spamandham

Your premise is plausible for the most part, just not the simplest explanation. I think I've said this many times.

Doug Shaver

No need to suppose. I do accept it.

I thought I answered that in my last post. You're not providing any evidence to support it. Or at least, I'm not seeing any.

You're apparently attempting to present a probabilistic argument, but you're omitting a lot of premises that would have to be included to make it cogent.

spamandham

Here is the evidence:
- All the letters are purported to be written by Paul
- All the letters have similar construct, a letter from Paul providing some kind of guidance
- All the letters have arrived to us via the same entity
- Six of the letters are established to be frauds
- The remaining 7 letters are not established to be authentic.

Since we have no a priori knowledge that any of the texts are authentic, and have no special knowledge that the remaining texts are more likely authentic than those that are proven inauthentic, in effect, we have drawn 6 texts at random from an equivalent set, and all turned out to be inauthentic.

Let p be the probability that a given text of the set is authentic. The probability of selecting 1 inauthentic text from the set of 13 is (1-p).

Given that you have selected an inauthentic text, the probability of an authentic text in the remaining set of 12 is increased, since you've removed one of the inauthentic ones. The probability of an authentic text in the remaining 12 is now p*13/12.

The probability of selecting an inauthentic text is now (1-p*13/12). Again, the probability of an authentic text is increased, now by 12/11, so it is now p*13/11, and so on.

The probability of selecting 6 inauthentic texts in a row is thus:
P = (1-p)*(1-p*13/12)*(1-p*12/11)*(1-p*11/10)*(1-p*10/9)*(1-p*9/8)

Now we can try various values of p that make this a reasonable probability. The goal is to be able to say "With {X} confidence p is less than {Y}".

p 0.5	0.36	0.2	0.1	0.04	0.03	0.02	0.01
P 0.01	0.05	0.2	0.5	0.77	0.82	0.88	0.94

From the table we can make the following statements:
a. With 50% certainty, we know the probability of an authentic text is less than 10%

b. With 80% certainty, we know the probability of an authentic text is less than 20%

c. With 95% certainty, we know the probability of an authentic text is less than 36%.

Considering that in this field we are generally dealing with lots of uncertainty, (b.) is probably already overly generous. The probability that the remaining texts are authentic is (1-(1-.2)^7) = 0.000001, ....1 in 100,000

This is getting close to lottery odds. It's crazy to give the idea any serious consideration. You should be chastised for demanding these calculations. Common sense would have given you the same conclusion.

hjalti

Nope.

This is simlar to having 13 women taking a test that can only give the results "pregnant" or "don't know". If the 13 women take the test, and we get 6 "pregnant" and 7 "don't know", I would not conclude that the 7 other must be pregnant.

spamandham

The one sided nature of the test does not significantly impact the sample probability. But if it makes you feel better, I'll go ahead and spot you 2 orders of magnitude and say the odds are only 1 in 1000 that the remaining 7 are authentic.

Do you want a 3rd order of magnitude?

aa5874

The authenticity of the Pauline letters are not at all similar to YOUR pregnancy tests.

The Pauline letters are all claimed to be from a single writer but it has been deduced that there were more than one author.

Now, if a woman takes 13 pregnancy tests at the very same facility and 6 of 13 are negative what are the chances that she is really pregnant?

hjalti

If your calculations are flawed, raising the the odds arbitrarily isn't the right response.

Doug Shaver

If that's how you feel about anyone who disagrees with you, then I see no point in continuing this discussion.

DCHindley

I tried your suggestion, and was able to see a different portion of the text than before. It seems that the selection you can see varies upon each access or day. Luckily I could see most of the Thesis statement, and I'll comment on it later after I have had a chance to review it.

DCH

spamandham

You haven't identified any flaws in the calculations, nor in the methodology. All you've done is vaguely assert there is something wrong because the test is only capable of identifying fraud, and even then only sometimes. You haven't explained how that fact impacts the calculations, or the probabilities.