The solipsist
This work responds to a hypothetical person called a solipsist. A solipsist would be someone who genuinely denied the existence of an external world, believing that reality was a dream fashioned for their sole enjoyment. The belief is a kind of extreme belief in Cartesian dualism, because a solipsist gets to Descartes's famous idea that "I think therefore I am," but then they also say, "...and also nothing else is." He responds through essay to this hypothetical person.
Reality as a mystery
Reality is mysterious, and philosophy's skepticism about reality is well-deserved, feels G.E. Moore, but then again, he feels that to say, "There is no external world," is to throw the baby out with the bath water, because there is clearly an experience of external reality, but that experience is mysterious, allowing for multiple conclusions at once. He feels this is the crux of the issue.
The motif of common sense
Many times in this Proof, Moore appeals directly to common sense. He urges his reader to consider how blindly one sacrifices their common sense to assume that reality isn't real. Although he admits there is value in skepticism, he reminds his reader of his personal conviction that everyone should use their common sense so they don't end up in ridiculous hypotheticals.
The allegorical nature of skepticism
Once a person decides to start questioning reality, they enter a narrative arc, suggests Moore. He views his work as an urgent reminder of wisdom during a time when he felt the school of Philosophy was veering too far from objective participation in reality. He says there is a right way to do skepticism, and an absurd way, and he encourages his readers to try and understand reality, instead of just denying its existence. He views solipsism as a kind of failure to adjust.
The motif of sensory perception
Again and again, the question returns to the ontological nature of human experience, but one could easily argue that a person is only observing through their senses, so the issue of perception continues to come up, because a solipsist is in denial of his own senses of reality, choosing to interpret reality some other way than the obvious way.
