Aquinas and Descartes

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what are aquinas' and descartes' versions of the first cause argument?

The most famous of all arguments for the existence of God are the "five ways" of Saint Thomas Aquinas. The argument is basically very simple, natural, intuitive, and commonsensical. We have to become complex and clever in order to doubt or dispute it. It is based on an instinct of mind that we all share: the instinct that says everything needs an explanation. Nothing just is without a reason why it is. Everything that is has some adequate or sufficient reason why it is.
Philosophers call this the Principle of Sufficient Reason. We use it every day, in common sense and in science as well as in philosophy and theology. If we saw a rabbit suddenly appear on an empty table, we would not blandly say, "Hi, rabbit. You came from nowhere, didn't you?" No, we would look for a cause, assuming there has to be one. Did the rabbit fall from the ceiling? Did a magician put it there when we weren't looking? If there seems to be no physical cause, we look for a psychological cause: perhaps someone hypnotized us. As a last resort, we look for a supernatural cause, a miracle. But there must be some cause. We never deny the Principle of Sufficient Reason itself. No one believes the Pop Theory: that things just pop into existence for no reason at all. Perhaps we will never find the cause, but there must be a cause for everything that comes into existence.
Now the whole universe is a vast, interlocking chain of things that come into existence. Each of these things must therefore have a cause. My parents caused me, my grandparents caused them, et cetera. But it is not that simple. I would not be here without billions of causes, from the Big Bang through the cooling of the galaxies and the evolution of the protein molecule to the marriages of my ancestors. The universe is a vast and complex chain of causes. But does the universe as a whole have a cause? Is there a first cause, an uncaused cause, a transcendent cause of the whole chain of causes? If not, then there is an infinite regress of causes, with no first link in the great cosmic chain. If so, then there is an eternal, necessary, independent, self-explanatory being with ...