The poem is heavily influenced by Dante's Divine Comedy, and by his view of Ulysses, which was, itself, influenced by Vergil in the Aeneid.
I believe Mount Purgatory is a metaphor for life upon this earth; and, in accordance with Philippians 2:12, is where a Christian works out, in ordinary life, the implications of Salvation. This provides, within the metaphor, the slope of Mount Purgatory; whereas those without faith, or those who refuse faith, fall into the flat sea, without slope, as Ulysses does in this poem.
