(Huh. One of the ancestors to this comment - several levels up - has been downvoted enough to require a karma penalty. I wonder if there should be some statute of limitations on that; whether, say, ten levels of positive-karma posts can protect against a higher-level negative-karma post?)
A4. Let S be any endless chain in E. Then there is some z in E such that every x in S is a proper part of z.
An interesting assumption. Necessary for theorem 3, but I suspect that it'll mean that the original cause described in theorem 3 will then very probably be an entity z that is the earliest cause.
I also note that, while z consists of all the parts in the endless chain, there is no guarantee that any of the elements in the chain, even those that cause other elements in the chain, is in any way a cause of z. In fact, the way that z is defined, z may well be causeless (or, then again, z may have a cause). While I can't actually find anything technically invalid in theorem 3, or in assumption 4, I get the general feeling of wool being pulled over my eyes in some way.
When I consider B3, it becomes even more important to note that z as a whole is not necessarily caused by any element that is a proper part of z. The cause of a part may or may not be the cause of the whole.
Hmmm... B4 appears to be pretty much just shoehorning monotheism in. It seems a questionable assumption; if I decide to get into my car and drive, and you decide to get into your car and drive, and we drive into each other, then we both are causes of the resultant accident but we are not the same. (We are not causeless, either, so it's not quite a counterexample, just an explanation of why I don't think B4 is justified,) B5 is unsupported, but I can prove that all entities that I will ever observe evidence of are causally connected (i.e. they are connected to the effects on my actions of having observed them) so it will look true whether it is or not.
Though I can raise questions about your assumptions, I can't find anything wrong with your logic from then on. So congratulations; you have a very convincing argument! ...as long as you can persuade the other person to accept your assumptions, of course.
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