I’m actually not sure what argument you’re implying by your past examples. 1500 years ago the denial of Euclid’s parallel postulate wouldn’t have been taught—does this have implications for modern mathematics education?
It has implications for physics. If you re run the history of thought with even more emphasis on what’s currently believed to be true,and even more rejection of alternatives, then you just slow down the acceptance of revolutionary ideas like non Euclidean geometry.
But past mathematicians already just taught what they thought was true then. I’m not asking why they didn’t do that even harder, I’m asking what relevance you think it has for current math education. (And by extension, what relevance you think the education system of the Scholastics has for modern philosophy education.)
As it is said, keep an open mind, but not so open your brain falls out. Teaching a specific thing impedes progress when that thing is wrong or useless, but it aids progress when that thing is a foundation for later good things. This framework largely excuses past mathematicians, and also lets us convert between the “cautiousness” of philosophy education and a parameter of optimism about the possibility of progress.
But past mathematicians already just taught what they thought was true then.
But we don’t know that we are living in the optimal timeline. Maybe relativity would have arrived sooner with fewer people in the past insisting that space is necessarily Euclidean.
I’m asking what relevance you think it has for current math education.
The topic is philosophy education. Science can test its theories empirically. Philosophy can’t. Mathematics can take its axioms for granted. Philosophy can’t.
As it is said, keep an open mind, but not so open your brain falls out. Teaching a specific thing impedes progress when that thing is wrong or useless, but it aids progress when that thing is a foundation for later good things.
The difficulty is that we don’t have certain knowledge of what is in fact right or wrong: we have to use something like popularity or consensus as a substitute for “right”.
It may well be the case that one can go too far in teaching unpopular ideas, but it doesn’t follow that the optimal approach is to teach only “right” ideas, because that means teaching only the current consensus, and the consensus sometimes needs to be overthrown.
The optimal point is usually not an extreme, or otherwise easy to find.
If you did that 1500 years ago, then theism would appear clear cut in hindsight.
If you did that 150 years ago, then reductionism would appear obviously false.
As opposed to what? Would you be doing anyone any favours by rounding off “seems true to us, here now” as the last word on the subject?
Yes. Favors would be done.
I’m actually not sure what argument you’re implying by your past examples. 1500 years ago the denial of Euclid’s parallel postulate wouldn’t have been taught—does this have implications for modern mathematics education?
It has implications for physics. If you re run the history of thought with even more emphasis on what’s currently believed to be true,and even more rejection of alternatives, then you just slow down the acceptance of revolutionary ideas like non Euclidean geometry.
Would they? Can you explain how and why?
But past mathematicians already just taught what they thought was true then. I’m not asking why they didn’t do that even harder, I’m asking what relevance you think it has for current math education. (And by extension, what relevance you think the education system of the Scholastics has for modern philosophy education.)
As it is said, keep an open mind, but not so open your brain falls out. Teaching a specific thing impedes progress when that thing is wrong or useless, but it aids progress when that thing is a foundation for later good things. This framework largely excuses past mathematicians, and also lets us convert between the “cautiousness” of philosophy education and a parameter of optimism about the possibility of progress.
But we don’t know that we are living in the optimal timeline. Maybe relativity would have arrived sooner with fewer people in the past insisting that space is necessarily Euclidean.
The topic is philosophy education. Science can test its theories empirically. Philosophy can’t. Mathematics can take its axioms for granted. Philosophy can’t.
The difficulty is that we don’t have certain knowledge of what is in fact right or wrong: we have to use something like popularity or consensus as a substitute for “right”.
It may well be the case that one can go too far in teaching unpopular ideas, but it doesn’t follow that the optimal approach is to teach only “right” ideas, because that means teaching only the current consensus, and the consensus sometimes needs to be overthrown.
The optimal point is usually not an extreme, or otherwise easy to find.