Right, I think it's fair to say Deixian philosophy diverges from our own. As far as I can see, I was the first to ever raise the question of how the average Deixian sees the world and how philosophies would have to adjust, but it's pretty clear that it was always understood and individually adapted, however for the sake of canon consistency let's trudge through this meta-stuff and see what we get.
The major divergence point from earth is that Your mind makes things real. This has been done before. Many, Many Times. Where Deixis diverges from this is that the PC and everyone else is aware of it.1
God: This one has been done in depth and is explained in the rules, I think the conclusion is satisfying; Gods exist in the world but are created by belief (again, not exactly new). The primary question between atheists and theists follow the old Nietzsche quote: “Is man merely a mistake of God's? Or God merely a mistake of man's?”
Theism isn't about proving the dude with long scraggly hair, a beard and nightgown next door is Jesus, it's proving that his dad popped the Deixis out from sheer conviction, if that makes him God or just a really powerful philosopher, the distinction between the two, and just as often, which one of the scraggly long-haired dudes is, in fact, the original Jesus or if that even matters. Also, for those more willing to get their heads fucked with; does enough people believing in God make things retroactively change?2
Science; Again, greatly discussed in the rulebook. In a world shaped by belief, science can either be a work of faith or seeing how things work when you do not believe in a specific outcome. After that it mostly follows the religious debates above. Scientific experience must also be objective in a sense different from ours; If the scientists wants a result badly enough he can inadvertently alter the results, though this is more of a societal implication than a philosophical one.
Pacifism; Likely arguing and forcing your opinion on others is seen as equivalent to punching them in the face. Actual punching only works as well as the person believes it would, and is considered a crude form of argument.
Conversion; I think this one was settled as well, though never overtly stated; someone is K.O.'d from despair and disillusionment rather giving up their philosophy. One can be slowly converted and change over time or be sent into despair and 'rewired' (more or less brainwashed, this should have mechanics or possible be considered for place as a common skill with parallels to necromancy).
Money; This has been skimmed over, but society would need a means of regulating shit where belief alters reality.3 I think the simplest solution would to expand and canonize the idea of separate currency between the population and philosophers or simply show an abundance of old text in the market. The latter actually makes more sense, all in all, provided we get people on expanding on this.
This is all that I could propose off the top of my head, but there's plenty more, certainly enough to warrant a thread of it's own. Post questions, propose answers and etc.