Since accessteacher used Act III, scene 3 and you did not specify which soliloquy, I shall talk about his first one which begins Act I, scene 2.
In th beginning of the play, Glouchester and Kent are chatting and his father makes rude jokes about his inception. Edmond is there but says nothing.
It is at the beginning of the second scene that Edmond tells us how he really feels.
I had the privilege of being in a workshop conducted by Cicely Berry, the head of voice for the Royal Shakespeare Company where we worked on this speech.
First, she asked us to free associate the word nature and we responded with beauty in nature. She then asked us about nature in the negative and we responded with things like severe storms, floods, earthquakes, etc. She then asked us which nature Edmond was calling his goddess.
She then asked us to think of something in modern society which would make a person an outcast. The best we could come up with was AIDS. As she explained it to us, being a bastard in that world meant being an outcast. A good example of this is Glouchester's attiude toward him especially compared to Edgar.
Being illegitmate brands him and to demonstrate this, she choose one of the young men in the group to repeat over and over until she told him to stop, the lines about being branded a bastard. She then approached two other young men and a young woman to whom she gave her pen then whispered her instructions to them.
These three people approached the other person and the two men grabbed him and wrestled him to the floor and the girl straddled his chest and using the reverse side of the pen, began to "brand" his forehead with the word bastard. Throughout it all he continued to repeat the given lines but once they wrestled him to the floor, his voice became angry. She stopped the excerise and asked him to say the lines and he was extremely convincing.
Edmond is an angry young man but he knows that to "win" he must outsmart his father and brother.
You have not specified the act and scene in which the soliloquy appears, so I am assuming you are refering to his soliloquy in Act III scene 3, where Edmund sees his opportunity to betray his father openly, having already betrayed his brother in secret, thanks to some information that Gloucester shares with Edmund regarding the invasion of a French army to revenge the "injuries the King now bears." Gloucester's own removal to attend to Lear and his instructions to Edmund give him the perfect opportunity to make his move and reveal this information to Cornwall, anticipating his inheritance of his father's title, wealth and estate once he is put to death:
This courtesy forbid thee shall the Duke
Instantly know, and of that letter too.
This seems a fair deserving, and must draw me
That which my father loses--no less than all.
The younger rises when the old doth fall.
Note how Edmund is presented in this soliloquy as a backstabbing, selfish and opportunistic individual who will stand at nothing to succeed in his goals and aims. His perceived slighting at being the bastard son of Gloucester causes him to plot his own father's downfall, and we can imagine his gloating as he delivers the final line of this soliloquy.
Edmund or Edmond is a fictional character and the main antagonist in William Shakespeare's King Lear. He is the illegitimate son of the Earl of Gloucester, and the younger brother of Edgar, the Earl's legitimate son. Early on in the play, Edmund resolves to get rid of his brother, then his father, and become Earl in his own right. He later flirts with both Goneril and Regan and attempts to play them off against each other.