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> It's often said that one of the benefits of studying math is that it improves critical thinking skills. I believe this to be true, but I also believe that if

by dsacco 9y ago

> It's often said that one of the benefits of studying math is that it improves critical thinking skills. I believe this to be true, but I also believe that if our primary concern is improving our day to day critical thinking skills, then we would be better served studying natural language philosphy than mathematics, because on a day to day basis we tend to think and reason and debate and engage with one another in natural language. I agree. For this reason, my favorite philosopher has always been Wittgenstein. I also have an affection for the existentialists, but language games demonstrate that philosophy can be eminently practical and relevant despite the pejorative connotations of the term, "philosophizing." That said, I really don't think philosophy should be its own major in most schools. It would be better, in my opinion, to teach philosophy as we teach arithmetic and language, rather than a focused degree.

meri_dian 9y ago
Wittgenstein is one of my favorites as well for the same reason. The Tractatus should be required reading for everyone, not just philosophy students.
- otoburb 9y ago
  If one reads Tractatus, then a reading of Philosophical Investigations is likely needed shortly thereafter.
- philipov 9y ago
  Philosophical Investigations is better.
- fastaguy88 9y ago
  I can't resist: https://www.youtube.com/watch?v=uSdHoNJu5fU https://www.youtube.com/watch?v=uSdHoNJu5fU
goatlover 9y ago
And what if someone wants to become a philosopher? That's like saying we shouldn't teach match as a major because every kid gets taught arithmetic. Well, some people want to do more with math than arithmetic.
- dsacco 9y ago
  Frankly, I disagree that mathematics should be its own degree at the undergraduate level as well. Let me clarify: I think people should be able to become philosophers, just like they can become mathematicians. But I’d advocate for changing the undergraduate curriculum - move proof-based mathematics into a targeted graduate degree, and emphasize computational mathematics like calculus and (linear) algebra, but make them core components of a much more generalized degree. Add in language and logic studies that borrow significantly from philosophy. With very few exceptions, you’re not doing research mathematics (i.e. being a mathematician) without significant graduate study. Similarly, for majors like philosophy that are “watered down” until graduate or postgraduate work, I don’t think they should be eligible for targeted degrees at the undergraduate level. This would have the added benefit of 1) delaying time to major decision for college-aged students and 2) keeping their options open for eligibility to targeted graduate degrees later on, by limiting the number of prerequisites. You don’t need undergraduate number theory to do well in an early graduate number theory course. The 300 and 400 level philosophy courses you take in an undergrad setting will mostly not have value on paper, so in my opinion we should shift them to the degree that has value on paper. But at this point I’m pontificating about the education system, not philosophy in particular :)
  - chongli 9y ago
    If you don't teach proof-based mathematics at the undergraduate level then aspiring mathematicians would have to take those courses at the graduate level. This would cause advanced degrees to take considerably longer to obtain. Like programming, writing proofs is a skill that takes practice to get good at. If you were to suggest that we shouldn't teach programming until graduate-level CS courses, you would be laughed out of the room. I think the best mathematicians in history started learning how to prove things as children. How about we start there, instead?
    - dsacco 9y ago
      > If you don't teach proof-based mathematics at the undergraduate level then aspiring mathematicians would have to take those courses at the graduate level. This would cause advanced degrees to take considerably longer to obtain. No it wouldn't. Most math PhDs require six or so courses before the research - you can begin with analysis or abstract algebra for proofs. The current system does have unnecessary redundancy. > Like programming, writing proofs is a skill that takes practice to get good at. If you were to suggest that we shouldn't teach programming until graduate-level CS courses, you would be laughed out of the room. Programming is more comparable to the computational mathematics that I've already mentioned should be in undergrad; more to the point, a lot of computer science theory need not be taught in undergrad either. Computer science theory is much closer to proof-base mathematics. > I think the best mathematicians in history started learning how to prove things as children. Approximately no one is one of the best mathematicians in history. That's an attractive idea, but I think it's more realistic to assume they were extraordinarily precocious than that proofs are easier to digest at a younger age. I could point to people who mastered computational mathematics at a young age too (like Einstein, at 14), but that doesn't say anything about which is easier to learn. I'm talking about which is more widely applicable for practical work.
mathattack 9y ago
I concur with your last statement. Similar to mathematics, it make sure a very good second degree as well. Econ majors are a dime a dozen, but Econ/philosophy double majors are much more likely to Ben precise thinkers. Same benefit to precision when pairing it with CS.

by dsacco 9y ago

meri_dian 9y ago

Wittgenstein is one of my favorites as well for the same reason. The Tractatus should be required reading for everyone, not just philosophy students.

otoburb 9y ago
If one reads Tractatus, then a reading of Philosophical Investigations is likely needed shortly thereafter.
philipov 9y ago
Philosophical Investigations is better.
fastaguy88 9y ago
I can't resist: https://www.youtube.com/watch?v=uSdHoNJu5fU https://www.youtube.com/watch?v=uSdHoNJu5fU

goatlover 9y ago

And what if someone wants to become a philosopher? That's like saying we shouldn't teach match as a major because every kid gets taught arithmetic. Well, some people want to do more with math than arithmetic.

dsacco 9y ago
Frankly, I disagree that mathematics should be its own degree at the undergraduate level as well. Let me clarify: I think people should be able to become philosophers, just like they can become mathematicians. But I’d advocate for changing the undergraduate curriculum - move proof-based mathematics into a targeted graduate degree, and emphasize computational mathematics like calculus and (linear) algebra, but make them core components of a much more generalized degree. Add in language and logic studies that borrow significantly from philosophy. With very few exceptions, you’re not doing research mathematics (i.e. being a mathematician) without significant graduate study. Similarly, for majors like philosophy that are “watered down” until graduate or postgraduate work, I don’t think they should be eligible for targeted degrees at the undergraduate level. This would have the added benefit of 1) delaying time to major decision for college-aged students and 2) keeping their options open for eligibility to targeted graduate degrees later on, by limiting the number of prerequisites. You don’t need undergraduate number theory to do well in an early graduate number theory course. The 300 and 400 level philosophy courses you take in an undergrad setting will mostly not have value on paper, so in my opinion we should shift them to the degree that has value on paper. But at this point I’m pontificating about the education system, not philosophy in particular :)
- chongli 9y ago
  If you don't teach proof-based mathematics at the undergraduate level then aspiring mathematicians would have to take those courses at the graduate level. This would cause advanced degrees to take considerably longer to obtain. Like programming, writing proofs is a skill that takes practice to get good at. If you were to suggest that we shouldn't teach programming until graduate-level CS courses, you would be laughed out of the room. I think the best mathematicians in history started learning how to prove things as children. How about we start there, instead?
  - dsacco 9y ago
    > If you don't teach proof-based mathematics at the undergraduate level then aspiring mathematicians would have to take those courses at the graduate level. This would cause advanced degrees to take considerably longer to obtain. No it wouldn't. Most math PhDs require six or so courses before the research - you can begin with analysis or abstract algebra for proofs. The current system does have unnecessary redundancy. > Like programming, writing proofs is a skill that takes practice to get good at. If you were to suggest that we shouldn't teach programming until graduate-level CS courses, you would be laughed out of the room. Programming is more comparable to the computational mathematics that I've already mentioned should be in undergrad; more to the point, a lot of computer science theory need not be taught in undergrad either. Computer science theory is much closer to proof-base mathematics. > I think the best mathematicians in history started learning how to prove things as children. Approximately no one is one of the best mathematicians in history. That's an attractive idea, but I think it's more realistic to assume they were extraordinarily precocious than that proofs are easier to digest at a younger age. I could point to people who mastered computational mathematics at a young age too (like Einstein, at 14), but that doesn't say anything about which is easier to learn. I'm talking about which is more widely applicable for practical work.

mathattack 9y ago

I concur with your last statement. Similar to mathematics, it make sure a very good second degree as well. Econ majors are a dime a dozen, but Econ/philosophy double majors are much more likely to Ben precise thinkers. Same benefit to precision when pairing it with CS.