John Loftus, probabilities and the Outsider Test of Faith

John Loftus is a former fundamentalist who has become an outspoken opponent of Christianity which he desires to debunk.

He has created what he calls the “Outsider Test of Faith” which he described as follows:

“This whole inside/outside perspective is quite a dilemma and prompts me to propose and argue on behalf of the OTF, the result of which makes the presumption of skepticism the preferred stance when approaching any religious faith, especially one’s own. The outsider test is simply a challenge to test one’s own religious faith with the presumption of skepticism, as an outsider. It calls upon believers to “Test or examine your religious beliefs as if you were outsiders with the same presumption of skepticism you use to test or examine other religious beliefs.” Its presumption is that when examining any set of religious beliefs skepticism is warranted, since the odds are good that the particular set of religious beliefs you have adopted is wrong.”

But why are the odds very low (instead of unknown) to begin with? His reasoning seems to be as follows:

1) Before we start our investigation, we should consider each religion to possess the same likelihood.

2) Thus if there are (say) N = 70000 religions, the prior probality of a religion being true is 1/70000 p(R), p(R) being the total probability of a religious worldview being true.

(I could not find a writing of Loftus explicitly saying that but it seems to be what he means. However I could find one of the supporters of the OST taking that line of reasoning).


Objective Bayesianism and the principle of indifference


This is actually a straightforward application of the principle of indifference followed by objective Bayesians:

In completely unknown situations, every rational agent should assign the same probability to all outcomes or theory he is aware of.

While this principle can seem pretty intuitive to many people, it is highly problematic.

In the prestigious Standford Encyclopedia of philosophy, one can read in the article about Bayesian epistemology :

“it is generally agreed by both objectivists and subjectivists that ignorance alone cannot be the basis for assigning prior probabilities.”

To illustrate the problem,  I concocted the following story.

Once upon a time, king Lothar of Lorraine had 1000 treasures he wanted to share with his people. He disposed of 50000 red balls and 50000 white balls.

Frederic the Knight (the hero of my trilingual Christmas tale) has to choose one of those in the hope he would get one of the“goldenen Wundern”.

On Monday, Lothar distributes his treasures in a perfectly random fashion.
Frederic knows that the probability of finding the treasure in a red or in a white ball is the same: p(r) = p(w) = 0.5

On Tuesday, the great king puts 10% of the treasure within red balls and 90% within white ones.

Frederic  knows that the probabilities are   p(r) = 0.10   and    p(w) = 0.90

On Wednesday, the sovereign lord of Lorraine puts 67% of the treasures in red balls and 33% in white ones.

Frederic knows that the probabilities are p(r) = 0.67 and p(w) = 0.33

On Thursday, Frederic does not know what the wise king did with his treasure. He could have distributed them in the same way he did during one of the previous days but also have chosen a completely different method.

Therefore Frederic does not know the probabilities;   p(r) = ?  and p(w) = ?

According to the principle of indifference, Fred would be irrational because he ought to believe that p(r) = 0.5 and p(w) = 0.5 on the grounds it is an unknown situation.

This is an extremely strong claim and I could not find in the literature any hint why Frederic would be irrational by accepting his ignorance of the probabilities.

Actually, I believe that quite the contrary is the case.

If the principle of indifference were true, Fred should reason like this:

“I know that on Monday my Lord mixed the treasures randomly so that p(r) = p(w) = 0.5
I know that on Tuesday He distributed 10% in the white ones and 90% in the red ones so that p(w) = 0.10 and p(r) = 0.90
I know that on Wednesday He distributed 67% in the white ones and 33% in the red ones so that p(w) = 0.67 and p(r) = 0.33
I know absolutely nothing what He did on Thursday, therefore I know tthat the probabilities are p(r) = p(w) = 0.5 exactly like on Monday. “

Now I think that this seems intuitively silly and even absurd to many people. There seems to be just no way how one can transform an utter ignorance into a specific knowledge.

Degrees of belief of a rational agent

More moderate Bayesians will probably agree with me that it is misguided to speak of a knowledge of probabilities in the fourth case. Nevertheless they might insist he should have the same confidence that the treasure is in a white ball as in a red one.

I’m afraid this changes nothing to the problem. On Monday Fred has a perfect warrant for feeling the same confidence.
How can he have the same confidence on Thursday if he knows absolutely nothing about the distribution?

So Frederic would be perfectly rational in believing that he does not know the probabilities p(r) = ? and p(w) = ?

Likewise, an alien having just landed on earth would be perfectly rational not to know the initial likelihood of the religions:
p(Christianity) = ?     p(Islam) = ?     p(Mormonism) = ? and so on and so forth.

But there is an additional problem here.

The proposition “the religion x is true one” is not related to any event and it is doubted by non-Bayesian (and moderate Bayesian) philosophers that is warranted to speak of probabilities in such a situation.

Either x is true or false and this cannot be related to any kind of frequency.

The great science philosopher Elliot Sobert (who is sympathetic to Bayesian epistemology) wrote this about the probability of a theory BEFORE any data has been taken into account:

Newton’s universal law of gravitation, when suitably supplemented with plausible background assumptions, can be said to confer probabilities on observations. But what does it mean to say that the law has a probability in the light of those observations? More puzzling still is the idea that it has a probability before any observations are taken into account. If God chose the laws of nature by drawing slips of paper from an urn, it would make sense to say that Newton’s law has an objective prior. But no one believes this process model, and nothing similar seems remotely plausible.”

He rightly reminds us t the beginning of his article that “it is not inevitable that all propositions should have probabilities. That depends on what one means by probability, a point to which I’ll return. The claim that all propositions have probabilities is a philosophical doctrine, not a theorem of mathematics.” l

So, it would be perfectly warranted for the alien to either confess his ignorance of the prior likelihoods of the various religions or perhaps even consider that these prior probabilities do not exist, as Elliot Sober did with the theory of gravitation.

In future posts, I will lay out a non-Bayesian way to evaluate the goodness of theory which only depends on the set of all known facts and don’t assume the existence of a prior probability before any data has been considered.

As we shall see, many of the probabilistic challenges of Dr. Richard Carrier against Christianity kind of dissolves if one drops the assertion that all propositions have objective prior probabilities.

To conclude, I think I have shown in this post that the probabilistic defense of the Outsider Test of Faith is unsound and depends on very questionable assumptions.

I have not, however, showed at all that the OST is flawed for it might very well be successfully defended based on pragmatic grounds. This will be the topic of future conversations.