First order logic, set theory and God

[Belacqua]

Now for P3, on the other hand, I don't fully agree with.

Agreed, P3 is less self-evident. I was trying to think of counter-examples on the bus this afternoon.

P3. The principle of limitation: For all A, where A is an element of B, B -> A does not hold. This says a system (which Hatcher represents as a set) cannot be the cause of its own components. Hatcher justifies this by explaining any system has (1) form (the parts) and (2) function (the relationship between the parts). A car (the system) cannot be the cause of its own steering wheel (a part), because the car does not even logically exist until the steering wheel exists. Thus the car's existence cannot precede the steering wheel's existence.

So let's take this at face value... The parts separately, before they are assembled, cannot be caused by the car. Because the car doesn't exist until the parts are assembled. 

Of course we have to distinguish here the essence of the car from the accidents of the car. The parts that are essential -- that define what a car is -- have to be assembled to make a car. That seems right. Once the car is assembled it might include a little 3-D printer that adds non-essential parts, like a hood ornament. But we can't say that a 3-D printer is a part of the car until the car exists. 

So I'm not seeing the fault in P3 yet, if there is one. 

Earlier on, Reltzik made a reasonable objection to this, by saying that all the components of a set or system as currently existing may have been formed by previous parts of that set. His example was just the group of all people. He rightly pointed out that all currently alive people have been made by the group of people, some of whom are still alive and some of whom aren't. 

dron3 replied this way: 

Let E be the collection of all components of H, such that E∈H

[...]

Precisely because the whole H does not even exist (to be a cause of anything) until all of its components E exist. However, the premise that " every (present) component of H owes its existence to H itself" is not fallacious by any means, since nothing excludes that a phenomenon (in this case H) cannot contain within itself a cause E for its existence. The conclusion you draw from it however, is logically unsound. It's not because the cause E originates within H that H is therefore, self-caused. It simply means that H is other-caused by E. E being the cause of H for which it is part, certainly doesn't imply that H→H but instead E→H.

This is a little tricky for me. But maybe I can extend the 3-D printer analogy... Suppose we have a little 3-D printer that extrudes all the parts of the car and somehow assembles them, in the process embedding the printer into the car. As far as I can tell, dron3 would say that this doesn't mean the car is self-caused. He would say it is other-caused by thingy which is (later on) included in the car. 

I freely confess this is all a work in progress as far as my understanding is concerned. If you have objections to this I'd be glad to read them.

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Do we really have any reason to think that infinite phenomena have causes? All phenomena we have observed are finite, so that suggests that we only know about finite phenomena.

I'm not sure what you mean by "infinite phenomena." Are you thinking that a First Cause has to be infinite? 

I don't think we've gotten to that part of the argument yet.

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Well, I don't think that resolves it to a single PSR, but let's see what we can do with it.  

It's the PSR that the OP's argument asks us to use. So for the purposes of the argument, that's what we're using. 

First, I think that it's rather elementary that a thing cannot cause itself, otherwise that thing would exist before it exists, and that would be absurd.

OK, so I think you're on board with P1. 

 So that leaves only other caused things, which yields an infinite series of ordered causes and no first cause.  Do you agree?

I think you're anticipating the end of the argument here. dron3 claims that with the combination of the three principles laid out in the OP, he avoids an infinite regress of causes. So I'm waiting to figure that out before I agree. 

Personally I don't see yet how it avoids such an infinite regress, but I'm still working on it. I hope that dron3 wasn't driven off by the childishness earlier on the thread, because I hope he can clarify.

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Once you complete the car, removing any piece or function of that car will not stop it from being a car, but rather just a broken car.

Right, this is relevant, I think. 

Aristotelians talk about essentials and accidents, and how to define a thing. A dog is a thing with four legs, and if it loses a leg or two it is still a dog, but a sort of non-standard one. How much you can take away and still have a dog is kind of a tricky question.