The Identities Of The Kingdoms In Daniel's Interpretation of Nebuchadnezzar's Dream.
31-46 discusses the dream of Nebuchadnezzar and its interpretation by Daniel. The dream is a bright image with a head of fine gold, chest and arms of silver, a stomach and thighs of copper, and legs of both iron and earthenware. Daniel then interprets the dream as an allegory of kingdoms that are to come. Nebuchadnezzar, the leader of Babel, is the head of gold. Then a second, weaker (as shown by the distinction between silver and gold), nation will rule the world after the demise of the Babylonian empire. The third country, represented by the copper will rule the whole earth as well, to be followed by the fourth, which is as partially strong as iron, and will be divided, with the other half weak like earthenware. After these four empires will cease to rule the earth, God will establish His kingdom, which will rule forever.
While Daniel explicitly identifies the first empire as Babel, but there is some discussion as to who the other kingdoms are. Due to the course of history, which saw Persia and Media succeed the Babylonian kingdom, the second, weaker, empire is considered Persia and Media. The third empire, which "will rule the entire world," always includes the kingdom under the rule of Alexander the Great, being the Macedonians, and is extended to the Greeks as well. There is much discussion as per who the fourth empire is, and these calculations can affect the identies of the other kingdoms, as well.
R" Saadia Gaon feels that the fourth, split, kingdom consists of both the strong Aram and the weak Ishmael (as quoted by Abraham ibn Ezra). It can be assumed that by "Aram" he is referring to Rome, which was the next world power after Greece. Aram, where Abraham originally came from, is usually described as Arabia, so one possibility is that Saadia is postulating that the Romans are called Aram, which could be because the words Aram and Rome are similar, implying either that one represents the other or that he genuinely believes that they descended from one another.
