It greatly depends on the context and the truth you are seeking.

Someone once said that humans are evolved to reason and solve problems in an environment where medium sized objects move at medium speed, in a relatively short time span (human life).

So in that context intuition could be lifesaving. But when it comes to evolutionary biology, for example, our intuitions about “how much is 1 million years?” are simply useless most of the time.

I’ll give you an example I’ve heard in some podcast: picture your family in the past, like 15 generations ago. You’ll see the same humans but with very different habits, so different that you could be shocked. Now go back 30 generations more: even more differences, and it seems crazy!

Now realize that if you go back enough time, enough generations, what you see in your genealogical tree is a fish. Does that sound strange when your read it?

That’s because your intuitions about evolutionary timescales are useless.

Same applies for other fields of human knowledge. Try “understanding” the fact that your atoms were formed inside a star, hence you are literally made of stardust.

Does that sound ok to you? It doesn’t because in The Life of Primates there’s no environmental pressure to grasp such concepts, or knowledge.

Abstract: Using intuitions as evidence is a common practice in analytical philosophy, but critics have argued our intuition cannot be trusted, quoting examples of thought experiments where cognitive biases and demographic differences have impacted their outcome. Nevin Climenhaga comes to the defence of common sense, arguing that there can be good and bad intuitions and there are ways in which we can differentiate the first from the latter. Intuitions can be tested either through experiments or “armchair” philosophical reasoning which help identify whether the content of a particular intuition is based on truth or not. One avenue for testing our intuitions in the absence of reliable experimental data is to see how well it fits in with other intuitions. If a single philosophical theory can explain a diverse set of intuitions, this makes it unlikely that either of those intuitions can be explained away through experimentation or armchair error theories. Validating philosophical beliefs using intuitions is not a simple task, but this should not mean we must dismiss intuitions as generally unreliable, argues Nevin Climenhaga.

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I recommend recommend Hintikka's The Emperor's New Intuitions (1999) for arguments why intuitions as a source of evidence are useless and a huge scandal in philosophy. Intuitions used to be a methodological shortcut in natural language syntax because native speakers have (to a certain extent, which used to be a bit exaggerated) a capacity to judge the grammaticality of sentences even in light of frequent performance errors. There is no evidence of such a capacity about philosophical matters. To be honest, I doubt a single "datum" could be discerned in philosophy that is established by intuitions about which other philosophers don't have intuitions to the contrary.

The use of "intuition" in contemporary philosophy illustrates the lack of a commonly agreed upon methodology and subject matter.

The point of training is to refine our intuitions.

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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