Just to add yet another definition of 'open' to the mix: "A closed system is one in which the knowables are fixed. Examples of this kind of system would include any in which most of its answers are either yes or no, right or wrong, clearly and without any other possibility." Cited by Scott McLeod, this is from Teaching As a Subversive Activity. It should not surprise readers to know that I am more inclined toward 'open' than 'closed' in this system too. And yes, even for things like mathematical and logical knowledge, systems I believe are highly contingent and context-sensitive (cf Philip Kitcher, The Nature of Mathematical Knowledge).
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