in D; I denote them as D1,...,D13. If we assume conditional independence under ~R, then
.
Recall that the McGrews do not argue that this assumption is plausible. Instead, they feel that the failures of this assumption tend to favor their argument, that is,
.
Since the quantity on the left hand side represents the denominator of relevant Bayes factor - where the numerator is 1 by assumption - increasing it decreases the Bayes factor. Given the general likelihood formula (p.26), the McGrews argue in my notation and with our shared assumptions the following (p.42):
where p(D1|~R) is an approximate average of the 13 p(Di|~R). From the messiness of this formula, one can see the allure of independence. But remember the crucial detail is the inequality, not the equality, of the left hand side and right hand side in the above formula. And note that regardless of independence, one must explain at least one disciple's testimony without relying on the others.
Here is where we turn to their defense of this thesis (pp.40-46), which, just as in our previous discussion of the strength of a disciple, goes wrong for the following reason: the McGrews assume that the only significant, explanatory alternatives to the Resurrection are those which claim that the disciples were frauds, pranksters, cynical, or the victims of hallucination or delusion. As I mentioned, I am quite willing to agree that the disciples were devout, sincere, and dedicated followers of Jesus, and that they were not likely the victims of elaborate pranks, and that they were not likely to forge conspiracies without good reason. But just as in the discussion of Paul's conversion, the McGrews expend little effort imagining how it is that Jesus' followers may have realistically reacted to Jesus' death. They never say, or do not closely pursue, something like, "given that the Resurrection did not occur, here are several likely ways that the disciples may have reacted..." They instead assume that no such plausible reaction would at all explain their later behavior.
I think it plausible that the Crucifixion occurred and that the Crucifixion surprised the disciples. I doubt they would expect their Messiah to die the humiliating death of a criminal. But I think this for a good reason: I do not think that anyone there would have expected that, except for those who already condemned him as a heretic. Why is this important? Because this is exactly how skeptics argue. They do not need to invent vivid hallucinations to explain the disciples' commitment. Instead, they ask how well-intentioned followers would likely react and argue from there.
For example, suppose that you are one of Jesus' disciples. He has been dead for some time now, and you are frustrated. You are frustrated because you still believe that Jesus was the Messiah, and because you believe that the Messiah has appointed you to spread his message. The end of the world is coming soon, and Jesus will be the judge. It is vitally important that others in these troubled times understand and believe. But unfortunately, the audience is not receptive. What good, after all, is a dead Messiah for liberating the Jews from the Romans and restoring the Law? There are rumors among followers and admirers of Jesus, especially in distant regions, that he could not have died as he did. Why shouldn't there be? Nobody expected this, of all horrors, to happen. But you did not waste your life by abandoning your family to follow Jesus. His moral message is still sound, and the brotherhood of your Christians is still precious to you. The communalistic message of Christianity can provide for the poor and the beggars and others who live as you have lived.
You are faced with a choice: (1) lie, exaggerate, fail to discredit rumors, or otherwise insist that Jesus better fulfilled the expectations of doubters, or (2) quash the rumers, alienate the faithful, and suffer virtually no success against the skepticism of your peers. Pace the McGrews, you have every incentive to choose (1), as do the other Appointed. You are already willing to risk persecution and death for Jesus' teachings. Why risk dying without successfully guiding others to Salvation? The Messiah did not do as you expected, but he will one day return to rule the world, and he had always explained why your mortal expectations were presumptuous before. Yes, Jesus is currently dead, but why should his teachings die before he returns? You've been tested before; now you are ready to pass the test.
Even this scenario, which I do not think too implausible, is too simplistic. The dilemma may have been the same, but the psychology leading to the preaching of the Resurrection was probably nowhere near this crude. If you like, you can imagine other, similar scenarios which you find more plausible. The question you must address is this: were Jesus to die and remain dead, how likely is it that the disciples would have gone quiet, abandoned Jesus' teachings, and renounced their appointed status? To answer this is to partly answer the important question: what do you expect to have happened if the Resurrection did not occur? Do you expect that the disciples might have rationalized the Crucifixion? If so, how? Is a rationalization like the Resurrection story deeply unlikely, say p(`rationalization'|~R)=10-10?
It is hypotheses like these, unconsidered by the McGrews, that make the difference and undermine their defense of independence, because we need not dispute that the disciples were courageous, committed men in order to maintain it. In fact, these hypotheses are the product of their dedication. To ask how strongly this affects the Bayes factor is to ask how likely it is that the disciples would not have agreed to `lie in the service of the Truth' or would not have been able to rationalize this testimony in some other manner, or at the very least, would not have initially struck down the rumors among the faithful, and eventually come to believe them, or believe that their `essence' was true, or some other such thing. I do not think I need to list precedents of such behavior.
I think that this consideration alone, pursued in detail, is enough to push the Bayes factor way down; I think that others cleverer than myself can explore other plausible alternatives as well. But if we assume that this hypothesis does not share the bulk of p(~R), it is worth asking what the rest of the elements in ~R might look like. The McGrews appear to assume that it is dominated by completely un-explanatory hypotheses, i.e. H:p(H|~R)=0, but I do not think that this is the case. At the very least, I think that this is a very poor approximation whenever we start tossing around numbers like 1039.
How exactly should this affect p(D|~R)? Suppose that the hypothesis I outlined with respect to a single disciple gives us something like p(D1|~R)=0.01, an estimate which I think rather conservative. Now we ask how this should affect the other disciples: here, look at the same dilemma again, adding that other disciples are already claiming R. By the time we reach 7 or 8 disciples, the others follow very naturally. In this way, we can be sure that the independence assumption is overly hard on skeptical alternatives. More formally, we can give a tentative estimate of p(D|~R)=10-4 or p(D|~R)=10-5, and plausibly something higher.
So a tentative readjustment of the multiplicative contribution of the disciples to the cumulative Bayes factor is 105. I think that this is generous, and I think that skeptics can ground this or a lower value. But I am still admitting the following: given the characterization of the texts and the history of the McGrews, the testimony of the disciples is best explained by the Resurrection. What I dispute is how significant this detail must be.
Taking stock, our reduction of the Bayes factor is from 1044 to 107. The last fact which the McGrews discuss is the testimony of the women (W). That will be the topic of my next post. After that detail - perhaps unimportant relative to the other aspects of the argument - I can round all of this noise up and see where it leaves us.
We are now ready to focus on D, the facts about the witness of the disciples, and the independence assumptions which the McGrews make in arguing that this multiplicatively contributes 1039 to a final Bayes factor. We have already reduced the cumulative Bayes factor from 1044 to 1041 by arguing that Paul's conversion does not significantly contribute to the likelihood of the Resurrection. As noted in the last past, we are also accepting the characterization of the factual record which the McGrews make, leaving dispute of that question to a more general analysis, the outlines of which are to be found in part 2. The relevant facts, and some of the argument, which I assume in this post are to be found in part 5. You will not understand this post if you have not closely followed the previous discussion.
For simplification, we may assume - and safely - that p(D|R)=1. If you think that this compromises accuracy or is unfair, try ascribing to it a value of 1/2 or 1/10 or even 1/100, and see how much it affects my conclusions. It won't prove to be crucial. There may be room to dispute it, but that discussion falls outside of the matter at hand, which is to question the conclusions of the McGrews while sharing their premises. This done, we may focus entirely on p(D|~R). This single value is the most important that occurs in their analysis, so it merits the closest focus.
Recall that there are 13 disciples in D; I denote them as D1,...,D13. If we assume conditional independence under ~R, then
.Recall that the McGrews do not argue that this assumption is plausible. Instead, they feel that the failures of this assumption tend to favor their argument, that is,
.Since the quantity on the left hand side represents the denominator of relevant Bayes factor - where the numerator is 1 by assumption - increasing it decreases the Bayes factor. Given the general likelihood formula (p.26), the McGrews argue in my notation and with our shared assumptions the following (p.42):
where p(D1|~R) is an approximate average of the 13 p(Di|~R). From the messiness of this formula, one can see the allure of independence. But remember the crucial detail is the inequality, not the equality, of the left hand side and right hand side in the above formula. And note that regardless of independence, one must explain at least one disciple's testimony without relying on the others.
Here is where we turn to their defense of this thesis (pp.40-46), which, just as in our previous discussion of the strength of a disciple, goes wrong for the following reason: the McGrews assume that the only significant, explanatory alternatives to the Resurrection are those which claim that the disciples were frauds, pranksters, cynical, or the victims of hallucination or delusion. As I mentioned, I am quite willing to agree that the disciples were devout, sincere, and dedicated followers of Jesus, and that they were not likely the victims of elaborate pranks, and that they were not likely to forge conspiracies without good reason. But just as in the discussion of Paul's conversion, the McGrews expend little effort imagining how it is that Jesus' followers may have realistically reacted to Jesus' death. They never say, or do not closely pursue, something like, "given that the Resurrection did not occur, here are several likely ways that the disciples may have reacted..." They instead assume that no such plausible reaction would at all explain their later behavior.
I think it plausible that the Crucifixion occurred and that the Crucifixion surprised the disciples. I doubt they would expect their Messiah to die the humiliating death of a criminal. But I think this for a good reason: I do not think that anyone there would have expected that, except for those who already condemned him as a heretic. Why is this important? Because this is exactly how skeptics argue. They do not need to invent vivid hallucinations to explain the disciples' commitment. Instead, they ask how well-intentioned followers would likely react and argue from there.
For example, suppose that you are one of Jesus' disciples. He has been dead for some time now, and you are frustrated. You are frustrated because you still believe that Jesus was the Messiah, and because you believe that the Messiah has appointed you to spread his message. The end of the world is coming soon, and Jesus will be the judge. It is vitally important that others in these troubled times understand and believe. But unfortunately, the audience is not receptive. What good, after all, is a dead Messiah for liberating the Jews from the Romans and restoring the Law? There are rumors among followers and admirers of Jesus, especially in distant regions, that he could not have died as he did. Why shouldn't there be? Nobody expected this, of all horrors, to happen. But you did not waste your life by abandoning your family to follow Jesus. His moral message is still sound, and the brotherhood of your Christians is still precious to you. The communalistic message of Christianity can provide for the poor and the beggars and others who live as you have lived.
You are faced with a choice: (1) lie, exaggerate, fail to discredit rumors, or otherwise insist that Jesus better fulfilled the expectations of doubters, or (2) quash the rumers, alienate the faithful, and suffer virtually no success against the skepticism of your peers. Pace the McGrews, you have every incentive to choose (1), as do the other Appointed. You are already willing to risk persecution and death for Jesus' teachings. Why risk dying without successfully guiding others to Salvation? The Messiah did not do as you expected, but he will one day return to rule the world, and he had always explained why your mortal expectations were presumptuous before. Yes, Jesus is currently dead, but why should his teachings die before he returns? You've been tested before; now you are ready to pass the test.
Even this scenario, which I do not think too implausible, is too simplistic. The dilemma may have been the same, but the psychology leading to the preaching of the Resurrection was probably nowhere near this crude. If you like, you can imagine other, similar scenarios which you find more plausible. The question you must address is this: were Jesus to die and remain dead, how likely is it that the disciples would have gone quiet, abandoned Jesus' teachings, and renounced their appointed status? To answer this is to partly answer the important question: what do you expect to have happened if the Resurrection did not occur? Do you expect that the disciples might have rationalized the Crucifixion? If so, how? Is a rationalization like the Resurrection story deeply unlikely, say p(`rationalization'|~R)=10-10?
It is hypotheses like these, unconsidered by the McGrews, that make the difference and undermine their defense of independence, because we need not dispute that the disciples were courageous, committed men in order to maintain it. In fact, these hypotheses are the product of their dedication. To ask how strongly this affects the Bayes factor is to ask how likely it is that the disciples would not have agreed to `lie in the service of the Truth' or would not have been able to rationalize this testimony in some other manner, or at the very least, would not have initially struck down the rumors among the faithful, and eventually come to believe them, or believe that their `essence' was true, or some other such thing. I do not think I need to list precedents of such behavior.
I think that this consideration alone, pursued in detail, is enough to push the Bayes factor way down; I think that others cleverer than myself can explore other plausible alternatives as well. But if we assume that this hypothesis does not share the bulk of p(~R), it is worth asking what the rest of the elements in ~R might look like. The McGrews appear to assume that it is dominated by completely un-explanatory hypotheses, i.e. H:p(H|~R)=0, but I do not think that this is the case. At the very least, I think that this is a very poor approximation whenever we start tossing around numbers like 1039.
How exactly should this affect p(D|~R)? Suppose that the hypothesis I outlined with respect to a single disciple gives us something like p(D1|~R)=0.01, an estimate which I think rather conservative. Now we ask how this should affect the other disciples: here, look at the same dilemma again, adding that other disciples are already claiming R. By the time we reach 7 or 8 disciples, the others follow very naturally. In this way, we can be sure that the independence assumption is overly hard on skeptical alternatives. More formally, we can give a tentative estimate of p(D|~R)=10-4 or p(D|~R)=10-5, and plausibly something higher.
So a tentative readjustment of the multiplicative contribution of the disciples to the cumulative Bayes factor is 105. I think that this is generous, and I think that skeptics can ground this or a lower value. But I am still admitting the following: given the characterization of the texts and the history of the McGrews, the testimony of the disciples is best explained by the Resurrection. What I dispute is how significant this detail must be.
Taking stock, our reduction of the Bayes factor is from 1044 to 107. The last fact which the McGrews discuss is the testimony of the women (W). That will be the topic of my next post. After that detail - perhaps unimportant relative to the other aspects of the argument - I can round all of this noise up and see where it leaves us.
Tim and Lydia McGrew on the Resurrection, part 5
[Continued from Part 4.]
In addition to the items summarized in the last post, we have now seen that there is little reason to regard Paul's conversion as itself making significant contribution to a cumulative Bayes factor, even when taking the relevant salient facts of the McGrews at face value - where they are consistent and actually salient. We have therefore reduced the McGrews' final Bayes factor from 1044 to 1041. Admittedly, this change is very slight. As previously discussed, the most important features of CCRJ are as follows: the independence assumptions and the effect of the disciples, particularly in conjunction. These ideas alone contribute a multiplicative factor 1039 to the McGrews' final likelihood ratio. Before discussing the details surrounding the disciples, their independence should be treated first.
The McGrews do not argue that their conditional independence assumptions are plausible. On the contrary: "the invocation of independence assumptions at several points is contestable; in fact, we believe that the case of the calculation for D the independence assumption almost certainly breaks down." So why do they invoke it? Because "this fact does not necessarily lessen the strength of the argument. Everything depends on the balance of considerations regarding the direction and extend of the breakdown of independence under R and ~R" (p.40). This approach is quite sensible: start out with an admitted simplification, critique it, and argue that the critiques generally favor the proponent of the argument.1 I think that the only other even approximately accurate response available on the web - at least that I know of - fails to adequately address this.
Allow me to motivate the discussion by being self-referential. If one grants a significant number, say n, of events Ei where i is a positive integer less than or equal to n, and one can assume that the Ei are conditionally independent under a hypothesis H and its negation ~H, then even a very small individual factor
is a big deal. With only 13 witnesses, even assigning a Bayes factor of 10 to each individual - even this seems uncharitable - still gives you a cumulative factor of
,
where the notation is exchanged as needed. This is a big number, even if its nowhere near that proposed by the McGrews.2
As we noticed, the McGrews will not be surprised if we directly challenge independence. Instead, we have to focus on pages 40-46 of the CCRJ. In order to do this, we have to start discussing and disputing facts about the disciples. This is because of the straightforward fact I noted in the other post in the context of evidential variety: the invocation of independence across a significant number of events `filters out' hypotheses which do not convincingly allow these events to be correlated. Less abstractly, the fact that the disciples not only witnessed as they did individually but did so in agreement must be plausibly explained by some element in ~R, if we grant that agreement.3 `Bad' hypotheses, for our purposes, are those which are intrinsically implausible and those which are only plausible with respect to one or a few disciples. Even if a hallucination happened to plausibly explain the witness of one disciple, it does not without lots of dubious conjecture help to explain the correlation of the witnesses.
The key facts about the disciples4 are as follows:
1. They were not expecting the Crucifixion or Resurrection in advance.
2. They were willing to die - or at least take great risk - in order to spread Jesus' message. (pp.17, 20-24, 30-37.)
3. There was little to no material or social advantage in preaching this message.
4. They attested to a physical resurrection. They claimed to have seen him and spoken with him for some lengthy period of time, e.g. 40 days. (pp.17-8)
5. They did not present a self-flattering account of the Resurrection. For example, they claimed to not readily understand, to be fearful, to have doubts, and to be chided and corrected by Jesus. (pp.17-8)
A hefty confidence in these is required to stick to the McGrews' analysis. For example, the importance of consensus amongst the disciples, and that there were no omitted complaints from purported witnesses, is of central importance (p.32). While I agree with the McGrews that it is very difficult to seriously attribute most or all of the disciples' testimony to cynicism or fabrication, my confidence in the uniformity of their testimony with respect to these key facts is much less. There is little reason, had there been substantive dissent, to expect that it would have made it into the gospels. Still, my purposes at this time are not to dispute these items. However, such discussion will be an important part of a general analysis like that presented in part 2.
Now, I agree with the McGrews that `external' theories, e.g. the `stolen body hypothesis', do very little to explain the facts in question (p.32). The point is to account for these facts in a convincing manner, and their origin is not at all explained by people stealing Jesus' body to corroborate the claims of early Christians. What we are looking for are `internal theories', i.e., those which convincingly explain the actions and statements of the disciples. It is here that I think the McGrews grossly underestimate the strength of potential naturalistic alternatives.
Before moving on, I should say something about the significance of these facts, especially (5). The idea is that were the disciples to be manufacturing stories or exaggerating in order to advance their cause, we might reasonably expect them to not be so hard on themselves. I do not think, especially in the context of Christianity, that this is a significant consideration. I think we are all familiar with examples of false humility, or we understand at the very least that confessions of guilt and personal inadequacy are very often encouraged in Christian communities, even admired. Perhaps my personal experience is overshadowing the general picture, but I understood early as a child that confession of guilt in church and begging for redemption was admired and expected of me. That the disciples do not flatter themselves is insignificant in the context of Jesus' teachings, quite apart from the Resurrection, "for all have sinned and fallen short of the glory of God." There are similar considerations for (1). Evidently, and I think everyone involved agrees, Jews did not expect that the prophesied Messiah would be anything like Jesus. That the disciples understood, empathized, or even shared in part this lack of expectation is not overly surprising. What matters is how we would expect the disciples to "normally behave" after Jesus' death.
To address naturalistic alternatives to the Resurrection which explain (1)-(5), the McGrews rework in probabilistic terms the good ol' "nobody would die for a lie" claim. This argument has its merits, as far as it goes, but it does not go as far as the McGrews think.
The previous considerations apply to the "disciples witnessed but did not really believe" section of alternatives. Now we can look at the "disciples witnessed and really believed" section of alternatives. Here is where we find claims about delusion and hallucination:
Assuming plausibly that p(D|R) is quite high - say 1 for purposes of simplification - our attention focuses entirely on p(D|~R). We want to know whether or not p(D|~R)=10-39 is at all realistic. Although I agree with the McGrews that hallucination, delusion, and cynical fabrication are very unlikely, we still need to know whether their disjunction is well below 10-39. Unlikely as I think these are, I think that they are at least slightly more credible than that. However, if we are to propose a substantial increase in p(D|~R), we are going to have to look elsewhere. Namely, we want to look for alternative hypotheses H such that p(H|~R) and p(D|H) are significant. In the case that H is `fully explanatory' of ~R, the former quantity is p(H)/p(~R). Assuming that our prior confidence in ~R is high, this approximates the absolute probability p(H). The moral of the story? If you are proposing alternatives to the Resurrection which are designed to completely explain it, you have to be careful to avoid ad hoc thinking: you have to argue that all concerned should find that alternative explanation plausible for reasons other than that the Resurrection has low prior plausibility.
Failing to find any explanatory hypothesis of significant probability, the McGrews assign p(`a disciple'|~R)=0.001, which with independence gives a Bayes factor of 1039.
In order to discuss significant alternatives, question their defense of independence, and propose an alternative Bayes factor, we need to compare the independence case to the more general likelihood formula, which they provide in a footnote (p.26). This work will be formal, abstract, and address the most important part of their argument, so I give this work its own post.
1. To avoid confusion, the vernacular sense of `independent witnesses' is completely opposite to that of the probabilistic sense of `independent witnesses'. What we expect witnesses to do, if none influence the other and the circumstances are clear, is to produce correlating accounts. That is, what one witness says usually strongly affects what we expect other witnesses to say, which is the very opposite of conditional independence.
2. We'll see that the disciples should contribute heavily to the Bayes factor if one is willing to grant near-certainty to all of the important premises entertained by the McGrews. I do not think that skeptics should want (or need) to conclude something other than the following: if the gospel accounts are accurate as regards the relevant, secular evidence for R, then they strongly evidence R. I accept what probability tells me I must, if I assent to the following:
3. There's much more to be said about this, but that discussion falls well outside of the salient facts as characterized by the McGrews.
4. Recall that there are 13, counting the original disciples minus Judas, Mathias, and James the Just (called `Brother of Jesus'). The details about James are sufficiently different that I would in future analyses recommend separating him from the rest of the disciples. In particular, he is argued to not have been a believer before Jesus died (p.22), and quite plausibly was not present to witness the events attested by the others (p.34).
5. I add also that we have many cases where people are willing to die for false witness. Does anybody here watch House? Have there ever been false confessions to murders? I'll leave this tangent to others.
In addition to the items summarized in the last post, we have now seen that there is little reason to regard Paul's conversion as itself making significant contribution to a cumulative Bayes factor, even when taking the relevant salient facts of the McGrews at face value - where they are consistent and actually salient. We have therefore reduced the McGrews' final Bayes factor from 1044 to 1041. Admittedly, this change is very slight. As previously discussed, the most important features of CCRJ are as follows: the independence assumptions and the effect of the disciples, particularly in conjunction. These ideas alone contribute a multiplicative factor 1039 to the McGrews' final likelihood ratio. Before discussing the details surrounding the disciples, their independence should be treated first.
The McGrews do not argue that their conditional independence assumptions are plausible. On the contrary: "the invocation of independence assumptions at several points is contestable; in fact, we believe that the case of the calculation for D the independence assumption almost certainly breaks down." So why do they invoke it? Because "this fact does not necessarily lessen the strength of the argument. Everything depends on the balance of considerations regarding the direction and extend of the breakdown of independence under R and ~R" (p.40). This approach is quite sensible: start out with an admitted simplification, critique it, and argue that the critiques generally favor the proponent of the argument.1 I think that the only other even approximately accurate response available on the web - at least that I know of - fails to adequately address this.
Allow me to motivate the discussion by being self-referential. If one grants a significant number, say n, of events Ei where i is a positive integer less than or equal to n, and one can assume that the Ei are conditionally independent under a hypothesis H and its negation ~H, then even a very small individual factor
is a big deal. With only 13 witnesses, even assigning a Bayes factor of 10 to each individual - even this seems uncharitable - still gives you a cumulative factor of
,where the notation is exchanged as needed. This is a big number, even if its nowhere near that proposed by the McGrews.2
As we noticed, the McGrews will not be surprised if we directly challenge independence. Instead, we have to focus on pages 40-46 of the CCRJ. In order to do this, we have to start discussing and disputing facts about the disciples. This is because of the straightforward fact I noted in the other post in the context of evidential variety: the invocation of independence across a significant number of events `filters out' hypotheses which do not convincingly allow these events to be correlated. Less abstractly, the fact that the disciples not only witnessed as they did individually but did so in agreement must be plausibly explained by some element in ~R, if we grant that agreement.3 `Bad' hypotheses, for our purposes, are those which are intrinsically implausible and those which are only plausible with respect to one or a few disciples. Even if a hallucination happened to plausibly explain the witness of one disciple, it does not without lots of dubious conjecture help to explain the correlation of the witnesses.
The key facts about the disciples4 are as follows:
1. They were not expecting the Crucifixion or Resurrection in advance.
2. They were willing to die - or at least take great risk - in order to spread Jesus' message. (pp.17, 20-24, 30-37.)
3. There was little to no material or social advantage in preaching this message.
4. They attested to a physical resurrection. They claimed to have seen him and spoken with him for some lengthy period of time, e.g. 40 days. (pp.17-8)
5. They did not present a self-flattering account of the Resurrection. For example, they claimed to not readily understand, to be fearful, to have doubts, and to be chided and corrected by Jesus. (pp.17-8)
A hefty confidence in these is required to stick to the McGrews' analysis. For example, the importance of consensus amongst the disciples, and that there were no omitted complaints from purported witnesses, is of central importance (p.32). While I agree with the McGrews that it is very difficult to seriously attribute most or all of the disciples' testimony to cynicism or fabrication, my confidence in the uniformity of their testimony with respect to these key facts is much less. There is little reason, had there been substantive dissent, to expect that it would have made it into the gospels. Still, my purposes at this time are not to dispute these items. However, such discussion will be an important part of a general analysis like that presented in part 2.
Now, I agree with the McGrews that `external' theories, e.g. the `stolen body hypothesis', do very little to explain the facts in question (p.32). The point is to account for these facts in a convincing manner, and their origin is not at all explained by people stealing Jesus' body to corroborate the claims of early Christians. What we are looking for are `internal theories', i.e., those which convincingly explain the actions and statements of the disciples. It is here that I think the McGrews grossly underestimate the strength of potential naturalistic alternatives.
Before moving on, I should say something about the significance of these facts, especially (5). The idea is that were the disciples to be manufacturing stories or exaggerating in order to advance their cause, we might reasonably expect them to not be so hard on themselves. I do not think, especially in the context of Christianity, that this is a significant consideration. I think we are all familiar with examples of false humility, or we understand at the very least that confessions of guilt and personal inadequacy are very often encouraged in Christian communities, even admired. Perhaps my personal experience is overshadowing the general picture, but I understood early as a child that confession of guilt in church and begging for redemption was admired and expected of me. That the disciples do not flatter themselves is insignificant in the context of Jesus' teachings, quite apart from the Resurrection, "for all have sinned and fallen short of the glory of God." There are similar considerations for (1). Evidently, and I think everyone involved agrees, Jews did not expect that the prophesied Messiah would be anything like Jesus. That the disciples understood, empathized, or even shared in part this lack of expectation is not overly surprising. What matters is how we would expect the disciples to "normally behave" after Jesus' death.
To address naturalistic alternatives to the Resurrection which explain (1)-(5), the McGrews rework in probabilistic terms the good ol' "nobody would die for a lie" claim. This argument has its merits, as far as it goes, but it does not go as far as the McGrews think.
It is sometimes urged that kamikaze pilots, suicide bombers, and Nazis were willing to give their lives for what they believed was true. The objection may be put more broadly. Virtually every religion has its zealous adherents who have been willing to die for what they believe; why, then, should the willingness of the apostles to die as martyrs be of special epistemic interest? The answer is that this description blurs the distinction between the willingness to die for an ideology and the willingness to die in attestation of an empirical fact. (p.32) [citations omitted.]
It is clear that neither kamikazes, Nazis, nor suicide bombers died to affirm the reality of something that they had seen with their eyes and their hands had handled. Thus, their deaths and the falsehood of some of their beliefs tell us nothing about the probability that a man will die to make an affirmation like that of the apostles when it is in fact false. The educational resources of an entire nation, applied over the course of a decade or more to minds at their most impressionable stage, may be sufficient to induce in the young the general belief that their country or their religion is worth dying for. But what would induce grown men to break with the religious community in which they had been raised and confess with their blood that they had seen with their own eyes and handled with their own hands their dead rabbi raised again to life? (p.33) [Emphasis in original.]The McGrews partially answer their own question or are really asking it to themselves. The disciples had already broken with their religious background to follow Jesus - with the possible exception of James. They were already committed to the heretical philosophy of Jesus. They were not merely dying to attest the Resurrection; they were dying for the belief that the Messiah had arrived, that only His followers would find salvation, and that the end was near. The distinction which the McGrews make is valid, but it is extremely narrow in this context.5 To divorce the Resurrection from the other claims, moral and otherwise, of Christianity is misleading.
The previous considerations apply to the "disciples witnessed but did not really believe" section of alternatives. Now we can look at the "disciples witnessed and really believed" section of alternatives. Here is where we find claims about delusion and hallucination:
Suppose, on the other hand, that the witnesses did have good reasons for their belief in the resurrection but were nevertheless mistaken. How is this supposed to come about? The hallucination theory has at least this advantage over both external naturalistic explanations and the appeal to enthusiasm: the supposition that the disciples suffered from sufficiently vivid and persistent hallucinations provides the resources to explain why they firmly believed they had seen Jesus risen. But this gain in explanatory power comes at a prohibitive cost in prior probability... (p.33) [Citations omitted]Instead of looking at how the McGrews corroborate this last statement, try imagining for yourself why this should be. Is it really at all likely that these committed disciples should individually experience vivid hallucinations or powerful delusions on the event of their Messiah's death, and that these delusions, if that is what they were, should have the staying power that they did? How common are events like this at all? If we want to substantially reduce the Bayes factor proposed by the McGrews in a way that should be at all convincing to both skeptics and believers, we need to look elsewhere for alternatives. As the McGrews note, "the problem with the hallucination theory is that it has a vanishingly small probability conditional on ~R. The sort of complex, repeated, integrated hallucination that would be required to maintain even one disciple's testimony and willingness to die for it would represent a serious mental illness" (p.35). There are qualifications to the McGrews' argument that I would add, in particular that extreme distress can very plausibly result in a resilient, complex delusion, and need not require the positing of serious mental illness, but I will not dwell on these details. The fact remains that there is little reason to think such a thing happened, or would likely happen, and ultimately result in the texts as we find them.
Assuming plausibly that p(D|R) is quite high - say 1 for purposes of simplification - our attention focuses entirely on p(D|~R). We want to know whether or not p(D|~R)=10-39 is at all realistic. Although I agree with the McGrews that hallucination, delusion, and cynical fabrication are very unlikely, we still need to know whether their disjunction is well below 10-39. Unlikely as I think these are, I think that they are at least slightly more credible than that. However, if we are to propose a substantial increase in p(D|~R), we are going to have to look elsewhere. Namely, we want to look for alternative hypotheses H such that p(H|~R) and p(D|H) are significant. In the case that H is `fully explanatory' of ~R, the former quantity is p(H)/p(~R). Assuming that our prior confidence in ~R is high, this approximates the absolute probability p(H). The moral of the story? If you are proposing alternatives to the Resurrection which are designed to completely explain it, you have to be careful to avoid ad hoc thinking: you have to argue that all concerned should find that alternative explanation plausible for reasons other than that the Resurrection has low prior plausibility.
Failing to find any explanatory hypothesis of significant probability, the McGrews assign p(`a disciple'|~R)=0.001, which with independence gives a Bayes factor of 1039.
In order to discuss significant alternatives, question their defense of independence, and propose an alternative Bayes factor, we need to compare the independence case to the more general likelihood formula, which they provide in a footnote (p.26). This work will be formal, abstract, and address the most important part of their argument, so I give this work its own post.
1. To avoid confusion, the vernacular sense of `independent witnesses' is completely opposite to that of the probabilistic sense of `independent witnesses'. What we expect witnesses to do, if none influence the other and the circumstances are clear, is to produce correlating accounts. That is, what one witness says usually strongly affects what we expect other witnesses to say, which is the very opposite of conditional independence.
2. We'll see that the disciples should contribute heavily to the Bayes factor if one is willing to grant near-certainty to all of the important premises entertained by the McGrews. I do not think that skeptics should want (or need) to conclude something other than the following: if the gospel accounts are accurate as regards the relevant, secular evidence for R, then they strongly evidence R. I accept what probability tells me I must, if I assent to the following:
In other words, is there anything in the reports coming out of the first-century church that is more like what you should expect if Jesus was raised than if Jesus was not raised. If the answer to that question is yes, then the evidence confirms the resurrection, but it might still be rejected by reasonable people on the grounds that a Resurrection would commit you to the existence of God, or other features of Christianity that you consider to be improbable. Fine, but you can at least say, in response to the evidence, that the evidence directly bearing on the resurrection of Jesus is easier to explain if the Resurrection occurred than if it didn't. In other words, we can isolate one particular piece of evidence from the total evidence we have that bears on the issue and ask whether this piece of evidence supports the Christian claim that Jesus was resurrected or not.Again, I think that the most important part of rejecting confirmation of R as derived from the Bayes factor is in rigorously defending a very small prior odds and presenting at least a very minimal case for skepticism as regards characterizations of the text like those employed by the McGrews. Both of these feats are easily done, I think, but I leave them to my betters for now.
3. There's much more to be said about this, but that discussion falls well outside of the salient facts as characterized by the McGrews.
4. Recall that there are 13, counting the original disciples minus Judas, Mathias, and James the Just (called `Brother of Jesus'). The details about James are sufficiently different that I would in future analyses recommend separating him from the rest of the disciples. In particular, he is argued to not have been a believer before Jesus died (p.22), and quite plausibly was not present to witness the events attested by the others (p.34).
5. I add also that we have many cases where people are willing to die for false witness. Does anybody here watch House? Have there ever been false confessions to murders? I'll leave this tangent to others.
Wednesday, July 27, 2011
Tim and Lydia McGrew on the Resurrection, part 4
[Continued from Part 3.]
I hope that by now readers - you better have read the previous parts if you are reading this! - understand that the McGrews' CCRJ cannot be dismissed in an ordinary blog comment which spells out things that are intuitive and obvious to a layman. I hope that I've convinced you already not to invest too heavily in highly dubious alternative explanations to the Resurrection. (I would hope that I wouldn't have to say that.) And I hope you have some idea of what to expect now that we are now actually calculating a Bayes factor to replace that proposed by the McGrews on their assumptions, roughly how we can expect to do that, and the limitations on our conclusions which that method imposes.
As I mentioned in Part 3, I for some time avoided mentioning explicitly the set of salient facts. As one reason, I gave that I do not accept the relevance of that set of salient facts. In particular, I do not think that the conversion of Paul should significantly affect a cumulative Bayes factor. Now that we've checked the depth of the waters so as to avoid high-diving into a kiddie-pool, we may now safely plunge into the subject. Recall that the McGrews place a value of 103 on the Bayes factor derived from conditioning on Paul's Damascene moment (See CCRJ pp.37-9 for their argument):
More specifically (p.39):
.
As against this, I propose that
,
where the bi-directional arrow denotes the equivalence of these claims. That equivalence is mathematically trivial, but conceptually challenging: why should I expect Paul's conversion to be equally likely whether or not the Resurrection occurred? I give a hint - also mentioned by the McGrews but not adequately pursued - that there is a qualitative difference between P and the other facts - recall that namely these are the women's testimony (W) and the witness of the disciples (D). I'll give another hint: how significant would Paul's conversion be in contrast to the range of reasonable argument over the contribution of the disciples - which alone, to the McGrews, is 1039 if you recall - if the factor produced by Paul's conversion can only be convincingly argued to be something as low as 5 or 10? In answering these, understand why I am not requiring that all involved recognize an exact equality. Given this sense of approximation and that I will be successful, reintroducing Paul's conversion as a significant fact should only be done after accepting that the more direct witness testimony is far less powerful and that the important range of priors includes some relatively large odds on the Resurrection.
The McGrews expend most of their brief effort on p(P|~R) and may not give any argument for p(P|R) at all. They say that "on the assumption of R there is no difficulty whatever in accounting for P" (p.39), making no other argument, unless their emphasizing that Paul would later insist on a physical resurrection is significant (p.38). On the contrary, I do not think that the facts around Paul's conversion support this `no difficulty' assertion at all. To see how this is the case, let's think about how their comments at the expense of a significant p(P|~R) reflect on p(P|R):
Before going further, something needs to be said about the inconsistencies in the scriptures describing Paul's conversion. I agree with the McGrews that one should not make too much of the minor inconsistencies in scripture, which they admit while pointing out that this is what we expect of any historical text (p.6). I'm not interested in inviting the hyper-literalists to the discussion. But I think that they are incautious wherever those non-fatal inconsistencies emerge. As I will discuss later, this is also important when they are describing some (relatively minor) secular facts surrounding the witness of the disciples. I think, in the argumentation for Paul's contribution especially, that the McGrews are sometimes uncharacteristically lax, uncharitable to skeptics, and preemptively dismissive. But then, this essay is part of an anthology, and there may have been space constraints. This would not excuse the casualness with which they approach these details, but it is worth keeping that eventuality in mind, along with the tentative and very restrictive nature of their conclusions.
To support these strong statements:
1. They claim that Jesus appeared to Paul in the flesh (p.38). To cut a quote from Loftus out of context and into context:
2. More culpable is their treatment of a hypothesis proposed by another scholar:
I agree with the McGrews that Paul can not credibly be thought of as a conscious fraud. I think that his conversion was sincere, and it is very well evidenced, as is Paul's historical personage. But they fail to imagine why Paul, a sincere convert, might manufacture a vision story because he's a sincere convert. Imagine that you are Paul: you have been overcome with horror at the guilt of your actions, and you wish to make amends. As a new-found Christian, you care deeply about Christians and the fate of the persecuted churches. There is, however, a small problem: you do not expect these beleaguered communities to accept a killer with open arms and smiles. You especially do not expect this beleaguered communities to recognize your education and expertise as conferring status upon you. What would you do to convince them? Claim a vision, and proudly, and take the very real risks of doing so.
This `emotive-incentive hypothesis', along with a serious look at Strauss' explanation, allows us to safely assert that p(P|~R) is not significantly less than the value of p(P|R), which has no convincing support.
Before moving on to the disciples and the women, a post on the assumptions of conditional independence, its importance, and how the McGrews actually employ it is in order, especially for the 13 disciples. Once this is addressed, I think that the tentative finish line will be in clear view.
I hope that by now readers - you better have read the previous parts if you are reading this! - understand that the McGrews' CCRJ cannot be dismissed in an ordinary blog comment which spells out things that are intuitive and obvious to a layman. I hope that I've convinced you already not to invest too heavily in highly dubious alternative explanations to the Resurrection. (I would hope that I wouldn't have to say that.) And I hope you have some idea of what to expect now that we are now actually calculating a Bayes factor to replace that proposed by the McGrews on their assumptions, roughly how we can expect to do that, and the limitations on our conclusions which that method imposes.
As I mentioned in Part 3, I for some time avoided mentioning explicitly the set of salient facts. As one reason, I gave that I do not accept the relevance of that set of salient facts. In particular, I do not think that the conversion of Paul should significantly affect a cumulative Bayes factor. Now that we've checked the depth of the waters so as to avoid high-diving into a kiddie-pool, we may now safely plunge into the subject. Recall that the McGrews place a value of 103 on the Bayes factor derived from conditioning on Paul's Damascene moment (See CCRJ pp.37-9 for their argument):
More specifically (p.39):
.As against this, I propose that
,where the bi-directional arrow denotes the equivalence of these claims. That equivalence is mathematically trivial, but conceptually challenging: why should I expect Paul's conversion to be equally likely whether or not the Resurrection occurred? I give a hint - also mentioned by the McGrews but not adequately pursued - that there is a qualitative difference between P and the other facts - recall that namely these are the women's testimony (W) and the witness of the disciples (D). I'll give another hint: how significant would Paul's conversion be in contrast to the range of reasonable argument over the contribution of the disciples - which alone, to the McGrews, is 1039 if you recall - if the factor produced by Paul's conversion can only be convincingly argued to be something as low as 5 or 10? In answering these, understand why I am not requiring that all involved recognize an exact equality. Given this sense of approximation and that I will be successful, reintroducing Paul's conversion as a significant fact should only be done after accepting that the more direct witness testimony is far less powerful and that the important range of priors includes some relatively large odds on the Resurrection.
The McGrews expend most of their brief effort on p(P|~R) and may not give any argument for p(P|R) at all. They say that "on the assumption of R there is no difficulty whatever in accounting for P" (p.39), making no other argument, unless their emphasizing that Paul would later insist on a physical resurrection is significant (p.38). On the contrary, I do not think that the facts around Paul's conversion support this `no difficulty' assertion at all. To see how this is the case, let's think about how their comments at the expense of a significant p(P|~R) reflect on p(P|R):
Delusions that change the minds of vicious persecutors and transform them into faithful martyrs are unfortunately quite rare; one looks in vain for comparable conversions among the notorious murdering zealots of the ages. (p.38)While I think we probably can find cases with important parallels, I'm not sure that the McGrews want to insist on this statement. If the Resurrection had occurred and is supposed to make at all probable that someone like Paul would be transformed through a vision into an apostle, why then are Pauls so rare? Do we lack similar circumstances where a persecuted Church is suffering under a hostile regime? We can ask other uncomfortable questions as well. Why would we expect Jesus to wait for martyrs like Stephen to become such before making Paul a martyr? Is that how we should expect Jesus to send messages? Why should skeptics accept that, and further, if that is the case, why are Pauls so rare? And why Paul? If he was, as the McGrews insist, an unrepentant, guiltless zealot up to the Damascene moment, why not appear to more powerful persecutors? Why wait until the 4th century to send the Emperor a sign? Nothing about the Resurrection makes Paul's conversion likely, and if it did, we may generate a powerful argument against the Resurrection from the rarity of such conversions.
Before going further, something needs to be said about the inconsistencies in the scriptures describing Paul's conversion. I agree with the McGrews that one should not make too much of the minor inconsistencies in scripture, which they admit while pointing out that this is what we expect of any historical text (p.6). I'm not interested in inviting the hyper-literalists to the discussion. But I think that they are incautious wherever those non-fatal inconsistencies emerge. As I will discuss later, this is also important when they are describing some (relatively minor) secular facts surrounding the witness of the disciples. I think, in the argumentation for Paul's contribution especially, that the McGrews are sometimes uncharacteristically lax, uncharitable to skeptics, and preemptively dismissive. But then, this essay is part of an anthology, and there may have been space constraints. This would not excuse the casualness with which they approach these details, but it is worth keeping that eventuality in mind, along with the tentative and very restrictive nature of their conclusions.
To support these strong statements:
1. They claim that Jesus appeared to Paul in the flesh (p.38). To cut a quote from Loftus out of context and into context:
...Paul [claimed] to have experienced the resurrected Jesus in what is surely a visionary experience (so we read in Acts 26:19, cf. II Cor. 12:1-6; Rev. 1:10-3:21--although he didn't actually see Jesus, Acts 9:4-8; 22:7-11; 26:13-14)...I have not seen McGrews cite Revelations, but Acts and II Corinthians are in necessary, regular appearance, and it is in Acts that it is not said that Paul actually saw Jesus, but only heard a voice. For example:
And he fell to the earth, and heard a voice saying unto him, Saul, Saul, why persecutest thou me? And he said, Who art thou, Lord? And the Lord said, I am Jesus whom thou persecutest: it is hard for thee to kick against the pricks. And he trembling and astonished said, Lord, what wilt thou have me to do? And the Lord said unto him, Arise, and go into the city, and it shall be told thee what thou must do. And the men which journeyed with him stood speechless, hearing a voice, but seeing no man. And Saul arose from the earth; and when his eyes were opened, he saw no man: but they led him by the hand, and brought him into Damascus. (KJV Acts 9:4-9)This passage also says that Paul's companions heard a voice. That is explicitly contradicted elsewhere. This the McGrews recognize and accordingly claim to place no weight on the experience of Paul's companions earlier in CCRJ (p.24). They do appear to insist on the visual hallucination (p.25), however, but I'm unsure as to whether the difference between a visual, as opposed to merely auditory, vision is supposed to have a great effect. They rely heavily on the `complexity of the vision' - I wonder where that is - in dismissing delusion and hallucination as explanations of Paul's conversion. (Complexity-of-recall concerning hallucinations would validate the seeings of many a schizophrenic.) This does not change that Paul's conversion is almost surely sincere and almost surely involved a dramatic moment - more on this next - but I do not think that the McGrews were sufficiently diligent in explaining what exactly they reject, what they allow others to reasonably reject, and how those details should or should not be significant in making their case. And they did not make clear at the outset that the account of Paul's subsequent blindness would be involved, as it turned out to be, just as the supposed reaction of his companions on the road to Damascus would later be employed (p.38).
2. More culpable is their treatment of a hypothesis proposed by another scholar:
Perhaps aware of just how feeble [explanations like Paul not really converting or that he was the victim of a clever prank] might be, Strauss suggests delicately that Paul might have been overcome by feelings of doubt and guild during a thunderstorm [citation omitted]. This remarkable conjecture might be worth discussing were it not for the fact that the doubt, the guilt, and the thunderstorm are all invented out of whole cloth. Having made the insinuation, Strauss wisely drops this hypothesis and takes refuge behind the claim that the book of Acts cannot possibly be historical. (p.38)Let's stop and ask: is the suggestion that Paul - evidently a man capable of great feats of conscience, as zealots often are - might have felt guilt over his actions ridiculously implausible? Even SS Concentration Camp guards occasionally felt guilt and uncertainty. This is dismissed out of hand, but the previously cited passage (Acts 9:4-9) makes the accusation of whole-cloth fabrication that much weaker: "it is hard for thee to kick against the pricks" naturally translates as "you know what you're doing is wrong, and it bothers your conscience." It appears elsewhere in the KJV, and does not appear in the NIV in Acts 9, so I'll leave whether or not this passage is crucial to those with more experience in textual criticism. It's just not obvious prima facie that Strauss was wise to drop that very very silly and unserious hypothesis of his. No effort was made here to state the case charitably. No mention of the fact that Strauss' proposed external stressor, a thunderstorm, was not crucial to his idea. Any strong stimulus or external stressor may have triggered a dramatic event, assuming Paul was predisposed to conversion. And though the McGrews say that it is "an odd sort of hallucination that is followed by three days of blindness," they give no reason why that blindness - if at all considered a common fact - should be expected (by skeptics) had Paul received a genuine vision (p.38). Nor do they mention that temporary blindness is known to be associated with severe emotional trauma and stress.
I agree with the McGrews that Paul can not credibly be thought of as a conscious fraud. I think that his conversion was sincere, and it is very well evidenced, as is Paul's historical personage. But they fail to imagine why Paul, a sincere convert, might manufacture a vision story because he's a sincere convert. Imagine that you are Paul: you have been overcome with horror at the guilt of your actions, and you wish to make amends. As a new-found Christian, you care deeply about Christians and the fate of the persecuted churches. There is, however, a small problem: you do not expect these beleaguered communities to accept a killer with open arms and smiles. You especially do not expect this beleaguered communities to recognize your education and expertise as conferring status upon you. What would you do to convince them? Claim a vision, and proudly, and take the very real risks of doing so.
This `emotive-incentive hypothesis', along with a serious look at Strauss' explanation, allows us to safely assert that p(P|~R) is not significantly less than the value of p(P|R), which has no convincing support.
Before moving on to the disciples and the women, a post on the assumptions of conditional independence, its importance, and how the McGrews actually employ it is in order, especially for the 13 disciples. Once this is addressed, I think that the tentative finish line will be in clear view.
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