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.
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.