I think a semantic check is in order. Intuition can be defined as an immediate cognition of a thought that is not inferred by a previous cognition of the same thought. This definition allows for prior learning to impact intuition. Trained mathematicians will make intuitive inferences based on their training, these can be called breakthroughs when they are correct. It would be highly improbable for an untrained person to have the same intuition or accurate intuitive thoughts about advanced math.
Intuition can also be defined as untaught, non-inferential, pure knowledge. This would seem to invalidate the example above since the mathematician had a cognition that relied on inferences from prior teachings. Arriving at an agreement on which definition this thread is using will help clarify comments.
The former definition sounds more promising. “Untaught” and “pure” are scary qualifiers to ask philosophers to be committed to when they probe themselves (or others) with thought experiments. Philosophical intuitions might be less rigorous or systematic than mathematical ones, but it’s not as though they come free of cultural trappings or environmental influences.
I think a semantic check is in order. Intuition can be defined as an immediate cognition of a thought that is not inferred by a previous cognition of the same thought. This definition allows for prior learning to impact intuition. Trained mathematicians will make intuitive inferences based on their training, these can be called breakthroughs when they are correct. It would be highly improbable for an untrained person to have the same intuition or accurate intuitive thoughts about advanced math.
Intuition can also be defined as untaught, non-inferential, pure knowledge. This would seem to invalidate the example above since the mathematician had a cognition that relied on inferences from prior teachings. Arriving at an agreement on which definition this thread is using will help clarify comments.
The former definition sounds more promising. “Untaught” and “pure” are scary qualifiers to ask philosophers to be committed to when they probe themselves (or others) with thought experiments. Philosophical intuitions might be less rigorous or systematic than mathematical ones, but it’s not as though they come free of cultural trappings or environmental influences.