Friday, April 3, 2015

Using the Proper Method of Proof

A while ago someone left a comment on my blog challenging me to use Baye's Theorem to find the probability that the Book of Mormon is a historical document. At the time it struck me as odd that some one would insist on using Baye's Theorem to prove a historical fact. But it prompted me to do some reading on Baye's Theorem and I found that there are a whole group of people who try to use Baye's Theorem to prove all sorts of things (there are also a great number of people who say they are wrong in doing so).

The reason why he insisted on using Baye's Theorem stems from the fact that all things pertaining to numbers and math are incontrovertible, at least to rational minds. The thinking goes that no rational person can deny that 1+1=2, and by extension, if something can be proved using math then no one can say otherwise (we'll just ignore the incompleteness theorem for now).

So there is a general feeling that if something can be proved or disproved, or found probable or improbable using math, then no one can say otherwise and every rational person must accept the same conclusion. Thus the thinking goes, "If person X is a rational person then they will apply math to problem A. X applies math to A and reaches conclusion Q. If X accepts Q then they are rational. If X rejects Q then they are irrational."

So when the commenter left his comment challenging me to use Baye's Theorem to find the probability that the Book of Mormon is a historical document his thinking probably went something like this, "I am a rational person and I know the Book of Mormon is not historical. Therefore if someone else uses math on the question of the historicity of the Book of Mormon, and they are rational, then they will come to the same conclusion that I did." (I would be surprised if he actually thought that.)

The tendency is to consider something we know to be true, and because we think we are thinking rationally, we conclude that if someone else uses a rational thought process they will always come to the same conclusion. If they come to a different conclusion then we tend to conclude that they are irrational, especially when there is *math* backing us up.

So I was challenged to use Baye's Theorem in the hope that I would come to the exact same conclusion that he did. Fortunately that is not how proof works. As Aristotle put it:
“It is the mark of an educated man to look for precision in each class of things just so far as the nature of the subject admits; it is evidently equally foolish to accept probable reasoning from a mathematician and to demand from a rhetorician scientific proofs.”
Sometimes people try to describe this and say, "The truth is messy." or "Proof in history/religion/field-of-study-that-is-not-based-in-math is messy." I prefer not to think of it in that way. Understanding the different methods of proof requires a certain level of humility and maturity of thought. When humility, maturity and direct experience with the subject matter are achieved then any proof is easy and flows naturally. It is only pride, immaturity, and inexperience that make any proof hard.

When we have gone through similar mental processes and have had similar experiences then arriving at the same conclusion is easy and natural. If not then proof is hard, if not impossible. This is perhaps what Wittgenstein was thinking when he wrote:
"This book will perhaps only be understood by those who have themselves already thought the thoughts which are expressed in it—or similar thoughts.... Its object would be attained if it afforded pleasure to one who read it with understanding."
If we are to prove something to anyone else we must recognize that it is not so much about the method of proof, for no single method can be used for all truth. You can't throw math at everything and think it constitutes proof. I think there is something inherent in all intelligence that requires personal experience for any proof to be accepted.

1 comment:

Anonymous said...

I think it's silly that someone would suggest using a theorem related to probability to prove/disprove the Book of Mormon...