“Robin previously posted (and I commented) on the notion of trying to distinguish correct contrarians by “outside indicators”—as I would put it, trying to distinguish correct contrarians, not by analyzing the details of their arguments, but by zooming way out and seeing what sort of general excuse they give for disagreeing with the establishment. As I said in the comments, I am generally pessimistic about the chances of success for this project”
I think the method that was taught in my family is better: become an expert on one or more subjects, so that you can know, by evaluating the evidence, which views are correct. Then, judge sources by their accuracy in those areas on which you are expert.
The method was not explicitly meant for contrarianism, but it works well there. Research some promising contrarian claims (perhaps those like diet & exercise which will most affect your life) so that you have pretty high confidence in whether they are correct. Then evaluate the accuracy of contrarians based on whether their claims agree with your research in those areas, and upweight the other things that those contrarians believe. Sure, you have to be smart enough to be a good evidence evaluator, but, hey, that sounds like us.
I think the method that was taught in my family is better: become an expert on one or more subjects, so that you can know, by evaluating the evidence, which views are correct. Then, judge sources by their accuracy in those areas on which you are expert.
Bertrand Russell used this method successfully to assess the value of Hegel’s philosophy:
When I was young, most teachers of philosophy in British and American universities were Hegelians, so that, until I read Hegel, I supposed there must be some truth to his system; I was cured, however, by discovering that everything he said on the philosophy of mathematics was plain nonsense.
Upon further inspection, I’ve concluded something is seriously wrong here (especially if Russell had much of an impact in shaping later philosophers’ view of Hegel). In Introduction to Mathematical Philosophy, Russell claims Hegel’s knowledge of mathematics is out of date and that he believed calculus requires infinitesimals. This is totally wrong. The longest (or one of the longest) sections in his Science of Logic is an attempt at refuting the validity of infinitesimals (while still affirming the validity of the differential and integral calculus).
This is not the only example of this sort of thing. Russell has a lot of examples like this where he clearly didn’t read the original sources and it suffers from this. There are similar issues where he bashes Aristotle for a lack of empiricism.
I don’t think it’s as simple as ‘agreement = competent; disagreement = incompetent’, for at least a couple of reasons.
First, when judging the credibility of a source, their views on a given issue will be weighted according to the confidence with which they’re expressed (i.e. the source’s level of claimed expertise in that area). Second, disagreement will have more weight the closer the matter is to being one of settled objective fact.
I’m by no means an expert on the philosophy of mathematics, but I imagine that at the very least it’s an area in which thoughtful, intelligent, honest people can disagree, and at the most it’s one in which there simply isn’t a single set of correct answers. So disagreement need not seriously undermine one’s confidence in a source, but that doesn’t mean that all answers are equally sensible or valid, nor that Hegel can’t have been talking credibility-destroying nonsense.
When Russell writes that Hegel’s views on the philosophy of mathematics are “nonsense”, I take him to express more than mere disagreement, and something closer to an indictment of Hegel’s epistemic standards (such as standards of clarity, precision and cogency) as revealed in that area of inquiry. Furthermore, Hegel (I believe) claimed to be speaking as an expert in the field, whereas this may not be the case with the physicists speaking about the foundations of mathematics. So Russell’s conclusions about Hegel’s views in metaphysics seem to be more justified than the corresponding conclusions that the philosophers of mathematics would draw about the physicists in your example.
Hegel was a brilliant artist, though I would argue he lacked the strength of his artistic convictions. The fact that philosophy decided to imitate his artwork seems disappointing, but perhaps Plato (or Nietzsche, had he existed) should have led us to expect it.
“Robin previously posted (and I commented) on the notion of trying to distinguish correct contrarians by “outside indicators”—as I would put it, trying to distinguish correct contrarians, not by analyzing the details of their arguments, but by zooming way out and seeing what sort of general excuse they give for disagreeing with the establishment. As I said in the comments, I am generally pessimistic about the chances of success for this project”
I think the method that was taught in my family is better: become an expert on one or more subjects, so that you can know, by evaluating the evidence, which views are correct. Then, judge sources by their accuracy in those areas on which you are expert.
The method was not explicitly meant for contrarianism, but it works well there. Research some promising contrarian claims (perhaps those like diet & exercise which will most affect your life) so that you have pretty high confidence in whether they are correct. Then evaluate the accuracy of contrarians based on whether their claims agree with your research in those areas, and upweight the other things that those contrarians believe. Sure, you have to be smart enough to be a good evidence evaluator, but, hey, that sounds like us.
Bertrand Russell used this method successfully to assess the value of Hegel’s philosophy:
Unpopular essays, chap. 1
Upon further inspection, I’ve concluded something is seriously wrong here (especially if Russell had much of an impact in shaping later philosophers’ view of Hegel). In Introduction to Mathematical Philosophy, Russell claims Hegel’s knowledge of mathematics is out of date and that he believed calculus requires infinitesimals. This is totally wrong. The longest (or one of the longest) sections in his Science of Logic is an attempt at refuting the validity of infinitesimals (while still affirming the validity of the differential and integral calculus).
Will investigate further when I have the time.
This is not the only example of this sort of thing. Russell has a lot of examples like this where he clearly didn’t read the original sources and it suffers from this. There are similar issues where he bashes Aristotle for a lack of empiricism.
Did you manage to research this issue further? I’m curious.
Would philosophers of mathematics agree with physicists on the foundations of mathematics? If not, should they dismiss their views on physics?
I don’t think it’s as simple as ‘agreement = competent; disagreement = incompetent’, for at least a couple of reasons.
First, when judging the credibility of a source, their views on a given issue will be weighted according to the confidence with which they’re expressed (i.e. the source’s level of claimed expertise in that area). Second, disagreement will have more weight the closer the matter is to being one of settled objective fact.
I’m by no means an expert on the philosophy of mathematics, but I imagine that at the very least it’s an area in which thoughtful, intelligent, honest people can disagree, and at the most it’s one in which there simply isn’t a single set of correct answers. So disagreement need not seriously undermine one’s confidence in a source, but that doesn’t mean that all answers are equally sensible or valid, nor that Hegel can’t have been talking credibility-destroying nonsense.
Well near as I can tell >90% of mathematicians are Platonists.
When Russell writes that Hegel’s views on the philosophy of mathematics are “nonsense”, I take him to express more than mere disagreement, and something closer to an indictment of Hegel’s epistemic standards (such as standards of clarity, precision and cogency) as revealed in that area of inquiry. Furthermore, Hegel (I believe) claimed to be speaking as an expert in the field, whereas this may not be the case with the physicists speaking about the foundations of mathematics. So Russell’s conclusions about Hegel’s views in metaphysics seem to be more justified than the corresponding conclusions that the philosophers of mathematics would draw about the physicists in your example.
Hegel was a brilliant artist, though I would argue he lacked the strength of his artistic convictions. The fact that philosophy decided to imitate his artwork seems disappointing, but perhaps Plato (or Nietzsche, had he existed) should have led us to expect it.