First order logic, set theory and God

[Reltzik]

Below is a copy-paste of my own thread that was posted in another forum. I'm reposting it here in hopes to spark an intelligent discourse on what I believe to be the most refined proof of God's existence.

Here it goes.

[snip]

With that being said, I would be more than curious to see if anyone could spot a noticeable error in Hatcher's logical deduction

I'd spotted some big errors in this before I'd even finished reading.

Let us consider phenomenon H, the set of all humanity, which is a composite consisting of all humans alive.  Leaving aside the question of where the first humans come from, is H self-caused?

Well, certainly a significant cause of each human's existence is the existence of their parents, who are also in H, or at least were at one time.  In this sense, H seems to be self-caused, because every (present) component of H owes its existence to H itself.  This seems to put the lie to the principle of limitation.  The counterexample provided -- that cars do not produce their own steering wheels -- is an appeal to a particular system which does not maintain and reproduce itself, and does not cover systems that do exactly that.

For another example, whether or not we appeal to dualism, we might consider any given human being B to include the sum of all their constituent cells (and chemicals and so forth) in their present arrangement.  Yet no adult human contains all their original cells.  Each cell currently in our bodies arose from the mitosis of previous cells in the system.   Nor can we appeal to the causation of the chemicals making up those cells, because the atoms in our bodies are not the ones we were born with.

In both systems, each component of the system is caused by the existence of the system itself.

A plausible objection to this might be that the system is defined in part by its components, and that every time a new component is produced and introduced into the system (a new human for H or a new cell for B, it produces a new system caused, in part, by the existence of the old system, which no longer exists because it has been transformed into the new system.  In other words, we might say that Hx -> Hx+1 and that Bx -> Bx+1 ... though I would caution against assuming that either process is mathematically discrete.  I would also caution against assuming a first cause in all such systems, such as an index of 1 or 0 before which no system of the sequence could exist.  That might be so in the case of both examples that I provided, but as the car example (yet again) illustrates reasoning from one specific example to the general case is bad logic.

However, plausible though this objection might be, it is clearly not one that the provided proof is ready to employ.  If we transform V, the universe, to a sequence of universe-states Vx, Vx+1, and so on, or perhaps a continuum of non-discrete states, then the logic no longer works.  We would again encounter infinite regress, which you say the proof avoids and does not address.

Yet even were we to accept the entirety of this proof as correct... what sort of god would have been proven?  It would be a simple god, one with no components whatsoever.  Such a god could not have emotions, or thoughts, or memories, or desires, or a plan, or goals, or anything approaching what we would think of as a mind or the components thereof. To call it a god at all is very much at ends with any god that a theist might be attempting to prove as well as anything a typical person might think of upon hearing the word "god". The proof appeals to a definition of God, but you have not provided that definition and so it cannot be addressed here. However, it is obvious that such a definition, if properly applied, is either far distant from or far too broad for any conventional notion of the word "god", and so should be referred to by a different word to avoid confusion.

As a third, related objection, how is this a proof of a god at all?  Suppose I were to say that G is not actually a god, but the sum total of all joules of physical energy in the universe.  Matter, motion, chemistry, et cetera are all basically energy arranged in different ways, and while energy might be transformed from one form to another, it does not appear to ever actually begin or cease to exist.  That would mean energy is either self-caused, which would make IT the unique self-caused phenomenon that God is supposed to be, or uncaused, which would undo the principle of sufficient reason and cause the whole logical house of cards to come crashing down.

Given how these problems quickly popped out to me, I'm sure there's a lot more wrong with this proof that an exhaustive survey would reveal. However, I just woke up, and I don't feel like chasing down all the rabbit holes.