Monday, January 12, 2015

Against objective probability

Faith is an attitude or feeling whereby believers attribute a higher degree of probability to the evidence than what the evidence calls for. (OTF, p.207)

This assumes that there is an objective quantity of probability that the evidence calls for. 

I am skeptical of this kind of claim. I don't think there is a non-relative probability that the evidence calls for. There are only probabilities relative to some existing prior probability. Evidence doesn't operate from a "ground zero" starting point, it starts from wherever people happen to be. 

I know that Richard Swinburne thinks that you can get to some Archimedean point through his conception of simplicity, and some people think you can get it from frequencies. I don't think these arguments work. 

Here is what I put in my Infidels paper on miracles

IV. Probability and its Empirical Foundations

According to Hume, probabilistic beliefs concerning the intentions of a supernatural being are inadmissible in reasonings concerning matters of fact because these beliefs fail to be grounded in experience. This insistence has been enunciated by Bayesian theorists, and it is the frequency theory. But the frequency theory has fallen on hard times, and most Bayesian theorists do not accept it, largely because of difficulties related to the problem of the single case.
The problem is this. Frequencies give us information as to how often event-types have occurred in the past. But we often want to know the probability of particular events: this coin-toss, this horse-race, this piece of testimony to the miraculous, etc. If we are to accept Hume's conclusion that testimony to the miraculous ought never to be accepted, we need to show more than just that rejecting testimony to miracles in general is a good idea because false miracle claims outnumber true ones. Many Christians are skeptical of miracle claims put forward by televangelists, but nonetheless believe that the evidence in support of the resurrection of Jesus, and perhaps in support of some modern miracles, is sufficient to overthrow our ordinary presumption against accepting miracle reports.
Frequentists have attempted to assess the prior probability of individual purported events by assimiliating them some class of events. Thus, we assess the probability of a particular coin-toss as 1/2 in virtue of its membership in the class of coin-tosses. But the question is which class the relevant reference class is. The claimed resurrection of Jesus falls into many classes: into the class of miracles, into the class of events reported in Scripture, the class of events reported by Peter, the class of events believed by millions to have occurred, into the class of events basic to the belief-system of a religion, etc. Of course it is what is at issue between orthodox Christians and their opponents whether the class of miracles in the life of Jesus is empty or relatively large.
Wesley Salmon attempts to solve this problem by defining the conception of an epistemically homogeneous reference class. A class is homogenous just in case so far as we know it cannot be subdivided in a statistically relevant way. Thus, according to Salmon, if Jackson hits .322 overall but hits .294 on Wednesdays, the Wednesday statistic is not to be treated as relevant unless we know something about Wednesday that makes a difference as to how well Jackson will bat. Thus, according to Salmon, the relevant reference class is the largest homogeneous reference class; we should try to get a sample as large as we can without overlooking a statistically relevant factor.[13]
There are two difficulties with this method as an attempt to satisfy Hume's strong empiricist requirements for properly grounded probability judgments. First, questions of statisical relevance cannot be fully adjucated by appeal to frequencies. Second, the very heuristic of selecting the largest homogeneous reference class cannot be read off experience.
On the first point, consider the situation of a baseball manager who must choose between allowing Wallace to bat or letting Avery pinch-hit for him. Wallace has an overall batting average of .272, while Avery's is .262. But the pitcher is left-handed, and while Wallace bats .242 against left-handed pitching, Avery bats .302. Nevertheless, the pitcher is Williams, and while Avery is 2-for-10 against Williams, Wallace is 4-for-11. Have these batters faced Williams too few times for this last statistic to count? And can this be straightforwardly determined from experience? What is needed is a judgment call about the relevance of this statistical information, and this judgment cannot simply be read straightforwardly from frequencies. The frequentist's epistemology for probabilistic beliefs, insofar as it is an attempt to conform to empiricist/foundationalist constraints, seems impossible to complete.
On the second point, is the heuristic of selecting the smallest homogeneous reference class justified simply by an appeal to experience? Admittedly it makes a certain amount of common sense. But this attempt to go from a statistical "is" to an epistemological "ought" seems to suffer from with the same (or worse) difficulties that getting "ought" from "is" suffers from in ethics, and here again Hume's empiricist/foundationalist assumptions impose an impossible burden on probability theory.
The frequency theory seems clearly to be the theory of priors that Hume would have adopted had he been involved in the contemporary Bayesian debate on prior probabilities. But even this theory fails to adjudicate the issue concerning miracles in Hume's favor or in favor of the defenders of miracles, because it lacks the resources within itself to select the appropriate reference class. This inability to provide determinate answers to questions of probability is what makes this theory inadequate for resolving the question of miracles. Therefore Hume cannot justify his claim that it is never rational to believe testimony to any miracle on the grounds that miracles are less frequent in experience than false miracle reports.[14]

That doesn't mean that we can't move toward objectivity. We can. Evidence, if pursued, can in theory "swamp the priors." I think science works that way. It isn't as if scientists all actually put aside their biases before starting to do science. It is just that, in many cases, priors are swamped, and maybe all the defenders of the opposite position all die off.

Here is Elliot Sober's treatment of Bayesian theory. 


Angra Mainyu said...


Even though the probability a person ought to assign to a hypothesis depends in part on the information available to that person (or the observations, if you like), that doesn't preclude objectivity in a colloquial sense - namely, that there is an objective fact of the matter as to what probability a specific person should assign, or shouldn't assign; this does not require specific precise numbers - as it does not preclude it in the case of morality (i.e., moral obligations depend in part on the information available to the person too). That does not entail objectivity in some other, technical senses, but seems to be enough for claim in the quote.

So, with regard to the quote, I've not read Loftus's book, so I don't know whether he requires that interpretation of probability elsewhere, but going by your quote, there are at least some ways in which one may say a person is assigning greater probability to a hypothesis than what the evidence calls for (or perhaps, what observations and arguments call for?; there are interpretations of evidence that wouldn't work here.):

a. Based on the prior probabilities and the observations, she ought to assign a lower probability.
b. She has wrong priors.
c. a. plus b.

In category a., the person is just making the wrong assessment given all of the observations available to them (even those prior to their exposure to the religion in question).

Category b. may be more controversial, since one may wonder whether there is such thing as the wrong priors. I think there is for humans, but in any case, it seems a. can [usually] do the work required here.
Take, for example, a hypothetical extreme presuppositionalist who claims he assigns the resurrection of Jesus a probability P=1, as a prior.
That seems to fall into category a, because even if he claims it's a prior, there was a time when he wasn't like that, and given his priors and all of the observations, he ought not to have given the resurrection a high probability, let alone one (of course, I don't expect Christians to agree that he ought not to have given the resurrection a high probability, but you may pick a hypothetical Mormon or Muslim or Hindu presuppositionalist if you like; the point about probability is the same).
Then again, it may be that after their commitment to their ideology (religion or not) affects the way their mind works, changing the priors into wrong ones, so b. applies too.

But now let's consider someone who isn't a presuppositionalist. One may claim that if they assign more than 1/2 (or, for that matter, more than 1/1000000, so put a number) to Jesus's resurrection - at least, in the context of today's world, after reading the Bible, having access to the internet and/or books, etc. -, they're assigning probability they ought not to assign; the observations do not call for that, given their priors - or else, they have the wrong priors.

Victor Reppert said...

When it comes to the Resurrection, I think the relevant issues are so complex, and involve so many factors, that I am very disinclined to issue irrationality charges either way on that issue.

Angra Mainyu said...

Okay, noted. We disagree about it, but we don't need to debate that in this context, since the point I was trying to make wasn't about the resurrection of Jesus (we might consider the claim that archangel Gabriel gave the Quran to Muhammad, or some claim about Joseph Smith, etc., instead.), but about a potential interpretation of "what the evidence calls for".

Victor Reppert said...

You can have irrationality, surely, and drawing of wrong conclusions. However, there is no probabilistic algorithm for correct priors.

Angra Mainyu said...

Do you think Loftus's quote above requires an algorithm for correct priors?

Maybe he requires that somewhere else (I don't know), but going just by that quote, there are plausible interpretations that do not require anything like that (e.g., see my first post on that).

Victor Reppert said...

Possibly not. But, do you think that it's plausible to define faith the way he does, making it out to imply fideism.

Angra Mainyu said...

I don't have a definition of "faith" to offer (or of most words that we use, beyond dictionary approximations, for that matter), and also, I do not intend to get into a comprehensive defense of my take on some aspects the psychology of religious and generally ideological beliefs (a matter closely tied to Loftus's definition) in this context. But that said, my impression is that and Loftus's definition gives an approximate though not entirely accurate description of a psychological phenomenon that is usually called "faith", in one of the senses of the word (there are several).

That sort of attitude is, in my view, widespread among religious believers - as well as believers in other ideologies not usually called "religion" -, but not universal: for example, some people would stop believing pretty quickly if they were to actually think about whether their religion is true (some do), often because they lacked the attitude in question - they are just mistaken, probably from childhood indoctrination, and they haven't actually looked at the matter yet.

By the way, I don't think the definition implies fideism, in the sense that a person may have faith without being a fideist - but again, I haven't read Loftus's book, so I may be misinterpreting -, for the following reason:

Fideism (going by Plantinga's definition; if you prefer another one, please let me know which one) requires that a person consciously, and deliberately, promote or choose faith.

On the other hand, the attitude involved in Loftus's definition (if I'm getting it right) does not require that a person even know that she has it.

For example, I think political ideologies like communism, or the belief that a person is a hero, a great leader, etc. (e.g., Fidel Castro, Che Guevara, Mao Zedong, etc.) are usually held on faith in the sense of the word in question (at least in the West; I don't know how it is in, say, China), even though most of the people who have such beliefs do not know that, and would strongly disagree with someone who said that they hold their beliefs on faith, or who (to avoid misunderstandings) tells them that they have that sort of attitude.