@Tim, I sympathize deeply with your attempts to reason here. But I think it’s of no use.
Some people understand the structure of reason. Others think that what must be well-bounded, well-defined, rigorous and compelling can be substituted for by a bag of half-eaten shmoos, some duct tape and a series of paper clips to sort of link the odd bits together. Such people see nothing the matter with pushing on a rope, since pulling on a rope works so well. And as they pile untenable proposition upon untenable proposition, they get a heady feeling that these saltations from one bad idea to another are really amounting to something, and that there is not only merit to the ideas but also a kind of brilliance that emerges from the cadence and the spirit of this awkward dance itself.
What I’m saying is: you want to save people from folly. But, regrettable though it may be, there are some who cannot be saved. They have to want to understand, and they have to have the inner conservative (small “c” here) nature that says that it is better to understand small things well than large things badly. To them, lack of rigor smacks of brilliance and outside-the-box thinking, even as the box rests over their own eyes.
@Faizal_Ali suggested, a long while ago, that ignoring this nonsense was the best way to go. I didn’t heed his advice then. But I am increasingly persuaded that he saw where this was headed, and I nominate him for the title of Prophet.