Then isn't the question what makes a good intuition and a bad intuition? Does it have to do with correctness or correspondence to the external world? This is just a description of the scientific method but for sentiments or for "gut" feelings, which doesn't necessarily encompass the philosophical topic/study of "theory of mind."

A few reading recommendations:

• Two Heads (a graphic novel)
• Fred Dretske, Naturalizing the Mind
• The Norton Anthology on the History of Mind (The edition I read got a black and white cover)

The article linked shows few examples of the purpose of or what specific situations would be applicable to intuitive judgements, and instead is falling into a deductive argument on "Are Intuitions True OR False"* or placing the philosophical function/role/application/method** of honing intuitions into the categories of logic or epistemology. From what I know, applied logic and applied epistemology (like in history of science*** or medical/scientific ethics) almost never relies on sentiments or prizes/utilizes intuition.****

The article is also using number theory for an argument about an idea that is inherently unquantifiable (infinity) in the example after the first quoted text. I think some of the rest of the article goes on to list other mathematical examples and uses a lot of mathematical terminology, but I stopped reading after I read something like "I can extend an intuition through a deduction" or something like that.

*Which kind of defeats the whole point of writing the article. Even though so many philosophers in the Analytic tradition love Kant (me too) it is very taxing and like chorework to read, write, and review papers on a bunch of self-contained mini-experiments and then go around poking holes in Why Or How This Thing Actually Wouldn't Work Or essentially write a manual for How One Ought To Comport Themselves In All Times At All Situations And Be Right Every Time.

**on "the method of honing intuitions," which may sound a bit New Age-y, there is a very nice allegory used in the first recommendation on the list above on how the neurons in your brain and body work to "hone"/"direct" impulses or intuitions/energy to "test" the accuracy of your perceptions

***which is really what a lot of philosophy amounts to

****except as conundrums, unsolvable problems, or other thought experiments/puzzles, you know, things philosophers like