I'm a fan of Thomas Aquinas, he contributed a fair share to philosophy. Among his better known contributions is the first mover argument, or the argument from first cause. This one goes waaaaay back to around 1250. Though Aquinas was a great thinker, he was a bit odd when it came to the supernatural: I heard he claimed to have flown around the towers of Notre Dame. This proof for God is as follows:
p1. Everything must have a cause.
p2. Nothing can cause itself.
p3. A casual chain cannot be infinite.
c1. Therefore, a first cause has to exist.
This seems like a fairly good argument to some people, but overall this is another argument of wanting, it only convinces those who are friendly to the conclusion to begin with. The first problem we see with this proof is familiar: it's illogical to simply plug your favorite god into the argument as the first cause, or the unmoved mover. This isn't 'Nam man, we have rules. If it can be the Christian God (CG), it can just as easily be the Flying Spaghetti Monster. It's another one of those arguments that starts with a canvas of logic, then quickly spirals into a work that resembles a confused watercolor from yours truly after half a day on the whiskey.
Putting that aside, another obvious problem is presented, a pretty bad self-contradiction haunts this proof. It's not kosher to say everything has to have a cause, then turn around and say that one special cause itself doesn't need any cause at all. This has the familiar stench of special pleading, which is reflective of the time Aquinas did his philosophy; back then, if your work didn't include the CG you may have found yourself out of the evolutionary contest.
Also, this argument calls for the question of where does the God come from? Does the God have a cause? If it does -- or could -- then all we've done is stalled the proof at the insertion of God with no empirical way to move forward. It may be said that adding the CG to this argument only muddles the infinite casual chain even more, since we can't determine if the CG has a cause or not.
On the subject of infinity, it's worth noting that our minds are not fond of dealing with it, but that doesn't mean the rest of reality shares our baggage with the concept. This solipsism is obviously not supported when we look at how little the universe seems to care about our comforts and welfare; are we supposed to believe that the universe with an age of about 14,000,000,000 years cares about the mental constraints of a young (200,000 years tops?) upstart race on a remote planet that itself is hostile to their very existence? Clearly, the universe doesn't have a care for us: one day it will give you beautiful child that fills your life with a purpose far beyond driven, and the next morning: a fatal brain aneurysm. It's clear to see that our kind isn't meant to stand as the primary benefactor of all creation, and it stands to reason that reality doesn't care about our uneasiness with infinity.
In relation to infinite casual chains, there have been more than a few scientists armed with information unknown to Aquinas, that have come forward to say that the big bang was the beginning of everything, in all dimensions, so asking what came before the big bang is like asking what's farther north than the north pole.
Overall, this argument isn't going to convince that many thinkers (anymore), but considering what Aquinas had to work with, and the conditions he had to work under, he made some real pieces of work that have lasted quite a long time.
Thanks for sticking through the longish article, I hope you found it worth the effort.
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