It's come up a fair few times recently, and I'd like to see what people think.
First, a few versions of it I have found
P1 Every finite and contingent being has a cause.
P2 A causal loop cannot exist.
P3 A causal chain cannot be of infinite length.
C1 Therefore, a First Cause (or something that is not an effect) must exist.
P1Whatever begins to exist has a cause.
P2The Universe began to exist.
C1Therefore, the Universe had a cause.
P1 Everything that exists contingently has a reason for its existence.
P2 The universe exists contingently.
C1 The universe has a reason for its existence.
P3 If the universe has a reason for its existence then that reason is God.
C2 God exists.
P1 Things exist.
P2 It is possible for those things to not exist.
P3 Whatever has the possibility of non existence, yet exists, has been caused to exist.
P4 Something cannot bring itself into existence, since it must exist to bring itself into existence, which is illogical.
P5 There cannot be an infinite number of causes to bring something into existence. (An infinite regression of causes ultimately has no initial cause, which means there is no cause of existence.)
C1 Since the universe exists contingently, it must have a cause.
C2 Therefore, there must be an uncaused cause of all things.
C3 The uncaused cause must be God.
There are several problems with all of these arguments. The first is that not one of them provides a reason for assuming the "uncaused cause" is anything remotely like "god".
The second is their denial of actual infinities in history. Several arguments are made against infinite histories
The most convincing I had seen was Kant's
The conditioned can only arise when its conditions are complete.
If they are infinite they can never be complete.
∴ They cannot be infinite.
Until I spotted that premise 2 is actually the very point in question.
An actual infinite cannot be completed by successive addition.
The temporal series of past events has been completed by successive addition.
∴ The temporal series of past events cannot be an actual infinite.
But this again seems not to quite work to me. Simply because there is no point in history where the set of past events was not infinite, so the infinite nature of it was not completed by successive addition, it was finite addition to an infinite, which will always produce an infinite.
In general I find the arguments against actual infinities far from compelling, for the simple reason that they try to ground in common sense, which infity does not hold to.
Several individual forms of the argument have their own issues. The premise "whatever begins to exist has a cause" for instance is not grounded in anything, our experience of beginnings is actually an experience of transformations and where we do appear to have seen things beginning they appear entirely uncaused.
From the cosmological argument, the only conclusions we can warrant are
"there is an infinite linear causal history Or there is a cyclical causal history, or there is a finite causal history"
"In all three cases there is an uncaused thing (the whole of the infinite history in the linear and cyclical cases), therefore something must have happened uncaused."
Now, remembering that uncaused does not mean necessary, there is very little we can conclude about this uncaused thing except that whether it is the infinite history or the cause of history, it exists.
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