What do we mean by proof?

One of my sons, who is a graduate student in astrophysics, posted a thought-provoking article on "Using the Proper Method of Proof." Although the initial question he addressed concerned the possibility of mathematically proving the truth of the Book of Mormon, the ideas he had refer to all sorts of historical proof issues including those relating to family history. One statement he made caught my attention:

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.

I could say exactly the same thing about family history, only I would slightly change the quote to read as follows:

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 are sources backing us up.

Family historians, especially those with some formal training and a lot of experience, tend to speak in terms of "evidence" and "proof" when what they are really saying is that they have examined a number of sources and made their own conclusions about what is correct. Any conclusion drawn from historical sources is subject to revision upon the discovery of additional historical sources. To put this into a commonly used form, I might say; any proof of an historical fact is subject to revision upon the discovery of additional evidence.

Let me illustrate this with a hypothetical situation. Let's suppose that I am a reasonably competent and experienced family historian and I am investigating an ancestor named "John Doe." I find a U.S. Census record showing that he was 10 years old in 1910. The question is: was John born in 1900? This would seem to be an immediate conclusion but since I know that the ages shown on U.S. Census records are often approximations and inaccurate, I am not inclined to put much weight on the date of John's birth using only a Census record. But then later, I find a World War I Draft Registration card for John, where he states that he was born in 1899. I also quickly discover that in the 1920 U.S. Census his age is given as 19. Later, I find another document. This is an insurance record for a claim he made where he lists his birth date in 1901. Of course, I could go on with my example, but what is the evidence and how do I prove John's "real" birthdate? Would you change your mind about the accuracy of the date you choose to record as his birthdate year if all of the documents agreed? Would your conclusion be any more accurate simply because the documents were consistent? Could I claim that any one of the documents trumps the others and that therefore I have proved the year of John's birth? Would you simply opt out of the whole question and record John's birth year as "abt 1900?"

Historical proof, if you decide you want to use that term, is always document and source dependent and is further, always subjective. By the way, my son's post refers to Bayes' Theorem. Here is the theorem:

The explanation of the theorem goes like this:

In this formula, T stands for a theory or hypothesis that we are interested in testing, and E represents a new piece of evidence that seems to confirm or disconfirm the theory. For any proposition S, we will use P(S) to stand for our degree of belief, or "subjective probability," that S is true. In particular, P(T) represents our best estimate of the probability of the theory we are considering, prior to consideration of the new piece of evidence. It is known as the prior probability of T. See Beyes' Theorem.

The theorem is a method of understanding how the probability that a theory is true is affected by an additional piece of evidence. Take my hypothetical situation above for example. If I discovered another document containing information about John Doe's birth, what is the probability that it would change the theory I had about his actual birth date?

It is my personal opinion that quantifying the proof process with a formula is not really much help at all. Because the content of any unknown document is, of course, unknown until it is found, in an historical context, we can never determine the probability of an document or source's effect on our subjective belief until the document turns up.

I see the issue of finality in family history as a major obstacle to research. The idea that you have proved a fact from documents you call "evidence" obscures the tentative nature of historical inquiry. I am advocating that family history is open ended. Sometimes the probability of finding additional sources is rather low, but there is always a chance that one more document will change our pet proofs.