Is Milton's Satan rightly regarded as a tragic hero?

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Is Milton's Satan rightly regarded as a tragic hero?

Aristotle, inventor of the concept of heroism, defined the hero as 'noble or honourable by birth or deed'. Both classical myth and history influenced Milton greatly in his writing, and no doubt he knew Aristotle's works and applied his formulae to the creation of perhaps his most attractive character, Satan. He is certainly of noble birth, having been created by God as the brightest of all the archangels, but do his deeds justify his title as 'a tragic hero'? Since the writing of 'Paradise Lost' there has been an ongoing argument as to whether Satan is a tragic hero. Romantics such as W. Hazlitt regard him as the 'most heroic subject that ever was chosen for a poem', whilst others, such as C.S. Lewis, see him as fundamentally flawed in both his tragic and heroic intentions.

Satan's conduct throughout Paradise Lost displays many attributes which facilitate his status as a tragic hero. He is tragic in the extent of his loss. He has fallen from Heaven's 'happy realms of light' to a 'dungeon horrible'. There is a tragic sense of waste in his fall; in Heaven he