Full of high sentence, but a bit obtuse;
“Full of high sentence” (“speaking all classy-like”) is an allusion to the General Prologue of Geoffrey Chaucer’s Canterbury Tales, in which the narrator describes the Clerk of Oxford as “Ful of hy sentence.” In Chaucer the description is a compliment, but Prufrock turns it around to sound pompous and silly.
Perhaps also, continuing the Hamlet allusion, a reference to Polonius, and to the Fool Yorick, who is already dead—anticipating the obsession with aging in the following lines.
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