I am currently an anti-realist in the school of Lakoff. I
believe the aims of mathematicians are achievable and new laws
will continually be discovered that will be able to describe
reality in a manner usable to the human species. We will be able
to build new technologies using its precepts and be able to
accomplish things through technology that seem like magic in
today's world. I would dare say that mathematics is the vehicle
(to use that metaphor) that allows - and will continue to allow
- for an extraordinarily precise abstraction of many, more, or
perhaps nearly all of the processes and patterns in the
Universe, for the use of humans and by humans. But while I love
Plato, I tend to believe his concept of the world of ideas (that
there is a perfected form that exists in a separate realm from
the observable world) is likely, ultimately, false and that
ideas are the product of humans, by humans, for humans; to
facilitate communication and mutual understanding of concepts. I
separate concept from idea as a concept is a human abstraction
whereas an idea is a bit of vague in general use; and with its
origins in Plato, it has a reality of its own. I'll have to look
up the origin of 'concept'. That being said, the faith implicit
in mathematical realism is perhaps a critical necessity to allow
it to function as well as it does in this point in human
history. The marriage of mathematics, physics, engineering and
technology is a marvelous partnership that is allowing us to
create amazing new concepts and creations and, honestly, I can
see no viable alternative at this point in human history for
anything that could conceivably work better than this
partnership for the furthering of the human race. And really,
when it comes down to it, an anti-realist perspective is
somewhat of a moot point. It is of an "The Emperor has no
clothes!" - but, nudist or not, the Emperor needs none, for he
is an effective ruler.
I believe that mathematics works well for a human description of
the Universe because I believe humans are pattern-seekers and
pattern-manipulators and there is currently no better
pattern-seeking and pattern-manipulation machine than
mathematics. I see it as a conceptual machine for humans that we
are able to better and better actualize, through our ability to
ALSO seek and manipulate patterns in the observable Universe. I
should rephrase actualize; I don't believe the workings of the
human cognitive processes are fictional; they are biological in
nature. Using "actualize" implies products of human
consciousness are "not true" whereas I believe they are true,
just operating in a more flexible space; the realm of concepts
working within human minds and 'realizable" through technology.
But I don't believe "world of ideas" and the "world of reality"
are separate things; I believe they are one thing; it's just
that concepts are more effective within our minds than they are
when working with objects, leading to an appearance of duality -
but I think the appearance of duality is a matter of "effective
space." In that sense, I don't believe math is a "fiction". It
is fact and has an ontological existence in the realm of human
concepts which are biologically supported by our ability as
humans to utilize them, but that ascribing it to having an
existence outside of the realm of human usage is a category
error of its ontology. But, ultimately an academic point either
way because I sure wouldn't want it to go away [this is the
"philosophical space" as it were, where humanities and sciences
butt heads; ultimately, the sciences are far more pragmatic
which is why I love them so, for as much as a humanist I seem to
be; I like "things that work" and humanities often sounds like
mumbo-jumbo when there's work to be done ]
