Wikipedia is a human project done collectively in a global scale. What is the philosophy or epistemology underlying this project? Has the idea been to establish sort of a "democratic" source of knowledge? And how can something be reliable with hardly any center of control?...
I would look to the French Encyclopedia, or a Systematic Dictionary of the Sciences, Arts, and Crafts as the model or template. The concept of an encyclopedia is much older, going back at least to Pliny The Elder. But in the era after the printing press, this represented an ideological project to democratise knowledge. It came to help define enlightenment thought, rational, empirical, curious.
It has the stated goal of developing and maintaining open content, wiki-based projects and providing the full contents of those projects to the public free of charge. Another objective is political advocacy.
See also their first press release.
I have certainly heard it put that Wikipedia's success is part of the case to support anarchist ideas. It's not straightforward to define anarchism, but while Wikipedia supports the case for distributed and non-hierarchical collaboration, it does not conform to some ideas about anarchism, as discussed here: Is Wikipedia an experiment in anarchy?
Like I would link the French Encyclopedie to the printing press, I'd link Wikipedia to the coding community. The zero marginal cost of reproducing digital media, and ease of peer-to-peer communication and collaboration shifted the incentives around knowledge - MOOCs are another example of that. The speed at which the coding world changes means a relevant degree is basically out of date by the time it's completed, leading to a need for a much more intensive continuing education that most jobs, who's only source could be other peers - that is the origins of the original Stack Overflow, and the Stack Exchange network. Also many coding-related journals chose to go Open Access, as part of a wider movement for researchers to be able to access each others work for free. And Open Source, which has helped curb monopoly distortions through things like the Linux operating system and Firefox browser.
I really recommend finding local unconferences, which also started from the coding world, to experience how there is something self-stabilising and self-reinforcing about this digital culture. I see it as comparable to the idea of 'enlightenment thinking', and I expect it to be considered a lot more important when we look back on our current era, than philosophy treats it now. There are major thinkers like McLuhan and Derrida on pre-digital media, I don't know of similar figures digesting the impacts of this cultural shift.