The main idea is that the world is built on logic and harmony which can be understood by an individual human mind. It was born from religious mysticism (Descartes, Leibniz)
Erm, Pythagoras was around a lot earlier than the likes of Descartes or Leibniz. Even the competing ideas that "the world is built on chance" or else that "all understanding is social" (or, to put it another way, "man is the measure of all things") are of comparable antiquity and not really more 'sophisticated' in any relevant way - except perhaps in an overly literal sense, being more conducive to "sophistry"!
Operating outside of ideology is extremely hard, if not impossible. Even groups that see themselves as non-ideological, still seem to end up operating within an ideology of some sort.
Take for example Less Wrong. It seems to operate within a few assumptions:
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These assumptions are also subject to some criticisms. Here's one criticism for each of the previous points:
I could continue discussing assumptions and possible criticisms, but that would be a distraction from the core point, which is that there are advantages to having a concrete ideology that is aware of it's own limitations, as opposed to an implicit ideology that is beyond all criticism.
Self-conscious ideologies also have other advantages: