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In the following link: https://plato.stanford.edu/entries/intuitionism/ in the last paragraph in Section 1, there is mention of the "lack of epistemological and ontological basis for Mathematics."

Apparently this was a debate between Hilbert and his contemporaries in the early 20th century - what exactly was the debate on? I can't seem to find any content on the topic...

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The debate is what is commonly referred to as the Foundational Crisis of the early XX century (https://en.wikipedia.org/wiki/Foundations_of_mathematics#Foundational_crisis). A well-known example of one of the issues from which this crisis stemmed is Russel's paradox in Frege's foundations for mathematics.

Hilbert's position on this is well explained in https://plato.stanford.edu/entries/hilbert-program/. Other relevant actors in the debate are Hermann Weyl, Henri Poincaré, Gerhard Gentzen.

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