I disagree in the strongest possible terms with your characterization
here.
In the 19th Century, we were learning new facts about Electricity and
Magnetism -- and Maxwell's equations constituted new information about
the topic -- most importantly, they had the interesting property of
predicting new facts like electromagnetic waves (thus forming the
cornerstone of all scientific thought, the falsifiable hypothesis.)
In the question of "is the Mandelbrot set 'real'", we have a very
different debate. All facts about the Mandelbrot set relevant to the
area are well known. The debate is entirely over how one defines
"reality". No information will come out of the discussion other than
perhaps "which definitions of 'reality' would apply to the Mandelbrot
set and which ones will not?" No falsifiable hypotheses result. No new
insights arise.
The person posing the question implicitly has already answered it if
he has properly stated the question. This means that the answer yields
all the thrill that you get in putting a number on a sheet of paper,
placing the paper into an envelope, and then attempting to guess the
number that you yourself wrote down.
> >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'.
>
> Except that nobody has a definition of reality that's worth a damn,
On the contrary. There are many reasonable definitions. Some of them
are even rigorous. None of them have the property of being what I
would call "interesting", however -- and none ever can.
There are whole rafts of such utterly meaningless "to be"
definitionalism questions that philosophers have tortured themselves
with over the centuries. "What is the meaning of life" is my favorite,
though "is X real" has been high up on the list ever since Plato came
up with the Metaphor of the Cave in "The Republic"...
Perry