Re: Is the Mandelbrot Set real?
Sun, 27 Jul 1997 00:28:55 -0400 (EDT)

In a message dated 7/26/97 2:05:03 PM, (John K Clark) wrote:

>Yes, and if you look up "reality" you will find "something that exists" or
>its equivalent, and looking up "being" will tell you it possesses the
>of reality. I have never found that a dictionary to be very enlightening
>philosophically, probably because lexicographers are not great philosophers
>but also because they get the knowledge to write their book from common
>and that not much use in philosophy where it's customary to push concepts to

>extremes to see where they'll break.

All very valid. I think the fundamental problem is that we form concepts by
finding similarities between exemplars of the properties. We don't really
think in terms of definitions. As a result, dictionary definitions end up
fundamentally circular, even though our concepts aren't. To fully transmit a
concept to somebody, you'd have to transmit all the experiences with which
you created a concept. Obviously that's a no-go. Usually we share enough
experiences that just a definition or analogy will suffice. With
higher-level concepts (and "exists" is a whopper) there's so much experience
behind the concept that such methods don't always cut the mustard. Our
disagreement here may fall into the category.

>By itself a dictionary is nothing but one big circular definition.
>All the definitions in a dictionary are made of words, and those words also
>have definitions made of other words also in the dictionary, and round and
>round we go. The way out of this paradox is the fact that much, perhaps
>of our knowledge in not in the dictionary because it's not made of words.

We seem to agree on this.

>You're saying that The Mandelbrot set does not exist because it's too
>only simple cartoon like things can be real. Well OK, but then who needs to
>be "real"? It would seem that possessing the quality of "reality" is not

Well, no, incredibly complex things exist (anything living, for starters).
The Mandelbrot set, however, requires infinite complexity. That's quite a
tall order.

>We can know something about the Mandelbrot set, we just can't know
>How is that different from a chair?

As I said, without humans, the Virgo cluster would still be here. (I'm going
to slide away from chairs because as human devices they don't fit this
counterfactual) But the Mandelbrot set wouldn't; it's only in our heads and
computers. Our heads and computers don't even have that; they have finite
approximations of it, and an equation which can generate it, which given an
aleph-one infinity time and storage (I'll assume that's the cardinality of a
line). But we don't have that much time or storage.

Now, to be fair, there are alternate meanings for "exist". For example, the
Mandelbrot set "exists" in a way that the rational square root of 2 doesn't.
The finite-operation squared circle doesn't "exist", but the squared circle
does "exist" in the same way as the Mandelbrot set (possible with an infinite
number of operations). I do find my meaning more handy, but to be precise
would require inventing more words.