A little too much to address given how much time I have today. I think you’re expecting him to present his argument in a logical progression, but he doesn’t really. You have to dig for it to see it, but he does address all your concerns in satisfactory ways. The reason I was patient enough to piece together his arguments is that I knew he was on to something, a whole bunch of things, and I was willing to wade through whatever I had to to get at it. I’m very glad I did, though. More later…
ETA:
"Gaede (falsely) believes that math is lower than natural language (in fact, he seems to think it’s completely useless).
Quick one: he means it’s completely useless for science, by which he means explanation, by which he means a movie of the unobserved mechanisms that are proposed to underly the observed phenomena. With this definition of explanation…
“Prior to Hume, it was intuitively understood that explanations explain things because they are predicting the behavior of the thing in question.”
…this takes on a different light and wouldn’t make sense. We explain in order to predict. That’s what the point of the other thread was.
“Furthermore, what is inconceivable about force fields? They feature prominently in all sorts of fiction and the movie producers have no problem adapting what the books have described in words and the audience who has read the books is not surprised by what they see. Of course there isn’t literally a “mathematical vector field” surrounding a magnet but it’s as if there were.”
Without even getting into the question of whether they are imaginable, more pressing is the fact that they are simply descriptions of what happens, not explanations of by what unseen mechanisms they may happen.
This is all addressed in the other thread more eloquently. Time and time again, I’ve seen people make some of the same points as Gaede does and get plenty of agreement because they know how to come off less abrasive and brash. Oh well - he’s got a 'tude. I wish he were nicer and more eloquent or whatever, but again beggars can’t be choosers; he’s one of the only people I’ve ever seen that get the subtleties at play here.