I'd like to read some well-vetted and modern pieces arguing for intuitionism (the "intuitionist stance"?), which I take to be:

As the intuitionist sees it, the rules of logic used by mathematicians have an empirical character. Certain methods of proof came to be commonly used by mathematicians, and, over the years, were codified into a body of rules. These rules were observably correct in their original context, but—after they were codified—they came to be used uncritically in totally different contexts in which they no longer applied...it is only when they[axioms developed constructively] are transposed to problems involving an infinite domain of objects, or in which the objects are not given by an explicit construction, that the rules are incorrect.

A question I have asked on the main site on this point is doing quite poorly, and I do not want to argue *for* it, but instead mainly understand why it is not a research level question.

I was hoping that I would get recommendations for articles that argue for intuitionism in way that makes, for example someone like Paul Halmos, understandable in his criticism of non-standard analysis, since he was of the "intuitionist constructivist" group founded by Brouwer. I left this sort of detail out, but perhaps that was a mistake?

What is it exactly, that's so convincing for him regarding this stance? I can barely get my mind around *why* intuitionism is even a thing, since in some sense, I view mathematics as the "careful manipulation of symbols, based on an arbitrary set of rules".

A link to the question in question: Powerful arguments for the intuitionist stance

internallyin a topos, classical modes of reasoning are no longer valid. You might start with Andrej Bauer's fine article: ams.org/journals/bull/2017-54-03/S0273-0979-2016-01556-4/… $\endgroup$becauseI intend to denigrate, but rather I share my bias to show how difficult/far removed intuitionist concepts are to me (likely because of the style of my education?). $\endgroup$I Want To Be A Mathematician). $\endgroup$wasmisconstrued, but there were no insults. I simply do not have a high enough opinion of myself to be able to imagine insulting others. In fact, I hoped to convey that while intuitionist ideas were very alien to me, there are people who clearly think in those terms, and its very likely I am missing something big. $\endgroup$