This topic came up recently in a conversation with a friend, in which I laid out my thoughts on the role of these arguments vis-à-vis David Hume's arguments against miracles. Then I came across this question in another website, so I put together this quick summary.
To my knowledge, the only "argument" for the existence of God given in the Torah itself is that He directly revealed Himself to us at Sinai:
Deut. 4:35 "Unto thee it was shown, that thou mightest know that the LORD, He is God; there is none else beside Him."Deut. 5:4, "The LORD spoke with you face to face in the mount out of the midst of the fire."
In other words, direct experience does not require philosophical proof.
Rabbi Jacob Emden expanded this argument into our own time, saying that, "When I consider these wonders [of the survival of the Jews in exile], they appear greater to me than all the miracles and wonders that God did for our ancestors in Egypt, and in the wilderness, and in the land of Israel." (See the full text in this previous post.)
All philosophical arguments for the existence of God made in traditional sources are only intended to reinforce this basic experiential knowledge that is the heritage of the Jewish people. While these arguments can serve to shore up our beliefs against challenges, many sources appear to see these arguments as serving mainly to help us acheive a more personal, immediate connection to God.
The most common such arguments found in Jewish works are:
- The Argument from Design - Many aspects of the natural world appear to have been been designed with intelligence and intent.
- The Cosmological or "First Cause" Argument - What set the world moving? Where did it come from?
- The famous Kuzari argument, that the Sinai revelation was a historical event witnessed by the entire nation. (This argument is basically just an extension of the Biblical "argument" that is intended to enable us to rely with confidence on our historical tradition.)
In my personal opinion, the various philosophical arguments for the existence of God are mainly useful for countering Hume's arguments against miracles. Briefly stated, he argues that no testimony of a miracle should be believed unless the falsehood of the testimony would be more improbable than the miracle itself. It follows, therefore, that one's ability to accept the testimony of the Jewish people's historical experience of miracles has an inverse relationship with the degree to which you think miracles are improbable.
All of the classical arguments for the existence of God are, fundamentally, arguments that we can perceive an element of the supernatural in the natural world itself. Thus, each such argument makes the possibility of miracles more plausible. At some point, it becomes more plausible that the Sinai Revelation really occurred than that it was made up (which, per the Kuzari argument, is very unlikely). Once you reach that point, then you have the Sinai Revelation to rely on for everything else.