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.
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.