I don’t exactly disagree (arguments that something proves too much themselves often prove too much). I don’t think it’s a very complete diagnosis of this kind of disagreement, nor of this specific one.
The root problem is handwaving the math. Especially for disagreements involving very large or very small factors, almost all of the disagreement is about magnitude, not shape. Note that there ARE disagreements about shape as well, but they tend not to be so hard to identify the cruxes.
using “nonzero” and “infinite” in a post is a strong indicator that the argument has this problem.
What do you mean by “this kind of disagreement” ? Edit: Also, what do you mean by “shape”? It seems to me that arguments involving infinities are of a qualitatively different ‘form’ from those involving finite or infinitesimal numbers. If this is what you mean by “shape”, then it seems to be the same thing as magnitude in this particular case.
I don’t exactly disagree (arguments that something proves too much themselves often prove too much). I don’t think it’s a very complete diagnosis of this kind of disagreement, nor of this specific one.
The root problem is handwaving the math. Especially for disagreements involving very large or very small factors, almost all of the disagreement is about magnitude, not shape. Note that there ARE disagreements about shape as well, but they tend not to be so hard to identify the cruxes.
using “nonzero” and “infinite” in a post is a strong indicator that the argument has this problem.
What do you mean by “this kind of disagreement” ? Edit: Also, what do you mean by “shape”? It seems to me that arguments involving infinities are of a qualitatively different ‘form’ from those involving finite or infinitesimal numbers. If this is what you mean by “shape”, then it seems to be the same thing as magnitude in this particular case.