Often, the inability to state something in a mathematically precise way is an indication that the underlying idea is not precisely defined. This isn’t universally true, but it is a useful heuristic.
Sure, but asking “can we take this idea and state it in terms of math” is a useful question. Moreover, for those aspects of philosophy where one can do, this this often results in it becoming much more clear what is going on. The raven problem is a good example of this: this is a problem that really is difficult to follow, but when one states what is happening in terms of probability, the “paradox” quickly goes away. And this is true not just in philosophy but in many areas of interest. In fact, one problem philosophy has (and part of why it has such a bad reputation) is that once an area is sufficiently precisely defined, which often takes math, it becomes its own field. Math itself broke off from philosophy very early on, and physics also pretty early, but more recent breakoffs were linguistics, economics, and psychology,
One way of thinking about the goals of philosophy is define things precisely enough that people stop calling that thing philosophy. And one of the most effective ways historically to do so is using mathematical tools to help.
Sure, but “It can’t be stated in a mathematical framework that already does a good job of answering a lot of these questions, maybe we should try to adopt it so it can be, or maybe we should conclude that the idea really is confused if we have other information indicating it has problems, or maybe we should wait until experts have hashed out a bit more exactly what they mean and come back to the idea then” are not the same thing as just throwing an idea out because it isn’t mathematically precise.
I think in general that LW should pay more attention to mainstream philosophy. I find it interesting how often people on LW don’t realize how much of the standard positions here overlap with Quine’s positions, and he’s clearly mainstream. It is possible that people on LW overestimate the usefulness of the “can this be mathematicized?” question, but that doesn’t stop it from being a very useful question to ask.
Well, I’d argue that in essence, all of the alternative scenarios you list for dealing with non-mathematicized problems do constitute throwing an idea out, insofar as they represent a reshaping of the question by people who didn’t initially propose it, i.e., a type of misrepresentation, although the last one (“maybe we should wait until experts have hashed out a bit more exactly what they mean and come back to the idea then”) is an adequate way to deal with such problems.
Often, the inability to state something in a mathematically precise way is an indication that the underlying idea is not precisely defined. This isn’t universally true, but it is a useful heuristic.
Hardly anything is mathematically precise. It’s not new that philosophy isn’t either.
Sure, but asking “can we take this idea and state it in terms of math” is a useful question. Moreover, for those aspects of philosophy where one can do, this this often results in it becoming much more clear what is going on. The raven problem is a good example of this: this is a problem that really is difficult to follow, but when one states what is happening in terms of probability, the “paradox” quickly goes away. And this is true not just in philosophy but in many areas of interest. In fact, one problem philosophy has (and part of why it has such a bad reputation) is that once an area is sufficiently precisely defined, which often takes math, it becomes its own field. Math itself broke off from philosophy very early on, and physics also pretty early, but more recent breakoffs were linguistics, economics, and psychology,
One way of thinking about the goals of philosophy is define things precisely enough that people stop calling that thing philosophy. And one of the most effective ways historically to do so is using mathematical tools to help.
“It can’t be stated in terms of maths, so throw it out” is not useful.
Sure, but “It can’t be stated in a mathematical framework that already does a good job of answering a lot of these questions, maybe we should try to adopt it so it can be, or maybe we should conclude that the idea really is confused if we have other information indicating it has problems, or maybe we should wait until experts have hashed out a bit more exactly what they mean and come back to the idea then” are not the same thing as just throwing an idea out because it isn’t mathematically precise.
I think in general that LW should pay more attention to mainstream philosophy. I find it interesting how often people on LW don’t realize how much of the standard positions here overlap with Quine’s positions, and he’s clearly mainstream. It is possible that people on LW overestimate the usefulness of the “can this be mathematicized?” question, but that doesn’t stop it from being a very useful question to ask.
Well, I’d argue that in essence, all of the alternative scenarios you list for dealing with non-mathematicized problems do constitute throwing an idea out, insofar as they represent a reshaping of the question by people who didn’t initially propose it, i.e., a type of misrepresentation, although the last one (“maybe we should wait until experts have hashed out a bit more exactly what they mean and come back to the idea then”) is an adequate way to deal with such problems.