What is the purpose of the brief Scene iv in Act IV of Hamlet?
This scene, while it builds the suspense of Fortinbras of Norway effectively invading Denmark on the excuse of the "conveyance of a promis'd march" (Riverside 1171,) serves another purpose. It is the site of yet another of Hamlet's introspective, philosophical soliloquies, in which he questions his own motives for inaction about his uncle's and mother's betrayal. Hamlet decides that he has been dishonorable by not taking action, since his cause (his father's murder and his mother's marriage) is so compelling. He compares his own righteous cause to Fortinbras' plans to march to faraway Poland, with many men, to fight for a small and worthless piece of land which would not have enough area to bury all the men who will die in the fighting over it. This scene is meant to show two things in Hamlet's character: his increasing willingness to take action against his uncle, and the beginning of the degradation of his reason. He knows that Fortinbras, in all good sense, should not march to Poland and waste so much money and so many lives on a "straw" (1172), but he uses this example of illogical defense of honor to build up his own courage to make his "thoughts be bloody" (Ibid). There is also some social satire here about the wasteful ambitions of princes, who would willingly fight and allow their subjects to die over nothing except an idea of honor, rather than a material gain.
Source: Riverside Shakespeare 1974