Making progress in the sciences requires that we reach agreement about answers to questions, and then move on. Endless debate (think of global warming) is fruitless debate. In the Monty Hall case, this social process has actually worked quite well. A consensus has indeed been reached; the mathematical community at large has made up its mind and considers the matter settled. But consensus is not the same as unanimity, and dissenters should not be stifled. The fact is, when it comes to matters like Monty Hall, I'm not sufficiently skeptical. I know what answer I'm supposed to get, and I allow that to bias my thinking. It should be welcome news that a few others are willing to think for themselves and challenge the received doctrine. Even though they're wrong.No, dissenters shouldn't be stifled. But in this case I can't think of any way in which dissent is a good thing. The Monty Hall problem isn't just considered settled, it is settled, with deductive certainty. Oh, sure, the principle of pluralism says it's healthy to have a diversity of views, but you have to think about why we value pluralism. I think pluralism is good because of the possibility that the consensus is wrong. That possibility simply doesn't exist here. Pluralism is bad in this case. It's okay, I'm sure we can find other things to disagree about.
The same goes for the following claims:
- 3.9999... is not equal to 4
- Maybe the brick puzzle has a solution, and we just haven't found it
- Math can't possibly handle concepts like infinity
