If I assert (as an axiom) that only I exist, and that the entire Universe exists only as a figment of my overheated dream-state imagination, a Matrix-like existence simulated for an audience of One, it is well known in philosophy that the resulting axiomatic system is logically unassailable. How can you prove me wrong? First of all, you are a figment of me, so only I can prove me wrong, but you can't because the Axiom is framed in such a way that it isn't falsifiable.
This sort of mindless philosophy (solepsism) is the kind of thing that makes ordinary people think of philosophers as jackasses. It was the sort of thing that Johnson was once cheered for ``disproving'' (not really, of course, but who cares) in open debate. What is really wrong with it?
It is inconsistent. If I am the only thing that exists, and the Universe is My Oyster served on a figmental half-shell, then why cannot I be surrounded by beautiful houris who do nothing but peel me half-naked grapes (or peel me grapes, half-naked) at a whim? Why do I have to plod along typing this instead of just wishing the lines onto the page? You see, Solesism alone isn't a sufficient axiom. I need more. I need axioms to explain why I sometimes hurt, why my eyes are gradually failing as I age, why I age. I need axioms to explain why my perceptions of what is nearby are so limited, but my perceptions of what is going on thousands of miles away through the glass teat of a television tube are crystal clear, complex, different, and correspond perfectly to what I see when I visit Paris, the Parthenon, India.
If all of this is a figment of ``my'' imagination, then I've successfully managed to split myself into at least two incredibly separate beings - the artist that is constantly making up the story that I find myself embedded in, and the audience (the ``me'' that is typing this on what appears to be a laptop computer obviously created by my artistic half). Since I never perceive the artist directly, how do I know that it is ``me''?
Indeed, consider the artist further. I run computer simulations of physical models as some of the research that I do in physics. In these simulations, I ``create'' a virtual world of microscopic entities. Each is labelled with coordinates that specify the ```state'' of my little mini-world. There are rules whereby they operate. Computer games played by my children are very similar, at a higher order. They hold a virtual terrain superimposed on their internal coordinates, and have many ``sprite''-based components and characters. Those characters, objects, devices all have independent programmed personalities, probabilistic behaviors, an underlying ``physics'' of their interaction with each other and their surroundings, and a ``plot'' that unfolds as the game proceeds. I am not my computer models, the computer games are not my kids.
As they increase in complexity, to the point where a whole world is perfectly simulated with perfect consistency, the artist itself complexifies, its non-audience ``self'' splitting up among all the virtual selves it creates. If all of these (you who are reading this, and your dogs and cats too) are really part of the artist, and the artist is equated with the audience, then Solepsism is isomorphic to Pantheism. We are all God, split into all that is. Somehow a Western Solepsist (driven to explain why he cannot bring a loved one back to life no matter how hard he tries) ends up an Eastern Hindu, accepting that Brahma split himself up to create the Universe (one fragment of which is him, all of which is still Brahma and eternal).
Ahh, but now you are wise and see the game I am playing with you. Axioms are neither true nor false, they just are. Logically there are many ways to convert one into another, adding an axiom here, altering an idea there, ultimately dividing by the zero that is their informational content and proving whatever you like. Axiom sets can be inconsistent. Axiom sets can be consistent, but they or the conclusions derived from them may not correspond to what we directly experience (and hence require special axioms to resolve the conflicts, which are then overcomplex and ugly).
So choose your axioms wisely my friend, examine them often for leaks.
Bail them out like a foundering float, burn the boat if it creaks.
Challenge the cherished old words, my friend, challenge the new ones too.
Avoid all beliefs that lead you to grief, and keep all the best ones for you.