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countable and uncountable, plural epistemologies
(uncountable) The branch of philosophy dealing with the study of knowledge; the theory of knowledge, asking such questions as "What is knowledge?", "How is knowledge acquired?", "What do people know?", "How do we know what we know?", "How do we know it is true?", and so on. quotations examples
were primarily concerned with epistemology and the foundations of the sciences; they often spoke as if we were separated from the real world by a screen of "representations" or "sense-data"; they tended to regard our approach to the world as one of disinterested observation.
2014 April 12, Michael Inwood, “Martin Heidegger: The philosopher who fell for Hitler [print version: Hitler’s philosopher]”, in The Daily Telegraph (Review section), London, page R10
(countable) A particular instance, version, or school thereof; a particular theory of knowledge. quotations examples
I believe that 'intuitionism' is usually, and rightly, taken to mean Brouwer's epistemology of mathematics, which is unrelated to the origin or content of topos theory.
1995, Colin McLarty, “Preface”, in Elementary Categories, Elementary Toposes, page vii