“Intuition” is just a name for the ideas and beliefs we arrive at without being able to articulate why. They’re all around us, not just in deep mathematics, but in trivial matters, like how I know I’m sitting in a chair right now. (If we could articulate things like that, we would already have humanoid robot servants that could take care of all the housekeeping.)
Intuitions can as easily be right as wrong, in fact more easily wrong than right, for truth is a small target. Look at all the stuff that here we would generally dismiss as “woo”: astrology, alternative medicine, chakras, etc. Pretty much all writings about these are based on no more than intuition. “Here’s a flower that looks like an eye—it must be good for treating eye diseases!”
To have right intuitions rather than wrong ones, then just as for explicit reasoning, one must have been entangled with the world in order to obtain those right intuitions. They will not happen by chance, by the raw animal spirit in a state of religious intoxication that Pbfgva Iynq Nynznevh (translate using rot13.com) (who has a BA in Mathematics) valorises. Even if we do not know the process by which, for example, we learn to ride a bicycle, there must be such a process. You don’t get to have the insight of a Gauss without having laboured long and hard over mathematics.
Neither do you get to be the Beatles without working at your craft, practicing and practicing while your age peers are out partying every night and lazing in in the morning. You don’t get to be the Beatles, or anything else of note, without putting in the work.
BTW, logic has moved on a long way from “syllogisms”, which is now a significant concept only in the history of logic, no longer in logic. I guess Pbfgva Iynq Nynznevh’f (translate using rot13.com) “BA in mathematics” did not include any courses on mathematical logic.
“Intuition” is just a name for the ideas and beliefs we arrive at without being able to articulate why. They’re all around us, not just in deep mathematics, but in trivial matters, like how I know I’m sitting in a chair right now. (If we could articulate things like that, we would already have humanoid robot servants that could take care of all the housekeeping.)
Intuitions can as easily be right as wrong, in fact more easily wrong than right, for truth is a small target. Look at all the stuff that here we would generally dismiss as “woo”: astrology, alternative medicine, chakras, etc. Pretty much all writings about these are based on no more than intuition. “Here’s a flower that looks like an eye—it must be good for treating eye diseases!”
To have right intuitions rather than wrong ones, then just as for explicit reasoning, one must have been entangled with the world in order to obtain those right intuitions. They will not happen by chance, by the raw animal spirit in a state of religious intoxication that Pbfgva Iynq Nynznevh (translate using rot13.com) (who has a BA in Mathematics) valorises. Even if we do not know the process by which, for example, we learn to ride a bicycle, there must be such a process. You don’t get to have the insight of a Gauss without having laboured long and hard over mathematics.
Neither do you get to be the Beatles without working at your craft, practicing and practicing while your age peers are out partying every night and lazing in in the morning. You don’t get to be the Beatles, or anything else of note, without putting in the work.
BTW, logic has moved on a long way from “syllogisms”, which is now a significant concept only in the history of logic, no longer in logic. I guess Pbfgva Iynq Nynznevh’f (translate using rot13.com) “BA in mathematics” did not include any courses on mathematical logic.