Additional implications of the Ancestor Paradox

In my last post, I began to explore the Ancestor Paradox, that is, that in each previous generation the number of your ancestors doubles. You don't have to go back more than a few generations before you realize that practically speaking, this cannot be true. So now let's look at some of the realities of genealogical research.

Although there are some people who can claim to have traced certain of their ancestral lines back 20 generations, in most instances, the practical limit is reached long before that number. In my case, after almost thirty years or so of genealogy, I have lines that end after only six generations. The main reason being the difficulty of identifying any further ancestors in female lines. But from lack of information, I have two lines that end in the 6th generation, nine that end in the 7th generation, thirty-two that end in the 8th generation and so forth. I could solve some of those problems, as did a few of my ancestors, by simply making up the next generation and linking into some famous or royal line of ascent.

But back to the issue at hand, even if there exists an Ancestor Paradox, what is the practical limit to modern genealogy? How far back can I expect to go in doing research? First of all, before you can answer this question, you have to make several invalid assumptions. In thinking this through, I have come up with what I will call the Ancestor Propositions.

Proposition No. 1: All historical (and genealogical) research will ultimately lead to unreliable or missing documents.

My first missing ancestor is the father or mother of Margaret Turner born about 1785.  Although recent research has identified her name, presently, no further information has been found about her parents. This is the classic "end of line." But let's suppose that I did more research and found her parents. That still leads to Proposition No. 1.

Proposition No. 2: All end-of-line ancestors, in fact, had parents.

Now why would I say this? Because we sometimes begin to doubt the truth of the statement. Some people just seem to arise spontaneously into the historical record.

Proposition No. 3: Despite the fact that all end-of-line ancestors had parents, all ancestral lines end.

This is really a re-statement of Proposition No. 1 as it relates to genealogical research. If you were Chinese or a Maori, you might have a line that goes back centuries, but still it would only be one line. All of the other millions of ancestors would be unidentified.

So how does this related to the Ancestor Paradox? The question is whether or not the paradox is purely logical or is based in fact. It is supposed that any vague property which is "sufficiently graded" originates a paradox similar to Heap Paradox. But since the term "ancestor" is not a fuzzy term but an historical verifiable fact, the paradox arises as a result of the lack of records.

Let's suppose, for purposes of this argument, that FamilySearch succeeded in working out the problems with New.FamilySearch.org and we could refer to a verifiable family tree of most of mankind. Would it prove or disprove the Ancestor Paradox? What is likely, is that it would take the same shape as my own genealogical lines that is, an engorged snake because it would prove the truth of Proposition No. 3.

Comments are appreciated.