I’d unify your “So What” with “meaningless” into a single category “does not constrain observations”. Math passes the test inasmuch as it constrains observations about outcomes of proof checking.
But now some people will complain (are already complaining) that we reject the majority of humanity’s thought.
Again, it does seem observable that nobody has explained why three is prime and four isn’t. (I’m not sure you can actually use ‘why’ in an intelligible way here; possibly I’m being confused by non-mathematical language applied to math.) It’s not an observation I would expect anyone to care about, and possibly it may be the equivalent of nobody having seen something invisible; but it does seem to make a statement that could in principle have gone the other way.
I agree that I’m not sure how you’re intending to use ‘why’ here, and I’m pretty sure there’s a good answer for any particular meaning.
To answer the question in a possibly unsatisfactory way, 3 is prime because it is a natural number which has exactly two distinct natural number factors, whereas 4 is not prime because it has more than two distinct natural number factors.
What humanity does isn’t “thought”, by and large. Not in any meaningful sense. It’s mostly the expression of prejudices combined with associational triggers and repeating what others say.
Part of becoming an effective thinker is recognizing that unpleasant realities need to be acknowledged even when we’d prefer they weren’t the case. For people living in this time, in this place, one of those truths is that we’re surrounded by blatant stupidity. Even worse, we’re blatantly stupid a lot of the time.
Deriving those conclusions from the evidence, and then acknowledging their validity, is one of the basic necessary steps to becoming better. No problem can be (expected to be) solved if we deny its reality.
I’d unify your “So What” with “meaningless” into a single category “does not constrain observations”. Math passes the test inasmuch as it constrains observations about outcomes of proof checking.
But now some people will complain (are already complaining) that we reject the majority of humanity’s thought.
Again, it does seem observable that nobody has explained why three is prime and four isn’t. (I’m not sure you can actually use ‘why’ in an intelligible way here; possibly I’m being confused by non-mathematical language applied to math.) It’s not an observation I would expect anyone to care about, and possibly it may be the equivalent of nobody having seen something invisible; but it does seem to make a statement that could in principle have gone the other way.
I agree that I’m not sure how you’re intending to use ‘why’ here, and I’m pretty sure there’s a good answer for any particular meaning.
To answer the question in a possibly unsatisfactory way, 3 is prime because it is a natural number which has exactly two distinct natural number factors, whereas 4 is not prime because it has more than two distinct natural number factors.
What humanity does isn’t “thought”, by and large. Not in any meaningful sense. It’s mostly the expression of prejudices combined with associational triggers and repeating what others say.
Part of becoming an effective thinker is recognizing that unpleasant realities need to be acknowledged even when we’d prefer they weren’t the case. For people living in this time, in this place, one of those truths is that we’re surrounded by blatant stupidity. Even worse, we’re blatantly stupid a lot of the time.
Deriving those conclusions from the evidence, and then acknowledging their validity, is one of the basic necessary steps to becoming better. No problem can be (expected to be) solved if we deny its reality.