"Expertise slows the progress of knowledge, some say. First, it delays arrival at the cutting edge: if you must master everything that came before, you may not begin original research until your 30s, when your brain is a rigid fossil and retirement is already near."
30 is before cognitive decline sets in in most people. It's really not that old.
"Also, it blinds you to new ideas: after years of seeing with accepted principles, reliance on those principles becomes second nature, a dusty, comfortable cow-path in your mind, and new and better ideas—the advances possible by coming at things sideways—become invisible."
This is why teaching is important. When students ask questions and look at the material with fresh perspectives, the teacher can use it as an opportunity to sharpen their thinking on the subject. The teacher can know whether the question has been answered before, how it's been answered before, whether a topic has been broached a certain way before, whether the current approach is sufficient.
"In The Lever of Riches Joel Mokyr documents one after another innovation created by amateurs just messing around, or discovered by accident by people working in other fields, while the so-called experts got nowhere. Serious money was invested by governments and corporations into the research and development of flying machines, only for all of them to be beaten by two bicycle mechanics from Ohio, working on their own."
Perhaps, this is why universities are so successful. It brings together the amateur (the student) and the expert. In addition, it exposes experts to the work done it different fields.
The success of these sorts of simple mathematical models mostly depends on clear thinking about the real-world variables that need to be incorporated. Yes, you need to be able to handle the necessary math, and you need to be able to handle it fluently, so you probably need to have studied one or two levels of math beyond what the models require. But studying three or four levels beyond what the models require is not going to help. To continue the language analogy: once someone has achieved basic competence in Japanese, studying the Heian-period literature isn't going to make it any easier to buy a train ticket.
And I think this may extend to the question of advanced logic training requirements for philosophy PhDs. I won't pretend to have real expertise (!) on that topic, but I'm skeptical that it offers the benefits you're suggesting, as opposed to being more like requiring accountants to study complex analysis. Furthermore, I'm not sure the overall impact of such requirements on the discipline as a whole are positive, since they may reinforce the unfortunate tendency in Anglophone philosophy to exaggerate the importance of formal(izable) arguments in philosophical thinking.
"Expertise slows the progress of knowledge, some say. First, it delays arrival at the cutting edge: if you must master everything that came before, you may not begin original research until your 30s, when your brain is a rigid fossil and retirement is already near."
30 is before cognitive decline sets in in most people. It's really not that old.
"Also, it blinds you to new ideas: after years of seeing with accepted principles, reliance on those principles becomes second nature, a dusty, comfortable cow-path in your mind, and new and better ideas—the advances possible by coming at things sideways—become invisible."
This is why teaching is important. When students ask questions and look at the material with fresh perspectives, the teacher can use it as an opportunity to sharpen their thinking on the subject. The teacher can know whether the question has been answered before, how it's been answered before, whether a topic has been broached a certain way before, whether the current approach is sufficient.
"In The Lever of Riches Joel Mokyr documents one after another innovation created by amateurs just messing around, or discovered by accident by people working in other fields, while the so-called experts got nowhere. Serious money was invested by governments and corporations into the research and development of flying machines, only for all of them to be beaten by two bicycle mechanics from Ohio, working on their own."
Perhaps, this is why universities are so successful. It brings together the amateur (the student) and the expert. In addition, it exposes experts to the work done it different fields.
I think Körner draws the wrong lesson here.
The success of these sorts of simple mathematical models mostly depends on clear thinking about the real-world variables that need to be incorporated. Yes, you need to be able to handle the necessary math, and you need to be able to handle it fluently, so you probably need to have studied one or two levels of math beyond what the models require. But studying three or four levels beyond what the models require is not going to help. To continue the language analogy: once someone has achieved basic competence in Japanese, studying the Heian-period literature isn't going to make it any easier to buy a train ticket.
And I think this may extend to the question of advanced logic training requirements for philosophy PhDs. I won't pretend to have real expertise (!) on that topic, but I'm skeptical that it offers the benefits you're suggesting, as opposed to being more like requiring accountants to study complex analysis. Furthermore, I'm not sure the overall impact of such requirements on the discipline as a whole are positive, since they may reinforce the unfortunate tendency in Anglophone philosophy to exaggerate the importance of formal(izable) arguments in philosophical thinking.