Bayes Theorem Argument of Dr. Peter van Kleeck

Starting at around the 48th minute of his debate with Dr. James White, Dr. Peter van Kleeck made the following argument (link to video): 

Thus far I have argued that 

1. God's word regards itself in autographic terms.

2. Given argument (1) the reformers historically regarded the TR as equal to the autographic New Testament text.

[3.] Finally my third argument is the probability that TR is equal to the autographic New Testament -- and this is very high. In order to make this argument, I borrow certain argumentative scaffolding from the Christian philosopher Richard Swinburne in his argument for the resurrection. If we are to make analysis of a given historical event -- like the TR as the word of God is equal to the New Testament autograph -- then we would expect to find three kinds of evidence:

[I] The first kind of evidence we would expect to find is posterior historical evidence, like artifacts, manuscripts, and testimony regarding the autographs.

[II] The second kind of evidence we would expect to find is called background evidence. This kind of evidence asks if there has been any past behavior on the part of the author of the autographs which would precipitate the existence of the autographs.

[III] Third and final | The third and final kind of evidence we would expect to find is prior historical evidence or the evidence that the author of the autographs would have good reason to bring the autographs into existence.

In short if the TR is the word of God -- is equal to the New Testament autographs -- we would expect that 

(1) God is the kind of being that created and preserved the autographs; 

(2) God would have good reason to create and preserve the autographs; 

(3) We would then expect to find artifacts, manuscripts, and testimony of the creation and preservation of the autographs.

For the Christian, that God is the kind of being that created and preserved the autograph seems obvious, seeing that God has promised to preserve his words and given the fact that | the autographs | the autographs are said to be God breathed. Furthermore, God has made the church to be of such a nature to receive these autographic words because the same God who gave these autographic words by inspiration also indwells the church.

Given number (1) that God would have good reason to create and preserve the autographs is very reasonable for the Christian and that as the Westminster Confession put it, God reveals himself through the autographs, "for the better preserving and propagating of the truth and for the more sure establishment and comfort of the church against the corruption of the flesh, the malice of Satan, and of the world," as a result of number (1) and number (2) we would expect to find the autographs and testimony to them among God's people. 

As I pointed out in my second argument above, that is indeed the case for the Protestant Scholastics. In sum, we see that God is the kind of being that would | create | preserve the autographs. Additionally, God had ample good reason to create and preserve the autographs. As a result, there is a robust testimony to the fact that we do indeed have the autographs in the Textus Receptus.

Let us now employ Bayes' theorem to determine the probability that the TR as the word of God is equal to the New Testament autographs given the evidence mentioned immediately above. 

Let the conjunction of these three types of evidence posterior, background, and prior be represented by E and let the assertion (I'll put it up here for you guys) and let the assertion that TR is the word of God is equal to the New Testament autographs be represented by T. As a result, we get the following probability equation.

The probability of T given E equals the probability of T given E, which is high, let's say 0.9, that number multiplied by the probability of E given T, which is also high, again let's say 0.9. This equals 0.89. 

We then move the numerator into the first set of brackets in the denominator and add that to the probability of not T given E, which is low given the converse in the numerator, let's say 0.1, multiplied by the probability of not E given T, which is also low given the converse in the numerator. 

As a result we get a .89 over 0.9, using a probability of 0.98 repeating or 98 percent -- greater than 98 probability, which is to say that under these conditions the fact that the TR is equal to the New Testament autograph is nearly certain.

Furthermore is highly improbable that God would create and preserve two contradictory autographs given our background evidence and prior evidence. Seeing then that the TR accords with the requisite background prior in posterior evidence thusly presented and that my opponent nowhere claims that he has an alternate but commensurate autograph, it || remains highly probable that the TR in the New Testament autograph || remains highly probable that the TR is the New Testament autograph, seeing that no meaningful undefeated defeater has arisen in the form of an alternate and superior autograph, which is also consistent with E. 

In conclusion, I have offered three arguments in defense of the proposition the TR as the word of God is equal to the New Testament autographs: 

argument one: God's word regards itself in autographic terms 

our argument two: because God's word regards itself in autographic terms the reformers historically regarded the TR as the autographic New Testament text 

in argument 3: the probability that the TR is equal to the autographic New Testament is very high.

As such, I encourage you, based on the autographic terminology of scripture, robust reform bibliology, and the overwhelming probability that TR is equal to the New Testament autograph, that you too accept the TR as the word of God and equal to the New Testament autographs. Thank you.

Bayes' Theorem is usually represented this way:

P(A|B) - The probability of A being true for a sample given B being true for the sample. 

P(B|A) - The probability of B being true for a sample given A being true for the sample.

P(A) - The probability that A is true for a sample.

P(B) - The probability that B is true for a sample.

We could take an intuitive American example as an illustration. Let

P(A|B) - The probability of [person in front of me is a cop] given [person in front of me has a gun]. 

P(B|A) - The probability of [person in front of me has a gun] given [person in front of me is a cop].  

P(A) - The probability of [person in front of me is a cop].

P(B) - The probability of [person in front of me has a gun].

P(A|B)	20%	0.20
P(B|A)	99%	0.99
P(A)	10%	0.10
P(B)	50%	0.50

P(A|B)	2%	0.02
P(B|A)	99%	0.99
P(A)	1%	0.01
P(B)	50%	0.50

P(A|B)	99%	0.99
P(B|A)	99%	0.99
P(A)	1%	0.01
P(B)	1%	0.01

Now when we consider PvK's argument, what are we supposed to use?

Solution	0.987804878
P(T|E)	0.9
P(E|T)	0.9
P(-T|E)	0.1
P(T|-E)	0.1

Solution	0.9
P(T|E)	0.1
P(E|T)	0.9
P(-T|E)	0.1
P(T|-E)	0.1

Solution	0.9
P(T|E)	0.9
P(E|T)	0.1
P(-T|E)	0.1
P(T|-E)	0.1

It looks as though PvK was not sure what the P(B) value was, and so was trying to substitute the law of total probability, namely:

P(B) = P(B|A)P(A) + (PB|-A)(P(-A)

That still doesn't quite work, though, so I'm not sure where he got his equation.

In any event, coming back to his notation:

E = The conjunction of posterior, background, and prior evidence

T = the TR is equal to the New Testament autographs 

The question to be solved is this: what is P(T|E)?

To answer that using Bayes' Theorem, we would do the following:

Ask the question, what is P(E|T)?  That is to say, given the TR is equal to the New Testament autographs, what is the probability of having the conjunction of posterior, background, and prior evidence? 

In other words, in what percentage of cases where the TR is equal to the New Testament autographs, will we get such a combination of evidence?  

We then need to ask, in what percentage of cases is the TR equal to the New Testament autographs, and in what percentage of the cases is there a conjunction of posterior, background, and prior evidence.

Literally all of this data is just made up.