Abortion argument updated

Some time ago, I posted this argument that the concept of life beginning at conception is a fundamentally flawed one by showing it led to a contradiction with (what I think) are axioms that are taken for granted by the greater portion of the population. (read the original post if you haven't yet. You may have to refresh your browser after clicking the link)

So why would someone be unconvinced by this argument?

I wonder this because I'm sure that a pro-lifer would remain unconvinced after reading it.

It's true that human thought is habitual rather than logical, but it would be too easy to assume those who disagree with me have only an emotional, rather than logical, basis for their arguments.

So the question is, what assumption is made by pro-lifers that would allow them to logically conclude that life begins at conception, and is this assumption untrue?

Mind you, when I say assumption here, I mean nothing intrinsically bad. Assumptions are a necessary part of logic. There are certain statements that need to be taken as true without any logical or factual backing for logical analysis to serve any benefit whatsoever. Because without basic premises to work with, logic can tell us nothing.

So, after thought, I realized the best term to give this fundamental concept is that of a "Genesis Point", where all things have some specific point of origin. In the case at hand, if something is alive, then there must be a point where that thing's life first began.

So is this assumption of the Genesis Point fundamentally flawed?

The answer is yes, but I warn you, the following explanation is very mathematic, and borrows concepts from Set Theory, so it may be harder to follow for the layperson than my first argument.

Okay then.

If we consider all points of time as a set, with standard chronological order, then it's easy to see that time is a dense set - which means, essentially, if you pick any two points in time there will always be a point in time in between.

Now, let's define "Genesis Point" mathematically: For any condition that is true at some point in time, there is an earliest point of time where that condition is true.

Which is equivalent of saying that for any subset of time, there exists an earliest point of time in that subset.

Which, mathematically, means that time is a well-ordered set.

But time is a dense set, we've already stated. And a dense set cannot also be a well-ordered set.

Thus the "Genesis Point" assumption brings up a contradiction, and is therefore untrue.

That was easy. Next argument?

Update/Afterthought: This is not to say that life doesn't have a Genesis Point, just that the Genesis Point isn't true in general. But if life doesn't begin at conception, then any other point would seem arbitrary, so I would lean toward assuming that there is no specific point where life begins, but I have no way to prove that, either logically or empirically.