Almost all such arguments boil down to questions of
definitionalism. "Is the Mandelbrot set 'real'", for instance, hinges
entirely on the question of how one defines 'real'. Answering such
questions does not seem to have much interest to me -- I do not find
the answers particularly enlightening since if one shifts the
defintion, the answer shifts, and thus no interesting data has been
revealed in generating the answer.
The use of e-prime sometimes points out when a question has this
property. Note that one can't ask the question about the Mandelbrot
set without the use of the verb "to be". This indicates to me that
answering the question will not increase my understanding of the
Mandelbrot set (or anything else) particularly much.
The closest you can model the question in e-prime is "does the
Mandelbrot set comply with definition X of 'real'", which I believe
points out my problem with this and all similar questions.
Perry