Regarding the first beast, its identification with Babylon/Nebuchadnezzar is underlined by the end of the sentence, which alludes to Nebuchadnezzar's recovery from beast-madness and return to sanity in chapter 4.
More generally, Daniel's vision of the four beasts is full of exegesis of earlier scriptures, notably the vision in Hosea 13:7-8 and the Merkavah vision in Ezekiel 1. Hosea's vision structures Daniel's, giving us the lion, the leopard, the bear, and the wild beast, in that order. Then details from the four "living creatures" of Ezekiel 1 fill out the picture of each beast. (The word translated "living creature" [חיה, ḥāyāh] is a Hebrew word that means "animal" or "beast" and is cognate to the Aramaic word [חיוה, ḥăwēyṯ] used in Daniel 4-8.) For example, Ezekiel 1 uses the terms lion and eagle and has various wings, four faces, and eyes on its four beasts. I call this "exegesis by bricolage": treating an earlier vision like a heap of bricks and reusing them to construct a new vision. This sort of exegesis is found in other visions in ancient Jewish literature.
And mixed in with all of that is an interpretation of the vision in Daniel chapter 2.
Incidentally, the ten toes in Daniel chapter 2 are missing in the Old Greek. They are probably a secondary addition in the Masoretic Text inspired by the ten horns in chapter 7.
My comments above are not meant to exclude the possibility that Daniel 7 is based on some sort of actual vision experienced by its author. Ancient visionaries were steeped in their scriptures and their visions naturally were full of scriptural themes and images.
For more on visionary scriptural exegesis, see my article “Seven Theses Concerning the Use of Scripture in 4 Ezra and the Latin Vision of Ezra,” in Old Testament Pseudepigrapha and the Scriptures (ed. E. Tigchelaar; Bibliotheca Ephemeridum Theologicarum Lovaniensium 270; Leuven: Peeters, 2014), 305-326.
I have noted earlier posts in Phil's series on Daniel, sometimes with my own commentary, here and links.
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