The arguer could then tweak premise 2 so it states that any such generalised infinite chain (one allowing repeated elements) still has a lower bound (some strict cause outside the whole chain) and apply an adapted version of Zorn's Lemma to still get an uncaused cause in the whole system.
That's just assuming the result you want. I don't think it makes a strong argument.
(But even then, there is a patch: the arguer could claim that the whole chain or loop should count as a combined "entity" with no cause, ie there is still some sort of uncaused cause in the system).
Counting a loop as a combined entity, on the other hand, could be very useful. The combined-entity loop would be caused by everything that causes any element in the loop, and would cause anything that is caused by any element in the loop. Do this to all loops, and the end result will be to eliminate loops (at the cost of having a few extremely complex entities).
This seems fine as long as there are only a few, causally independent loops. However, if there are multiple loops that affect each other (e.g. something in loop A causes something in loop B, and something in loop B causes something in loop A) then this simply results in a different set of loops. These loops, of course, can also be combined into a single entity; but if the causality graph is sufficiently well connected, and if there is a large enough loop, the end result of this process might be that all entities end up folding into one giant super-entity, containing and consisting of everything that ever happens.
I have heard the theory before that the universe is a part of God, backed by a different argument.
I agree with you that the really weak part is just defining the uncaused cause to be "God". Apart from confusing people, why do that?
It honestly looks like a case of writing down the conclusion at the bottom of the page and then back-filling the reasoning. He can't justify that part, so he defines it quickly and hopes no-one pays too much attention to that line.
And thanks for spotting the non-uniqueness by the way... the argument as it stands does allow for multiple uncaused causes. To patch that
Why do you want to patch that? A quick patch looks like (again) writing the conclusion first and then filling in the reasoning afterwards.
OK, I think we both agree this is not at all a strong argument, that the bottom line is being written first, and then the premises are being chosen to get to that bottom line and so on. However, I still think it is fun to examine and play with the argument structure.
Basically, what we have here is a recipe:
Take some intuitions.
Encode them in some formal premises.
Stir with some fancy set theory.
Extract the desired conclusion : namely that there is an "uncaused cause"
It's certainly interesting to see how weak you can make the ingredient...
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